Using Light (Longman Physics Topics)

LONGMAN PHYSICS TOPICS

General Editor: John L. Lewis

USING LIGHT W. Llowarch Formerly Senior Lecturer in Physical Science London University Institute ofEducation

and B. E. Woolnough Senior Physics Master Abingdon School

Illustrated by T. H. McArthur

LONGMAN

LONGMAN GROUP LIMITED

London Associated companies, branches and representatives throughout the world

© Longman Group Ltd 1970 All rights reserved. No part of this publication may be reproduced, stored in a retrieval system or transmitted in any form, or by any means, electronic, mechanical, photocopying, recording or otherwise, without the prior permission of the Copyright owner. First published 1970

SBN 582 32200 6 Printed in Great Britain by Butler and Tanner Ltd, Frome and London

I ACKNOWLEDGEMENTS I

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The authors and publishers are grateful to the following for permission to reproduce photographs: page 10 and page 11 Museum of the History of Science, Oxford; page 5 (below left) British Museum; pages 5 (below right), 40, 56 and 57 Tony Cowlin; page 13 (above) Pilkington Optical Division; page 13 (below) Esso Petroleum Company Ltd; page 5 (above) 16,17, 19, 22 (below), 23 (above left), 25, 27, 33, 35 and 44 (above) Science Museum, London (Crown copyright reserved); pages 21 and 36 Carl Zeiss; page 22 (above) Royal Scottish Museum, Edinburgh; page 23 (above right) Royal Greenwich Observatory, Herstmonceux; page 23 (below left) and pages 28-9 (margins) California Institute of Technology; page 29 (below left) Pilkington Brothers Ltd; page 34 E. Leitz (instruments) Ltd; pages 38 (diagram), 42 (diagram), 44 (below) E. Leitz (Instruments) Ltd; page 39 Will Green; pages 43, 44 (centre), 47 (top right and below right) Kodak; pages 45 and 46 (above) Dr H. E. Edgerton; page 46 (below) Associated Press; page 47 (top left) Royal National Orthopaedic Hospital, London; page 48 Omega; page 50 Camera Press; page 51 Central Office of Information (Crown copyright reserved); pages 53 and 63 Paul Popper; page 53 (left) British Museum (Natural History); page 54 Department of Machine Intelligence and Perception, University of Edinburgh; page 55 John L. Lewis; page 57 Belgravia Optical Company Ltd; pages 61 and 62 National Physical Laboratory (Crown copyright reserved). The photograph on the front cover is reproduced by kind permission of Osram GEC Ltd, and that on the back cover by kind permission of E. Leitz (Instruments) Ltd.

NOTE TO THE TEACHER

This book is one in a series of physics background books intended primarily for use with the Nuffield 0-Level Physics Project, and the team of writers who have contributed to the series were all associated with that project. It was always intended that the Nuffield teachers' materials should be accompanied by background books for pupils to read, and a number of such books is being produced under the Foundation's auspices. This series is intended as a supplement to the Nuffield pupil's material: not books giving the answer to all the investigations pupils will be doing in the laboratory, certainly not textbooks in the conventional sense, but books that are easy to read and copiously illustrated, and that show how the principles studied in school are applied in the outside world. The books are such that they can be used with a conventional as well as a modern physics programme. Whatever course pupils are following, they often need straightforward books to help clarify their knowledge and sometimes to help them catch up on any topic they have missed in their school course. It is hoped that this series will meet that need. This background series will provide suitable material for reading in homework. This volume is divided into sections, and the teacher may feel that one section at a time is suitable for each homework session for which he wishes to use the book. This particular book is written as a background book for the ray optics section in Year III of the Nuffield course. Pupils will investigate in the laboratory the basic principles behind telescopes and microscopes: this volume will extend that experience to actual instruments in the outside world. However, the central theme running through the book emphasises how greater and greater understanding of scientific principles led to progress in developing more effective optical instruments, progress which was enhanced further by increasing technological skills.

3

INTRODUCING THIS BOOK

I CONTENTS I

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In learning to make use of light, man has employed three different methods. First, in the earliest stages, he relied on trial and error. Then he began to study systematically how light behaves. This led to the discovery of principles, or laws, which could then be applied to the design of optical apparatus. The third stage in the application of man's knowledge of light to useful ends carne as a result of asking questions. The study of how light behaves leads naturally to the question 'Why?'. 'Why does light behave in these ways, why does it follow these laws?'. And this leads to the question 'What is light?'. A satisfactory answer to this question would give greater understanding of the laws or principles. It would, perhaps, enable man to apply the principles more intelligently, but it might do more than that: it might encourage him to think of new uses for light and lead to the discovery of more principles and useful properties. In this short book, we shall consider the first two stages in the development of man's control over light and illustrate each by examples of the application of the principles. Later in your course you will consider how theories on the nature of light have led to further developments. Though we deal fairly briefly with trial and error, let us not despise it nor dismiss it lightly. Discoveries made by accident in the early days aroused interest and led to the study of principles, and hence to further discoveries not only in the field of optics but in other branches of science, such as natural history, mineralogy and especially in astronomy. Note to the teacher 3 Introducing this book 4 Lenses 5 The telescope 15 Colour and the achromatic lens The microscope 37 The camera 39 The eye 50 The Schlieren effect 58 Appendix 64

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I LENSES

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Of all the devices which rely on light for their action, which single one has been of greatest importance? Surely the answer must be the lens, a piece of transparent material with two surfaces, one or both of them smoothly curved. It can concentrate rays of light or form images of objects. The images may be magnified or diminished, erect or inverted, real or virtual. Studying ancient history, we find records of such devices in use as long ago as 2500 BC. Pliny records the use of balls of glass or crystal as both burning glasses and magnifying glasses, while archaeologists have found what must be lenses in Egypt and Crete, from the second millenium BC.

WAS THE LENS AN INVENTION OR A DISCOVERY? 18th century burning glasses. The single lens was used by Priestley in the discovery of oxygen, and the double lens by Cavendish

Crystal plaque from Nimrod, 8th century B. C. Probably a jewellery inlay, but it also behaves like a converging lens

What we say about this must be largely conjecture: guesswork, but intelligent guesswork. What is the difference between inventing a lens, and discovering a lens? Invention is a deliberate process. We know what we want and we plan to make it: we draw up a design. What previous knowledge would be required to invent the lens? First, we must know the fact that light bends when it passes obliquely from air into glass.

5

I LENSES I

But knowledge of this fact is not enough; we must know the law which governs the bending and the relationship between the angles. Early man, spearing fish under water, must have been aware that this is a less straightforward operation than spearing an animal on the ground. But it is a long way from the observation of the apparent bending of a stick, partly immersed in water, to understanding the way in

which this depends on rays of light and the laws of refraction. Even if the laws of refraction of light at a flat surface were known, the inventor must have sufficient skill with mathematics to be able to work out the shape ofthe curved surface which would bend the various rays oflight from an object to bring them to focus in an image. The problem is obviously a difficult one, yet it is even more difficult than we have made it appear to be. We have used terms like ray, angle, focus, object and image, forgetting that these terms, which to us are everyday words, had themselves to be invented to describe certain ideas or concepts. Even the idea that light travels from the object to the eye and there affects the sense of sight seems to have been grasped very slowly. For a long time it was thought that rays travelled from our eyes to the object and somehow illuminated it, or made it visible. Plato put forward the view that sight results from the meeting of rays from the eye and rays from the object. 6

Something to think about I. Can you think of any observation which might lead to the theory that the eye is the source of light? 2. How would you try to convince someone that the theory* that rays travel from our eyes to the object is unsound?

Probably the lens was discovered by accident. Glass was discovered (or invented?) by the ancient Egyptians and lumps of glass with smooth round surfaces must have become fairly common. Clear lumps of resin, natural transparent gemstones and even icicles could have the required shape. The fact that they could concentrate sunlight and that objects seen through them might appear larger - and so be viewed more clearly - must have been realized at a very early stage in our civilisation. (Even a dew drop can display magnification.) Something to do Try using a drop of clear honey or syrup sitting on a small hole punched in a metal plate as a magnifying glass.

One can imagine objects which happened to have particularly smooth and regular faces being treasured and acquiring value because they gave clearer, less distorted images. The next step would surely be to try to improve the result by polishing the surfaces to make them smoother and clearer. Measurements might be made to determine the precise shape of good specimens, followed by attempts to copy this shape. It is recorded that hollow vessels filled with water or other liquids were used as burning and magnifying glasses. It would be easy to make such vessels with different curvatures and study the effect of filling them with different liquids, and so begin to discover the principles behind the action of a lens. Although this would take man beyond the stage of discovery by accident he would still be relying purely on experiment, using what we call rule of thumb or empirical methods. Such methods are often time-wasting. Rapid and certain progress can be made only when it is based on sound theory - in this case on the law of refraction. *The theory was finally killed by Scheiner in 1625, when he examined the eye ofa recently slaughtered animal and saw a tiny image formed on the back of the eye, much as a photographer sees an image on a ground glass viewing screen in some cameras.

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THE LAW OF REFRACTION The law was not discovered until 1618 when Willebrod Snell van Royen stated it, though not in a very convenient form. It was Descartes in 1637 who first stated it in its modern form, though it is often called Snell's law. It was known that light in passing from air to glass was refracted (bent), and that different materials refracted light by different amounts. If a line is drawn at right angles to the

surface (this line is usually called the normal), it is customary to call the angle between the incident ray and the normal the angle of incidence i, and the angle between the normal and the refracted ray the angle of refraction r. It is found that when a ray of light goes from air into glass it is always bent toward the normal. A ray leaving glass and entering air is bent away from the normal. However, to find a simple relationship between corresponding angles of incidence and refraction was a much more difficult matter than discovering that refraction occurred. Such a set of values might be: 10° 15° 20° 30° 40° 50° 6.6° 9.9° 13.2° 19.5° 25.4° 30.7°

r

Can you see any relationship? You may notice that, for the first four readings, i is ~ X r. In other words if r = 1.5 for small angles, but it fails at larger angles. iir

8

1·50

1·50

1·50

1·50

1·51

1·51

1·52 1·54

1·58 1·63

I LENSES

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Descartes was the first to see the relationship in the modern form we use today. He used trigonometry*. Below are shown the corresponding values of sin i and sin r: sin i 0·026 0·035 0·052 0·105 0·174 0·259 0·342 O· 5 0·643 0·766 sin r 0·017 0·023 0·035 0·070 0·115 0·172 0·228 0·334 0-429 0·511

When the value of

s~n ir is worked out in each case, it comes

SIll

to the same value whether i is small or large. sin i Sill r

1·50 1·50 1·50 1·50 1·50 1·50 1·50 1·50 1·50 1·50

Thus the form of Snell's law, restated by Descartes, is written: sin i .

- . - IS SIll r

a constant

Something to think about In the figures given in the table, i/ r was a constant, equal to \·50 for small values of i up to 6°. How big do you think i can be if you are content with an error of \ %? 3%? 10%')

The constant in Snell's law is given a special name and is called the refractive index of the substance. The refractive index has different values for different substances. A substance that refracts the light strongly has a high refractive index. The refractive index for glass is approximately 1·5, for water 1·33 and for diamond 2·4. It is interesting that the Greek Ptolemy in 200 AD suggested the approximate law, i/ r = constant. Although the measurements did not support the law for large values of i and r they must have agreed with it for small angles. Moreover, the Greeks had a knowledge of geometry which was certainly adequate for them to apply the law of refraction to understand the action of a lens. The fact is however that quite good lenses were made and used as spectacles and, later, lenses were combined to make microscopes and telescopes, all by accident or good fortune or *Ifyou have not done any trigonometry. do not worry. You can omit the nextfew lines.

9

trial and error, without the use of any laws of optics. Maybe in ancient Greece the liaison between theory and practice was poor. The thinkers were, perhaps, too much concerned with abstract thought - with pure science and pure mathematics - and left experiment and practical matters to their slaves. But even if they had solved the problem of lens action theoretically, and even if they had had technicians who could have put their ideas into practice, they would have made little progress until the art of making glass had itself developed into a science. A true science of lenses (or dioptrics, as it was called) did not begin until the remarkable discoveries made by means of the telescope (Galileo, Huyghens, Cassini) and the microscope (Leeuwenhoek, Malpighi, Swammerdam) stimulated man to seek for further improvement. In his Dioptrice, published in 1611 and about 80 pages long, Kepler used the approximate Greek law of refraction, combined with simple geometry, to establish the properties of lenses and lens systems, and so founded the theory of optical instruments. He devised the method of estimating magnifying power by looking through a telescope with one eye and comparing the magnified image with the object viewed directly by the other eye. English terrestrial about 1675

telescope, made

A simple microscope made by van Leeuwenhoek about 1680. The specimen is supported on the pointer and viewed through a tiny. spherical glass lens

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English compound microscope, made about 1700

DEFECTS IN LENSES The images formed by early lenses were very imperfect. They were distorted in shape and showed false colours, Improvements in the art of making clear glass, free from bubbles and striations, resulted in much truer images, but two defects which you will have studied in your own laboratory work - spherical aberration and chromatic aberration - obstinately remained. In fact, the better the quality of the glass, and the more perfect the curvature of the surfaces, the more certain did it become that these defects were natural to the lens. 11

Chromatic aberration, in which different colours, refracted different amounts, are focused at different points.

Spherical aberration in which rays passing through different parts ofthe lens are focused at different points.

Descartes, in his Dioptrices published in 1664, claimed that lenses whose surfaces had ellipsoidal or hyperboloidal shape would give superior results. Unfortunately such shapes are very difficult to make, whereas to produce a surface which is part of a perfect sphere is quite easy. The grinding of lenses If this statement causes you some doubts, consider the figure below. B is a glass disc which is fixed and A a similar disc which can slide over B. Some fine grinding paste is put between them and A is slid sideways over B, as suggested by the arrows, but in every possible direction, and rotated at the same time. A

E--B

---,

When A is overhanging B, as shown in the second figure, the pressure of the middle part of A on the outer part of B causes most wear on these parts, so that A becomes concave and B convex. Because of the continual rotation of A, combined with the sliding motion, A and B must eventually fit perfectly in all positions, and this can happen only if both surfaces are perfectly spherical with equal and opposite curvature. Finer and finer grades of grinding paste are employed and finally the glass is used to impress its own shape on soft pitch. When the pitch has hardened the glass is removed. The pitch is coated with wet rouge and used to polish the glass to perfect smoothness. Commercially, many lenses are ground at the same time. Flat glass discs are mounted on a suitably shaped dome. This dome is rotated underneath a matching cup while grinding pastes are introduced between the two surfaces. Starting with a very coarse abrasive, pastes of finer and finer constituency are added until the discs have the desired shape.

Something to think about The above procedure will produce a convex surface. Can you suggest how a concave surface could be manufactured?

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Lens grinding dome and cup

Rays passing through a lens near its edge must be bent more than those passing near the centre so that they will all come to the same focus. Your own experiments with rays of light will have shown you that cylindrical lenses overdo the bending of the extreme rays.

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You may also have discovered for yourself that whether you get a sharp image or not depends on which way round you put the lens.

In general, it is found that this 'spherical aberration' is less if the bending is shared between two surfaces than if all the bending takes place at just one surface, as in the second figure. A multiple lens system which shares the bending between many more surfaces produces an even sharper image. Such lens systems are used in good optical instruments to reduce spherical aberration. Something to do I. Use pencil and paper to show why the plano-convex lens is better than the double convex for parallel incident rays striking the curved face first, but worse than the double convex if it is used the wrong way round. Check your conclusions with ray streaks and suitable lenses. 2. Look at the image of a distant object formed by a large condenser lens, such as is used in a lantern slide projector. Such lenses are usually plano-convex. Find which way round gives a sharper image.

Huyghens and others understood these matters and were able to invent eyepieces, containing two planoconvex lenses, which caused very little distortion provided they did not attempt to make them too powerful.

Huyghens' eyepiece. The lens separation is equal to the average focal length of the two lenses

I ..

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d

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THE TELESCOPE

In your laboratory, you will have seen that a telescope can be made using two converging lenses. The first lens, the one closer to the object you are viewing, is usually called the objective lens. It forms a real image of the distant object. The second lens, which is closer to the eye, is usually called the eyepiece lens. It acts as a magnifying glass and magnifies the image formed by the objective lens.

Simple astronomical telescope

You will have found that the objective lens is a low power lens: it has a large focallength*. The eyepiece on the other hand is a high power lens: it has a short focal length. What is necessary in order to increase the magnification? Two things are possible. You could replace the objective with a lens of longer focal length. Or you could have an eyepiece of higher power, that is, of shorter focal length. *See page 64 lor the definition offocal length.

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I THE

TELESCOPE'

EARLY HISTORY OF THE TELESCOPE It is thought that the two-lens telescope was discovered by accident in about 1608. Hans Lippershey, a Dutch spectacle lens maker, found that a weak convex lens and a more powerful concave lens held in line before the eye made distant objects appear much larger.

Galilean telescope. What advantages has this over the simple astronomical telescopefor terrestrial use?

Replica of Galileo's original telescope

Galileo heard of this discovery and immediately copied it, his first telescope having a magnifying power of X 3, followed by one of X 8 and finally X 33.

Kepler invented the telescope which' uses two convex lenses and such telescopes were constructed by Scheiner from 1630. Huyghens made further improvements and discovered the rings of Saturn (which Galileo had mistaken for a triple star) and one of its satellites. The development of the theory of lenses showed that the magnifying power of the telescope is given by the ratio of the focal length of the objective to that of the eyepiece. Thus if F = the focal length of the objective and f = the focal length of the eyepiece, the magnifying power is PI! It can also be shown that the distance between the two 16

[ THE TELESCOPE

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17th century aerial telescope used by Hevelius in Danzig. With such telescopes he catalogued 1 564 stars and discovered 4 comets

*

lenses in a telescope is approximately equal to the sum of the focal lengths, in other words F + f Unfortunately, if the focal length of the eyepiece is made smaller and smaller to increase the magnifying power, the distortion will become serious. So to get high magnifying power, the focal length of the objective must be made greater and greater. With a very long focal length the objective lens would not need to bend the rays from the distant object through large angles and so would not itself cause much distortion. So we find what were called aerial telescopes being set up early in the seventeenth century.

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I THE

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The long focal length objective lens was mounted at the upper end of a pole of wood or very light framework, which was pivoted on a vertical post, with the eyepiece at the other end near the ground. There are reports of a telescope of this kind, set up in 1684, which was 64m long! Suppose that the focal length of the eyepiece were as great as 15cm; the magnifying power of this telescope would be about 400. How delightfully simple! But the results were disappointing because the images were so full of false colour that the great magnification merely led to worse confusion. It was extremely difficult to focus anything through the eyepiece. Unfortunately at this time the phenomenon of colour was not understood. Newton's famous experiments on the prism and its spectrum were undertaken partly to discover the 'cause of colour', as he put it - as a piece of research in pure science - and partly in the hope that when he knew how a colourless glass prism produced a spectrum from white light he could apply the principles to cure the colour defects of telescopes. Newton's experiments were most successful in achieving the first goal, but his results led him to conclude that refraction of light and dispersion into colours went hand in hand; that they were so linked together that the defect of chromatic aberration could be neither avoided nor compensated. He therefore turned his attention to developing the reflecting telescope.

THE REFLECTING TELESCOPE Most modern astronomical telescopes used nowadays do not collect the light with a convex lens but use a concave mirror. They are called reflecting telescopes as distinct from refractors. Why was the reflecting telescope not invented earlier? It is unlikely that it would have been discovered by chance, as the refractor is said to have been, though the curved mirror itself, like the lens, was probably discovered by chance. Curved pieces of polished metal (lids for vessels, shields, helmets, armour) would be seen to produce images 18

I THE TELESCOP~J

which might be magnified or diminished and concave mirrors could be used as burning glasses. Moreover, the law of reflection is so much simpler than the law of refraction that the science of mirrors (known at one time as catoptrics) could have been developed and applied to the design of perfect mirrors at an early stage in history. But can you imagine anyone happening to hold up two concave mirrors in such a position that he could see a magnified view of a distant object? Something to do Try making a reflecting telescope for yourself and you will find how difficult it is. Use a concave shaving mirror of focal length between 60 and 90cm, and a small laboratory concave mirror of focal length about l5cm. See if you can make it work. If you begin by trying to design it on paper, you will realise that one mirror tends to get in the way of the other, and your head gets in the way of both. It can be done, but it is most unlikely that it was ever found by accident. Of course, when Newton tackled the problem he had the example of the two lens telescope to guide him.

Newton's telescope

Newton used one concave mirror of long focal length instead of the telescope objective lens, while retaining a short focus eyepiece made of lenses. He solved the problem of the eyepiece and his head both blocking the light, by using a very small flat mirror to reflect the light sideways.

Newtonian reflecting telescope

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I THE

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The diagram shows the arrangement of Newton's reflecting telescope. Newton knew that a mirror whose surface was part of a sphere would not bring parallel rays to a perfect point focus but, like the lens, would suffer from spherical aberration. He also knew that for parallel rays, coming from a distant object such as a star, a paraboloidal mirror would give a perfect result, but he was unable to make the more complicated shape with sufficient accuracy, so he used the simpler, spherical curvature. The art of silvering glass on the front surface was not yet known, so Newton ground and polished his concave surface on a block of speculum metal (an alloy of I part tin and 2 parts copper). The mirror, unlike the lens, would obviously not give rise to chromatic aberration, and the eyepiece was fairly free from this defect, so that Newton's telescope was a big improvement on the previous refracting types. Something to think about Why does it say above that the mirror, unlike the lens, would obviously not give rise to chromatic aberration?

In this rapid survey of the history of telescopes, we have seen discovery by accident leading to rule of thumb procedure and this, in turn, giving way to design based on the application of principles. We have seen the development of the refractor halted because the principles governing the production of colour had still to be discovered. Another important factor controlling the rate of progress is the art and skill of the craftsman. Development of the refractor was retarded by the very slow improvement in the art and craft of glassmaking. This industry had not reached the stage where the quality of the glass could be closely controlled during manufacture, and the thick pieces of glass needed for the manufacture oflarger lenses were seldom free from internal bubbles and striations. However, two technical developments favoured the reflector. In the mid-nineteenth century Foucault discovered a method for silvering so that concave mirrors of glass with a highly reflecting surface could be used. Such mirrors were lighter in weight than those made of speculum metal, and the polished silver surface reflected a much greater 20

I THE

TELESCOPE I

Visual checkon purity ofan optical glass block

proportion of the incident light. Secondly, by varying the polishing stroke it was found possible to convert the spherical surface into a paraboloidal one, so that large aperture concave mirrors which would bring parallel rays into a perfect focus could be used. Both optically and mechanically it is easier to produce a large concave mirror than a large convex lens of the same quality. (Why is it desirable for a telescope to have a large objective?) So, up to the present day, we find the reflecting telescope leading the field, at least as far as astronomical work is concerned. Newton's telescope mirror had a diameter of 1 inch. Herschel in the late nineteenth century made his own telescope mirrors of 48-inch diameter, the Rosse telescope in Ireland (1845) measured 70 inches, the Mount Wilson telescope (1917) has a diameter of 100 inches, while the Hale telescope on Mount Palomar (1948) has a mirror measuring 200 inches across, with a focal length of 55 feet. The Isaac Newton telescope at Herstmonceux, Sussex (1967) has a 98-inch objective mirror of focal length 24 feet. By using ancillary convex mirrors effective focal lengths of 112 feet and 256 feet can be obtained. 21

I TH E TELESCOiiJ

Right: 18 incn Gregorian reflector made in 1742 by Short. It magnified 1200 times and cost 600 guineas

Below: Lord Rosse's 6 foot reflector (1845). With it he discovered the shape of spiral galaxies

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Above left: Herschel's reflecting telescope (1770). He discovered the planet Uranus and two satellites of Saturn

Above right: the 98 inch Issac Newton telescope ( 1967) at the Royal Greenwich Observatory, Herstmonceux, Sussex

Left: the 200 inch Hale telescope, Mount Palomar, California, at its dedication ceremony in 1948

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MODIFICATIONS OF NEWTON'S TELESCOPE There were other aspects of the design to be considered. Newton's arrangement has a serious disadvantage when used in a large telescope. The tube or framework carrying the mirrors and the eyepiece must be pivoted so that it can point anywhere in the sky. It will obviously be convenient for the observer if the pivot is near the eyepiece, but this means that the heavy mirror must be some distance from the pivot so that its weight must be counter-balanced. On the other hand, if we put the pivot near the concave mirror end of the structure, the observer will have to move about with the eyepiece as the telescope is swung to different positions.

These difficulties can be overcome by the following arrangement. The Newtonian plane mirror is placed at right angles to the axis and reflects the light towards a small hole in the centre of the concave paraboloid, where the eyepiece is mounted. Cassegrain (1660) devised a clever improvement; in his arrangement he used a small convex mirror instead of the plane mirror, as illustrated below. This system produces a greater magnification without increasing the length of the telescope.

Cassegrain reflecting telescope

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I TH E TELESCOPE]

An astronomer sitting in the 6 foot observer's cage at the focus of the 200 inch telescope at Mount Palomar

USE OF CAMERAS The large reflectors built in this century are seldom used for visual observation. They are used as gigantic cameras. The 200-inch Hale telescope on Mount Palomar, for example, has a cage 6 feet in diameter built inside the framework near the focus of the main mirror. Here are mounted the photographic equipment and other instruments, and the observer who controls them sits in this cage.

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[ THE TELESCOPE

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Something to think about I. It is natural to suppose that a 72-inch diameter cage in front of a 200-inch diameter mirror will cause a loss of light from-a star. In fact it is not more than 15 per cent. Why is this? 2. Using freehand sketches, can you persuade yourself that the cage will not blot out 15 per cent of the visible sky - indeed it will not obscure any part of it?

What is the advantage of the camera over direct observation? It lies in the fact that the effect of the light from a star can be accumulated, or stored up, in the photographic emulsion. Your eye cannot do this. When you stare fixedly at a source of light such as a planet it does not grow steadily brighter as more and more light from the planet falls on the same part of the retina. If anything, the image becomes fainter as the eye becomes fatigued. Something to do Stare fixedly at a red light for a minute, then transfer your gaze to a white wall. What you appear to see on the wall will confirm the theory that the eye has been temporarily fatigued for red light.

The combination of camera and telescope will give an enormous gain. The telescope mirror, say 200 inches in diameter, can collect far more light than the eye with its pupil of about t inch in diameter. (How much more?) Even so, the image of a star may be so faint that it cannot be seen by the eye. But this faint light, focused onto one crystal of silver bromide in the photographic emulsion, can accumulate its effect for hours and build up a latent image which, when developed, is visible to the eye. When we remember that the telescope is mounted on a platform (the earth) which spins on its axis once every 24 hours, we realise that to take full advantage of the telescope/ camera combination another difficult problem must be solved. The telescope must be kept pointing at exactly the same part of the sky so that the earth's motion is neutralised. (If the object is so faint that an exposure of more than, say, 12 hours is required a special problem arises !) To meet such demands the highest skills of mechanical, as well as optical, engineering are required. The problems encountered and overcome in making the great 200-inch telescope illustrate this. The work was started by Hale in 1928 and after a false start on the massive mirror, during

26

The star field in Orion photographed with a 3 foot reflector for 6 minutes and 68 minutes respectively

27

Three north-south orientations of the 200 inch telescope

which parts of the mould broke off as the molten glass was being poured, a perfect 200-inch pyrex disc was cast in 1934. A year was allowed for the 20-ton disc to cool slowly, to prevent internal strains being created in the glass. Next came the arduous job of grinding and polishing the disc to its correct shape. This was not completed until 1947, by which time over 5 tons of glass had been worn away and 30 tons of abrasive material used. But at the end the desired parabolic shape was perfect to a tolerance of two millionths of an inch. A reflecting surface of aluminium coats the disc which is mounted in a 55-foot long open tube, weighing 125 tons. This in its turn is mounted on a 300-ton yoke, which can rotate so that the telescope may cover the entire sky. Such massive mounting is necessary to keep the telescope steady on a given part of the sky as the earth rotates under it. But despite the size and weight ofthe telescope with its mounting, the whole structure is designed and constructed with such precision that one hand can turn it on its oil pad bearings. In normal use a 60 watt motor is used to keep the telescope aligned. The precision necessary makes these giant telescopes a triumph of engineermg.

THE REFRACTING TELESCOPE If the concave mirror solved the problem of chromatic aberration for the telescope, why did the refractor survive? There are several reasons. First, for telescopes of small size the refractor is more handy and it is more adaptable. Two of them side by side form binoculars. (Can you imagine a binocular reflector?) Secondly, less light is usually lost in refractors than in reflectors. One tends to think of a lens as transmitting all the light received and a mirror reflecting perfectly, but this is not the case. Stand in a lighted room and look out of a closed window on a dark night. Your image reflected in the glass shows that a small percentage of light is reflected. (You may even see a double image. What does this show?) About 5 per cent of the light striking the front surface of a lens is reflected back, and 5 per cent of what

28

l is transmitted is reflected at the second face. Furthermore, the glass itself is not perfectly transparent (seventeenth century glass was very poor in this respect). Taking everything into account, perhaps not more than 90 per cent of the incident light gets through the objective lens of the telescope to reach the eyepiece. Even so, the performance of the lens is better than that of a mirror. A mirror of speculum metal, when newly polished, reflects no more than 60 per cent of the incident light. (What happens to the other 40 per cent of the energy?) Furthermore, a mirror tarnishes readily and needs frequent re-polishing to prevent further loss of light. A glass mirror with a polished silver surface likewise needs re-silvering: it reflects more than 90 per cent of the incident light at the red end of the spectrum, but is less efficient for blue and violet and is very poor in the ultra-violet. (Why is ultra-violet important?) Aluminised mirrors are now extensively used as they give the best all-round performance, but they are not as efficient as lenses. Thirdly, a parabolic mirror works perfectly for rays parallel to its axis, but deterioration of the image sets in rapidly when rays inclined to the axis must be used. In Below: a test ina smoke box investigating the transmitted and reflected light with a piece of 24 oz sheet glass

Right: three east-west orientations of the 200 inch telescope

29

Telescopes being used to study a solar eclipse. A camera is mounted onto the small refractor, and a projection screen onto the 8 inch reflector. (Note: you should never look at the sun directly through a telescope)

30

other words, the field of view for good viewing is limited, more so than for a refractor. Finally, the wonders revealed by the microscope resulted in great demand for that instrument and this stimulated research to improve its performance. Any discoveries, or inventions, which led to improvement in the microscope were likely to be applicable to the refracting telescope as well. The first problem to solve was chromatic aberration and this is considered in the next section.

COLOUR ANDTHE ACHROMATIC LENS

Your experiments at school will have shown you that white light is made up of light of many colours (the colours of the spectrum). It had long been known that light in passing through various shaped pieces of glass became coloured, but it was believed that the glass had added the colours to the light. Newton was dissatisfied by this explanation and he put forward the theory that white light consisted of a mixture of all colours, supporting his theory with a series of experiments using prisms. He used a beam of sunlight, showing that not only was the light deviated from its original direction, but also dispersed into its component colours.

He also showed that the coloured light could be brought together again to give white light, by letting the light pass through a second prism the opposite way round.

Suppose that in the arrangement above the second prism could be made of a different kind of material, which would bend light on an average as much as the first prism, but would disperse light into its colours more strongly. Light passing through the two prisms, arranged to give opposing results, would emerge more or less parallel to its original direction, but the dispersion produced by the first prism would be overcompensated by the second. Thus 31

COLOUR AND THE ACHROMATIC LENS

the emerging beam, though undeviated as a whole, would still show some dispersion.

This would be a useful device. It could be used to make a 'direct· vision' spectroscope, one which produced a spectrum without bending the light through an awkward angle as happens with a single prism. One could look straight through it at a source of light and see the spectrum. But our problem is chromatic aberration, the colouring of the image produced by a lens. We want to produce a lens which bends rays of light without any dispersion. The two prisms above gave dispersion without deviation, but to solve our problem we need deviation without dispersion. Can you see how to get it? In the arrangement above, we assumed the second prism was made of a different kind of glass which bent light on the average as much as the first, but dispersed light more strongly. Suppose you could reduce the angle of the second prism; the dispersion would get less and less. If you chose the angle so that the dispersion produced by the second was equal to the dispersion produced by the first, then when these were put together the opposite way round, there would be no dispersion. But the deviation would no longer be equal and opposite - so we should have deviation but no dispersion.

32

COLOUR AND THE ACHROMATIC LENS

Fifteenth century glass works

Newton, and those who followed him, understood the principles behind the solution of the colour problem in lenses. Euler (1747) thought that the presence of liquids inside the eye helped to reduce colour defects in the image on the retina, and he suggested that hollow lenses filled with suit~ble liquids be used for the same purpose in optical instruments. Dolland (1707-1767) failed in attempts to construct such lenses, but eventually succeeded by using two kinds of glass. Glass can be made by fusing together a mixture of silica (sand), soda ash and lime. It was probably first made by accident as a result of the heating together of these commonly occurring substances in a fire. When the researches described above revealed the need for different kinds of glass, the industry was stimulated to try the effect of varying the composition of the mixture. Silica can be replaced largely, or entirely, by boric acid or by phosphoric acid, and lime by barium oxide. In this way were produced what are now known as crown glass and flint glass, and later dense flint and extra dense flint glass.

33

Twentieth century glass works: this photograph shows molten glass being cast

With these glasses, the average refractive index varies from about 1·5 to about 1·7. Glass

Refractive index

Crown glass Flint glass Dense flint glass Extra dense flint glass Double extra dense flint glass

1·51 1·53 1·62 1·70

1·93

But although the refractive index increases slightly from one to the next, the dispersive power increases much more rapidly. Thus a heavy flint prism does not bend light asa whole much more than a crown glass prism of equal angle, but it spreads out the light from red to violet about three times as much. To produce a lens without chromatic aberration, two lenses of different glass must be used. This is called an achromatic doublet and it can be made by placing together 34

An achromatic doublet

Fraunhofer's map ofthe solar spectrum. The upper graph shows the intensity of light for a particular colour

a double convex crown glass lens and a diverging flint glass lens. It is convenient to make the concave face of the diverging lens so that it fits exactly onto one convex face of the converging lens. The other face of the diverging lens is then almost flat. The dispersion produced by one lens is compensated by the dispersion caused by the other. The success of the search for different kinds of glass depended very much on the development of accurate methods for measurement of the index of refraction for different colours. Before the time of Newton it was sufficient to speak of the refractive index for white light of a transparent material such as glass or water. Newton improved upon this by showing that a transparent material has different refractive indices for different colours, but it was still difficult to be precise because there are in the spectrum many shades of red, green and so on, each merging imperceptibly into the next. Joseph Fraunhofer (1815), following up Newton's work, found a solution to the problem. He noticed that the spectrum of sunlight is always crossed by fine dark lines in fixed positions. He labelled the more prominent ones A, B, C etc., and they are now known as the Fraunhofer lines. He used them as landmarks in the spectrum, so that when a new kind of glass came to be tested he could specify the

35

COLOUR AND THE ACHROMATIC LENS

refractive indices for, say, the C, D and F lines (C being in the red, D in the orange-yellow, and F in the near blue). In this way it was possible to make measurements of such precision that the effect of a small change in the composition of the glass could be recorded, and of course these results could be used as a guide to suggest what effect further changes would produce. Thus it became possible to design a new kind of glass on paper before trying to make it in the glassworks. Something to do You can observe the Fraunhofer lines for yourself. Stand with your back to the sun and hold a bright, coarse sewing needle at arm's length. The sunlight reflected in it forms a fine line of light. Hold a 60° prism, or better still a diffraction grating, close up to one eye and look through it for a spectrum of light reflected from the needle. It will help if the background is dark.

The development of the achromatic lens is another very good example of the progress which can be made when trial-and-error and rule of thumb methods are abandoned and scientific principles are applied. Final preparation ofa Zeiss lens system

36

..., THE MICROSCOPE

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high power

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Modern microscope objectives

The basic principle of the microscope is similar to that of the refracting telescope. It contains an objective lens which forms a real image of the object, and this image is viewed by the eyepiece which acts as a magnifying glass.

With the telescope, the object was a long way away and the objective lens-had a long focal length. With the microscope, the object is very close to the lens, which will thus have a much shorter focal length: the object must be just outside the focal length if a real magnified image is to be obtained. On page 11 we saw that a simple lens gives blurred images because the outer parts cause too much bending of the rays compared with the parts near the axis. We also saw that this defect could be reduced by arranging the shapes of the two faces of the lens so that a ray is bent in two small steps rather than in one large step. In an achromatic doublet we have three curvatures to play with, and they can be arranged so that the bending is shared between them. This idea can be extended by building up a more complicated system. However, the problem here is a severe one, for the object is very close to the lens and to fill its front face the rays must spread out at a very wide angle. They have to be made to converge to form a real magnified image which can be further magnified by the eyepiece. 37

The problem is made more severe when we recall that the object is not merely one bright point on the axis of the lens system, but extends on either side. The objective has to accept wide beams of rays from various points and all the rays of all colours must be properly combined in the final image. We begin to appreciate what a complicated problem the design of a really good lens is. In a good microscope objective no fewer than 10 lenses may be used to bend the light in many small steps. Optical path ofLeitz Orthoplan microscope

..

In practice objective lenses of power more than 100 dioptres*, even as high as 1200 dioptres, may be used. The greater the power of the lens the greater the magnification produced. Something to do Look carefully at the same object, say a biological slide or a torn edge of paper, through a cheap 'toy' microscope and through a really expensive professional one. What differences do you notice? Can you explain them?

Something to think about Why is it important to illuminate an object so strongly if the microscope produces a magnification of, say, xIOO? *See page 64 for the definition of a dioptre.

38

...,

[THE CAMERA

I

You have seen in the laboratory how a pin-hole camera produces an image on the back of the camera, and how a series of pin-holes produces a series of images. A suitable converging lens in front brings all the images together into a single, clear image, much brighter than before. It is on this principle that a lens camera works.

39

I THE

CAMERA I

G. Zuiko lens system

The Chronos camera has bellows adjustment. The lens on the Zeiss Ikon 35 mm camera is on a screw thread

40

Cheap cameras will have a single lens. The lenses of most cameras, though less complicated than the microscope objective, may still contain more than two component lenses. This will account for a high proportion of the cost of a complete instrument. The diagram shows a complex lens system designed to produce a sharp image even with a large aperture. To focus an image on the film the distance between the lens and the film is adjusted. This used to be done by attaching the lens to a bellows system, but it is far more common now for the lens to be mounted on a screw thread so that it can be screwed in or out. A range setting is marked on the camera to correspond with different positions of the screw. This provides delicate adjustment for the lens position.

[THE CAMERA I

DEPTH OF FIELD With a particular camera, it is found that a person 4 metres away from the camera is sharply in focus, but trees 30 metres away and flowers 1 metre away are not. (Light from

any point on the flowers or the trees will form a small circle on the film, forming a blurred image.) If each point on the object forms a circle smaller than the grain size of the film, the image will appear sharp. The range over which an object produces a sharp image on the film is called the depth offield. Something to do 1. By drawing a diagram similar to that above, but with a smaller lens, can you convince yourself that the depth of field is increased as the aperture of the lens is decreased? 2. Look at an object about I metre away with one eye and you will see that both the background and also a finger placed about 30 ems away are out offocus: you need to re-focus your eye to see them clearly. Now take a piece of card and put a pin hole in it. Hold this pin hole close to the eye. What has happened to the depth of field as you have reduced the aperture of the eye lens?

Simple cameras have a small aperture lens and therefore they have a large depth offield, perhaps from 2 metres to infinity. In that case, there is no need to have a movable lens. This would be called a fixed focus camera. However, a lens of large aperture will need careful focusing. Why do we not always use a small aperture?

LIGHT REGULATION A given film requires a certain amount of light to expose it correctly. The amount of light entering a camera may be controlled by varying either the time for which the shutter is open, or the aperture of the lens (the amount the lens is open). 41

I THE CAMERA

I

The diameter of the lens opening is measured as a fraction of the focal length: f/8 means that the diameter of the aperture is one eighth of the focal length of the lens. The diaphragm of most cameras can be set at f/2·8, f/4, f/5·6, r/s, fill, fll6 and fl22. Something to think about 1. Can you show that the amount of light entering the camera approximately doubles as the f number decreases from one step to the next? 2. A setting of 1/l00s at fill is equivalent to 1/50s at f/l6 as far as the amount of light falling on the film is concerned. When would you want to use a fast shutter speed and large aperture? When would a slow speed and a small aperture be better?

THE VIEWFINDER The viewfinder is usually a small telescope mounted on top of the camera to show what picture the camera is taking. It is adjusted so that a distant view, seen in the viewfinder, will be the same as the picture in the camera. However, the line of the viewfinder is slightly above the line of the Optical path of Leicafiex SL. Can you suggest why a 5-sided prism. a pentraprism, is used in the viewfinder instead ofa 3-sided. 45 degree prism?

42

, [THE CAMERA

I

camera lens. With some close shots, this has the disadvantage that the two pictures will not quite coincide and that in the final photograph people's heads will tend to get cut off. This difficulty is solved in a reflex camera, in which the actual camera lens is used as part of the viewfinder. A mirror and prism reflect light, which has been passed through the camera lens, into the eyepiece of the viewfinder. When the shutter release is pressed, the mirror moves quickly up just before the shutter opens. In this way you see in the viewfinder exactly what will be formed on the film.

THE DEVELOPMENT OF THE CAMERA

'Wet plate' photography in the 18605

The first efficient photographic plates, made by Daguerre and Fox Talbot in the late 1830s, needed exposures of about 5 minutes. These cameras were merely light-proof boxes with a capped lens. In 1851 Archer invented a plate requiring an exposure of only a few seconds, but as his 'wet

43

One of the earliest Daguerreotype cameras,1839

The original 'Kodak'. Can you suggest why a circular mask was used to cut out the edges of the photo?

A modern 35 mm camera, the Leicaflex single lens reflex

44

., [THE CAMERA I

plates' needed to be prepared, exposed and developed on the spot they were very inconvenient. The first popular camera was Eastman's 'Kodak' (1889). This incorporated a fast, 100picture, flexible film, a fixed-focus lens, a shutter and a viewfinder. The camera was cheap enough to be returned, complete, to Kodak for development of the film. Modern cameras show little fundamental change from the 'Kodak', but each component has been considerably refined.

USES OF PHOTOGRAPHY

High speed photography. A flash of about IO microseconds from a Xenon lamp illuminates the subject at the appropriate moment. Thus a camera with its shutter open records the rifle bullet having cut the playing card

The improvements in lenses and the development of the chemistry oflight sensitive films have lead to great progress in photography in the last hundred years. Photography is important for domestic and family purposes and for recording historic events. It is also important in scientific and technological work. It permits records to be made of events which the eye could not see because they are too small, because they occur too fast or because the eye is not sensitive to their radiation. Various examples are shown below.

45

A stroboscopic photograph showing the action of a golfer. A flashing light illuminates the scene at a regular rate. about 100 flashes per second. Thus the position of the golfer at each of these instances is recorded on the film ofan open-shuttered camera Photography of Mars' surface showed it to be surprisingly similar to the surface of the moon. This photograph was taken from the Mariner 7 satellite

46

9

An X-ray photograph showing a SmithPeterson pin strengthening a broken femur

John Glenn filmed during his space flight

THE CINE CAMERA

Kodak Instamatic cine camera

A cine camera takes a series of still pictures of a moving subject in quick succession, usually 16 frames per second. The optical arrangement of such a camera is basically the same as that for a still camera. The film, however, is moved in jerks through the camera and a rotating shutter ensures that a picture is taken every time the film is stationary. When these still pictures are projected on a screen in quick succession the persistence of vision produces a sensation of steady movement. 47

I THE

CAMERA I

Something to think about What is the effect of projecting the pictures on a screen at a faster rate than they were taken, say 24 frames per second instead of 16?

Something to do Draw a series of simple diagrams on successive pages of a notebook showing a sequence of events: a car moving, a boy kicking a ball into a goal or a rocket being launched. Then flick the pages through and notice the sensation of steady movement. How could you make the movement steadier?

THE PHOTO-FINISH CAMERA

A sprint finish recorded by an Omega Photosprint timer

An ordinary photograph taken near the finish of a race might show A about to reach the finishing tape, leading by a metre from B, who is a few centimetres ahead of C. It would be safe to assume that A will win, but the results for Band C are by no means certain. B might stumble, while C makes an extra effort and gets his chest in front in order to gain second place. An ordinary photograph shows us the positions of the runners at a certain time, whereas what is needed is to know the relative time of the runners at a certain position (namely, the finishing line).

1111 I 1/11 I 1111111111111' 111111111111I11111111111111111111111111111111111111111111111111111111111111111'

. 48

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This can be done using a special camera. In this, the film moves steadily behind a screen in which there is a narrow vertical slit. The camera is aimed so that the image of the finishing line falls exactly on this slit. When the chest of the first runner reaches the finishing line, its image falls on the strip of film which is passing the slit at that moment. The film passes behind the screen, but the image ofthe next strip of the runner's head then falls on the next strip offilm, and so on for the complete runner. A little latertheimage of each part of the second runner will be recorded on the moving film, strip by strip, as he crosses the finishing line. Suppose the film is moving at one centimetre per second and that the second runner finishes one second behind the winner. On the film, his chest would be one centimetre behind that of the first runner. If the image of the third runner is one millimetre behind that of the second runner, he finished T~ second later.

[THE CAMERA I

Something to think about 1. If the film is made to go too fast in the camera, what difference will it make (a) to the placing of the runners (b) to the shape of the image of the athletes?

2. Why is an ordinary cine camera not used to record the finish? I I I

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49

I THE EYE \

This volume would not be complete without some reference to the optical instrument in greatest use of all, the eye. In the previous chapter, we saw how a camera can be adjusted to different light intensities by varying the aperture size. We also saw how a camera can be focused onto objects at differing distances away. By varying the speed of the film used, a camera can take good pictures either on a bright day or in a dimly lit room. A cine camera can take a series of pictures in quick succession. A television camera 'develops' pictures almost instantaneously, by electronic means. A single camera that did all these things would be a remarkable camera indeed, and an expensive one! Yet each of us possesses two optical instruments which do all this. In many ways our eyes can be likened to an automatic camera of the highest sophistication.

THE RETINA The optical system of the eye is very similar to a camera, producing a real, diminished inverted image on the retina. The light .sensitive retina consists of about 100 million cells, which are oftwo types, rods and cones. The cones are sensitive to colour and are the principle cells used for 50

...

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[THE EYE

I

aqueous humour crystalline lens -t-+:---...,+--cornea iris

Human eye

daylight vision. However, they are not as sensitive to light as the rods and it is the rods which are responsible for twilight vision in low light intensities. You will have noticed that the sensation of colour disappears at night time: everything appears in varying shades of grey, as there is not sufficient light to affect the colour-sensitive cones. Signals from the rods and cones pass through a highly complex system of nerves to the brain by way of the optic nerve. Where the optic nerve leaves the eyeball is a blind spot. Something to do Close your left eye and, holding this book at arm's length, look at the Queen's head with the right eye. Now move the book slowly towards you. Note what happens to the reverse side of the 50 penny piece. Does the same thing happen if you repeat the experiment with the right eye closed? What does this tell you about the position of the blind spot?

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i : ~~8 51

I THE

EYE I

Rods and cones are not distributed evenly throughout the retina. When you look directly at something, the light from it falls on a yellow spot on the retina, called the fovea. This is the region where the eye can see things most sharply. It consists entirely of cones. While it is the most important part of the retina, it is very small. The light falling on it is roughly equivalent to that from a thumbnail held at arm's length. The rest of the retina consists of rods and cones mixed in different proportions. As the image moves further from the fovea, it becomes less distinct.

FOCUSING THE EYE As with a good camera lens, focusing in the eye is shared by more than one lens, in fact by three. The aqueous humour forms a lens with refractive index 1·33, the crystalline lens another with refractive index 1-42 and finally the vitreous humour the third with refractive index 1·33. The distance between the lens and the 'screen' cannot be varied as it can in the camera, to allow for focusing on objects at different distances. Focusing in the eye is done by varying the power of the crystalline lens. The ciliary muscles cause the shape of the lens to vary. As the lens becomes fatter, the faces become more curved and the power of the lens becomes greater. Something to think about If your eye is distracted from this book to something outside the window, will the ciliary muscles make your eye lens more or less curved?

As the camera has an aperture control, so your eye has the iris diaphragm. Look at your eyes in a mirror and shine a torch into one of them. See how the iris, the coloured part of your eye, changes. The black part in the middle is the area through which the light passes; it is called the pupil of the eye. The iris diaphragm will cause the diameter of the pupil to vary between about 2 mm and 8 mm. 52

[THE EYE

q

I

Below left: eye of the nautilus Below right: multiple eyes of a fly

OTHER TYPES OF EYES Not all eyes are the same as human eyes and there is a great diversity of eyes among other living things. The eye of a nautilus, a mollusc, has no lens, but works like a pin-hole camera. Most insects have compound eyes consisting of up to 100000 independent units. The copilia, a microscopic seawater creature, has two scanning eyes. Each consists of a lens and a single lightsensitive receptor. The receptor is moved backward and forward, scanning the image as in a modern television camera. The scanning rate may be as fast as 5 a second.

53

The catfish and certain cold-blooded creatures have a retina in which the rods advance and the cones reiract in dim light, automatically changing the 'speed of the film'. Fish, butterflies, birds and reptiles are sensitive to colour, but most mammals are not. The bee's eye is sensitive even to ultra violet radiation, which the human eye is not, and so different white flowers in the garden may appear different to a bee as they reflect different amounts of ultra violet light. Nocturnal animals such as bats and hedgehogs have no cones in their retina, only rods. The giant squid has the largest known eye: it is 40 em in diameter!

Copilia: its eyes are about half the length of its body

54

DEFECTS OF VISION The most common defects of the eye are short-sightedness, long-sightedness, presbyopia, astigmatism and colour blindness. 1. Short sight (or myopia): a short-sighted person can see objects a short distance away, but cannot focus clearly on distant objects. (Idle pupils at the back of the class are safe from a short-sighted teacher without his spectacles.) The image of a distant object is focused in front of the retina, because the eyeball is too long for the strength of the eye lens. This can be counteracted by spectacles made with diverging lenses.

Mediaeval statue ofSt Matthew wearing spectacles, from Westminster Abbey

2. Long sight (or hypermetropia): a long-sighted person can see objects a long distance away, but cannot focus clearly on near objects. (Idle pupils are safer at the front of a class with a long-sighted teacher without spectacles). The image of a close object would be focused behind the retina, because the eyeball is too short for the strength of the eye lens. This may be counteracted by spectacles made with converging lenses.

55

I THE EYE I

3. Presbyopia: with some elderly people, the ciliary muscles become less flexible. They lose the ability to accommodate the eye (to adjust it so that it will focus clearly and without strain) on objects over a wide range of distances. They might need glasses both for reading and for long-distance viewing: they require two pairs of spectacles unless they use bifocals, the lower half of which has a lens for reading (a book is normally held down) and the upper half another lens for long distance viewing.

Half a pair of trifocals

Something to think about What type oflens is in the top, and what in the bottom section of bifocals?

4. Astigmatism: this is caused by a lack of symmetry in the curvature of the eye and it is usually corrected with a cylindrical lens. 5. Colour blindness: some people find it impossible to distinguish between certain colours. John Dalton, for example, saw red blood and green laurel leaves as the same colour and it was he who drew the attention of the scientific world to the problem in 1794. It is estimated that one man in twelve is to some extent colour blind. While this is unimportant to most people, in some professions it is an insurmountable handicap. For example, an engine driver who could not distinguish a red signal from a green one would not be very efficient. In what other jobs would colour blindness be a handicap? Spectacles were first suggested by Roger Bacon in the late thirteenth century and were in use at the beginning of 56

.....

was [THE EYE

the fourteenth century. Nowadays spectacles are not only functional but decorative too. Even so some people prefer to wear their lenses less conspicuously and use contact lenses. These are tiny lenses which are placed actually on the cornea and are held in position by surface tension forces. As the wearer blinks, the eyelid closes over the lenses and washes them. Such lenses are mechanically very strong and far less susceptible to knocks. They are therefore favoured by sportsmen.

A pair of18th century wig spectacles

A corneal contact lens

57

THE SCHLIEREN EFFECT

TESTING LENSES It is possible in theory to calculate as accurately as necessary the shapes which the various surfaces of a compound lens must have, but can the lens-maker produce these shapes with the necessary accuracy in practice? There is also the problem of how to test the completed lens. It is all right if we can see nothing wrong with the image, but this is not a scientific way to tackle the job of testing. Suppose that the image is slightly defective. We then require a test to reveal which part of the lens is at fault. There is a test which you can easily try for yourself. If some part of the lens under test is bending the rays a bit more, or a bit less than it should, this makes the part of the lens actually visible. It is best to start with a lens of high quality and the bigger the lens aperture the better. (If your school has an old epidiascope, the lens from it will serve excellently. A telescope objective lens, or one of the front lenses of an old pair of binoculars, will also be suitable.) Use the lens to form the magnified image of a 12-volt filament on a postcard screen, as shown in the diagram below. Arrange the filament vertically and focus the image onto the card close to one edge. Reduce the filament voltage until the filament can be viewed directly without glare or discomfort.

Now place one eye close behind the edge of the card and move the card very slowly sideways, as shown by the full arrow in the diagram, until the image of the filament begins to be exposed and some light from it can enter the eye. The whole aperture of the lens will appear to be uniformly illuminated. As the card is moved to expose more and more of the filament this aperture will become brighter and brighter. The rays from the middle part of the filament 58

THE SCHLIEREN EFFECT

which pass through the lens and enter the eye appear to be coming from all parts of the lens. Thus the whole lens appears to be lit up like a large circular source of light. Now repeat the experiment with a large cheap lens. A hand magnifying glass, of about the same focal length and diameter as the epidiascope lens, will serve. When the eye is placed behind the edge of the postcard and the card is slowly moved sideways, the surface of the lens will appear to light up and shine-but not evenly all over. Some parts are darker and some brighter than the average, and different parts of the lens may show different colours. It is not difficult to understand how this comes about. We know that rays from one part of the filament source, after passing through this simple lens, are not brought to a perfect focus at one point in an image. Some rays are bent more than is necessary, and some less, and different colours are bent to different extents. Thus when the postcard is placed so that it is cutting off half of the filament image it should be stopping half of the light from all parts of the lens, making the lens surface appear neither white nor black but a uniform grey. But if some parts of the lens bend the light too much to the right, these rays will by-pass

the card completely, enter the eye at full strength and make the part of the lens from which they come appear brighter than average. Similarly, parts of the lens which bend rays too much to the left, so that they are intercepted by the card completely, will appear darker than average. Can you now explain why some parts of the simple lens in this test show colours?

TESTING MIRRORS The experiment may also be done with a concave mirror, preferably one of long focal length. Place a lamp filament at X - see the diagram - a little to one side of the centre of curvature of the mirror C. 59

THE SCHLIEREN EFFECT

-----

--- --------- ------

~~card

--

_----.---

C

card

Focus the image of the filament on a card placed on the other side of C. Place the eye behind the edge of the card (using an extra shield between the eye and the lamp) and move the card sideways as before. If the mirror is a good one it will be possible to set the card so that the mirror surface appears uniformly grey all over.

TOEPLER'S EXPERIMENTS Toepler (1864) showed how the method of testing a lens could also make use of light in other ways, in particular to reveal normally invisible streams of air and other gases. You can repeat his experiments in a simple form by setting up the high quality lens as before and adjusting the card to give a uniform grey appearance to the lens surface. Support an electric soldering iron with the 'bit' a few inches in front of the lens (taking care that it is not so close that the heat will damage the lens surface). Switch on the iron and watch with your eye close behind the edge of the card. When the bit warms up the convection currents of hot air rising from it appear vividly, like clouds of steam and smoke arising from a conflagration. What does this show? How does it work?

60

.1

r' · ·

THE SCHLIEREN EFFECT

Schlieren photographs showing how air circulates above a radiator in a model room. The lower photograph shows how a small shelf over the radiator deflects the air currents away from the wall, keeping it clean

We know that the high quality lens alone is able to focus the rays accurately on the edge of the card. Yet, to produce the effects observed, the rays must be deflected from their true paths. This must happen after they have left the lens, and can occur only when they are passing through the streams of heated air rising from the soldering iron. Such bending, or deflection, of the light rays can occur only if the refractive index of the hot air is different from that of the colder air around it. A candle flame or a bunsen burner may be used instead of the soldering iron. The method has been used to study the flow of hot air from an electric lamp bulb around the lampshade and up the flex, with the aim of devising a shape for the lampshade which would deflect the hot air away from the flex and so protect the insulation. (You could use a 12-volt headlamp and miniature lampshade to investigate this.) The method has also been used to study such things as the flow of hot gases through a miniature, transparent model of a furnace and the air pressure waves caused by an airfoil. If you replace the filament as the light source by a very narrow, brightly illuminated slit you can make the method so sensitive that you can detect a heavy gas like carbon dioxide being poured downward out of a gas jar, or a light gas, such as hydrogen, being poured upward from an inverted jar, or jets of these gases issuing from the delivery tube of a Kipp's apparatus or other gas generator. Evaporation from a volatile liquid may also be studied. When air flows at high speed over a model in a wind tunnel shock waves are produced and are revealed by using Toepler's method. Toepler called this the method of striae, or in German the 'Schlieren Methode'. Finally, let us consider a property of light which may have been the first one ever to be noticed. Sunbeams, lantern beams in dusty air, the beam from a cine-projector in the smoke-laden air of a cinema or a searchlight beam, all suggest that light travels in straight lines. Textbooks on elementary optics describe experiments which attempt to test or demonstrate this, but you will surely agree that they are not very accurate. Yet in certain walks of life we rely very much on the assumption that light travels in straight 61

Schlieren photograph showing the shock wave around the Mercury space capsule re-entering the earth's atmosphere

lines. When you fire a rifle you know that the bullet will follow a curved path as it falls under gravity. You set the sights to allow for this, and aim off to counteract any drift caused by wind, but in pointing the rifle at the appropriate spot on the target you assume that light rays at least do not add to your problems by bending as they travel through the air. On a larger scale, we rely on the accuracy of rectilinear propagation of light in surveying with a theodolite by the triangulation method, and on a yet larger scale we use sighting with the aid of a telescope to map very precisely the positions of the stars and other heavenly bodies. Toepler's schlieren experiments showed you that this is not entirely trustworthy. Light passing through air, or other gases, where the temperature and pressure vary, does not travel in a perfectly straight line. The light from the heavenly bodies must reach us through the atmosphere, first encountering the very rarefied air at great heights and then passing through layer after layer with varying temperatures and increasing density. It therefore becomes important to estimate what amount of refraction does occur and whether it is sufficient to affect the most accurate measurements we can make. There is a simple way to estimate the magnitude of the possible error. When we observe an eclipse of the moon we say that the centres of sun, earth and moon must be in a straight line, so that the shadow of the earth falls on the moon. Yet observers have sometimes been able to see the sun about to set in the west and the moon, fully eclipsed, just visible above the horizon in the east. Each of these bodies subtends an angle of about half a degree at the earth's surface. It follows that the light by which we see them must have been bent by at least 30' of arc on its passage through the atmosphere to the observer's eye. Cal,"

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62

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THE SCHLIEREN EFFECT

culation shows that the bending can amount to 36' of arc for an object near the horizon. Why is this apparent elevation of the heavenly bodies above their true positions greatest for an object near the horizon? Is there any position for a star which will show no error? In the above discussion we have assumed that the density of the atmosphere increases smoothly as we approach the earth. But streams of hot air, rising from heated land and from cities where the atmosphere is contaminated, must cause irregularities in the refraction. This is noticeable when a heavenly body, such as a planet or the moon, is viewed through a high-powered telescope, especially when the object is low in the sky. The whole illuminated surface of the object appears to be shimmering or boiling, and it is difficult to observe fine detail. If the telescope is being used as a camera and a fairly long exposure is necessary, the result can be very disappointing. You will be able to understand now why observatories built in recent years have been located on high mountains in spite of the difficulty of access, and why, more recently, plans have been made to send telescopes and cameras high up into the stratosphere on balloons, or even right outside the atmosphere on rockets or satellites, in spite of the complications involved in aiming the telescope at the object to be photographed. Coming down to earth again, you may be able now to understand such phenomena as the mirage and the twinkling of the stars.

A mirage in the desert

63

TYPES OF LENS

I APPENDIX I

converging lenses

diverging lenses

,~

JUll980

I ]J

?

plano-convex convex

plano-concave

meniscus-convex

concave

meniscus-concave

FOCAL LENGTH

Rays parallel to the axis of a lens converge to the principal focus. The focal length is the distance of the principal focus from the centre of the lens

STRENGTH OF A LENS The strength of a lens is measured in dioptres. The number of dioptres

1. focal length measured III metres Thus a lens of focal length 10 em (or 0·1 m) will have a strength of _1_ or +- 10 dioptres. 0·1 Likewise a lens of strength + 7 dioptres will have a focal length in metres

=

~=

=

0·143 m or 14·3 em.

A converging lens will have a strength of + x dioptres, a diverging lens a strength of -x dioptres. 64