Physical optics; or, The nature and properties of light, a descriptive and experiment treatise

Preface

THE author, on commencing an experimental study of Physical Optics more than a quarter of a century ago, found a want of experimental guidance in the treatises upon the subject, and this want has not yet been supplied. It is true that experimental results have been described, but not with the experimental detail which the student needs, in order to abridge his labour and facilitate his progress. Like other physical sciences, its development rests almost entirely upon the application of mathematical analysis, and accordingly the discussions of the original investigators are frequently too mathematical for general readers. Though the author, from the commencement of his experiments, had an adequate store of mathematical knowledge for application to his own researches, and to follow the researches of others, yet he has continually seen that the introduction of mathematical formulae into treatises upon Physical Optics must restrict the study of the science to a smaller class than was desirable ; for many of the most expert experimenters have only slender acquirements in mathematical analysis.

It has been the author's object to supply the want of a descriptive, experimental, and popular treatise on Physical Optics, and to point out the bearing of the different results upon the nature and properties of Light.

IV PREFACE.

He feels that he has no need to apologize to the scientific world for describing the most homely contrivances for experiments, knowing that, with simple and inexpensive apparatus, the most important discoveries have heen made, and will continue to be made, in this science.

An ignorant man may smile equally upon the child blowing soap-bubbles for amusement, and upon the grave, thoughtful philosopher contemplating the fine colours they exhibit when very thin, and thinking of the explanation of them. The philosopher will continue nevertheless seriously to contemplate the soap-bubble, conscious that he comprehends what he sees ; which is beyond the feeble intelligence of the uneducated. The beautiful and often gorgeous phenomena which are continually presented to the observer in the experiments of this science, call forth exclamations of surprise from even the most ignorant ; and the question, how does this happen? is made with anxious countenance by those who are not prepared to understand the only answer which can be given to their own question. The author hopes that this question is answered in the present treatise, and in a manner comprehensible to all who have sufficient patience for the study, without entering into mathematical details.

He hopes that the mathematical student will find the present work an introduction to the science, which will enable him to examine for himself the experiments, and see their bearing upon the received theories. In another volume he will discuss mathematically the results described in the present treatise.

Contents

Page

INTRODUCTION 1

Origins of light — nature of light, 1 ; its properties, reflexion, refraction, dispersion, 2 ; definitions, 3 ; index of refraction, 4 ; the laws of reflexion and refraction, — the chromatic dispersion, 5 ; Fraunhofer's fixed lines of the solar spectrum, 6 ; experimental method of procuring a pure spectrum, 7 ; the velocity of light within transparent bodies, 9 ; Huygens proposed the undulatory theory of light, 10 ; comparison with sound, periodicity, and interference, 11 ; results of interference, 12 ; why a chemical theory must supersede the undulatory theory 13

Chapter I. On Double Refraction 14

Ordinary and extraordinary refraction, — bodies which possess these, — crystals which refract in different ways, 14 ; calc-spar, a uniaxal crystal, its properties, — how shown, 16; its ordinary and extraordinary refraction according to Huygens, 17 ; how two plane waves would traverse a crystal, 18 ; the two rays from a first crystal fall upon a second, 19 ; introduction of the term 'polarization ' into theories of light, 20 ; distinction in uniaxal crystals, quartz, 21 ; biaxal crystals, Fresnel's wave surface, 22 ; its form near the optic axes, — arragonite, 23 ; method of experiment with it, 24 ; results, true form of the luminiferous surface in biaxal crystals, 25 ; a feeble double refraction communicated to glass and other substances, 26 ; table of uniaxal and biaxal crystals 26

Chapter II. On The Polarization Of Light , 27

How exhibited by double refracting crystals, 27 ; Malus' law for the brightness of double refracted beams, 29; double image rhomb,

VI CONTENTS.

Page

NicoPs rhomb, how constructed, 30 ; Malus' discovery of polarization by reflexion, Brewster's law for the polarizing angle, 31 ; the polarization of refracted light in glass, of piles of plates of glass, 32 ; a simple form of polariscope, 33 ; the tourmaline, it transmits light polarized in one plane, 34 ; Dr. Herapath's artificial tourmalines, 35 ; compound beams of polarized light, 35 ; circularly polarized light, 36 ; how produced, Fresnel's rhomb, 37 ; right-handed and left-handed circularly polarized light, elliptically polarized light, 38; M. Jamin's results, the polarization of the two rays by biaxal crystals, M. Biot's laws, 39 ; how examined in arragonite, 40 ; conical refraction, polarization at the edge of the eyelet-hole, 42; unannealed glass, glass suddenly heated or cooled, or placed under the action of electro-magnets, &c., 43 ; polarization of the sky, the colour pencils of M. Haidinger, how observed 44

Chapter III. On The Interference Of Light 45

Newton's theory of fits of easy reflexion and transmission inadequate, 45 ; phenomena of interference may be classed under three heads, 46 ; how to obtain a luminous point, 47 ; M. Fresnel's experiment with two mirrors slightly inclined, it is the fundamental experiment of interferences, the results described, 48 ; M. Fresnel's use of an eye-lens to observe, 49 ; precautions in arranging the mirrors, 50 ; obtuse-angled prism for a like experiment, 51 ; mode of measuring the luminiferous interval 52

ON THE DIFFRACTION OF LIGHT 53

Dr. Young's simple experiment, 53; interference near the shadows of narrow bodies, 54 ; explanations of the cause of diffraction, 55 ; the light inflected and deflected from the edge and back of a razor, 56; the shadow of an angular opaque body, 57; interference of light through small apertures, 58; an angular aperture, a small round hole in a plate, 59 ; two or more apertures near together, 60 ; Lord Brougham's experiments, Mr. Barton's iris ornaments, colours of mother-of-pearl, colours seen through feathers, 61 ; M. Fraunhofer's interference experiments with a telescope, 61 ; effects of limiting the aperture of the object-glass, by a straight edge, 62; by two edges, a triangular aperture, a narrow slit, 63 ; square apertures, 64 ; wire-gauze before the object-glass, many small apertures in regular arrangement, Fraunhofer's grating 65

ON THE INTERFERENCE COLOURS OF THIN PLATES 66

Cases of thin films, soap-bubble, plates of glass pressed together, 66 ; how interference arises, 67 ; character of the interference, 68 ; New-

CONTENTS. Vll

Page

ton's rings, his measures of them, 69 ; table of the values of the luminiferous interval, 70; the reflected and transmitted rings are complementary, M. Arago's experiment, 71 ; the central black spot, 71 ; fundamental experiment for intensities, 72 ; the failure of the undulatory theory, 73 ; shown by experiments, the intensity or brightness of light, how expressed, 74 ; experiment for intensities, 75 ; Newton's rings formed between glass, diamond, metals, &c., 76 ; Newton's rings with water between lenses, velocity of light in water 77

ON INTERFERENCE NEAR A CAUSTIC 78

Caustics by reflexion and refraction, 79; interference near the caustic formed by a concave mirror, how observed, 80; the rainbows are interference phenomena near a caustic, 81 ; Newton's explanation, Dr. Young showed the supernumerary rainbows to be caused by interference, computations of the radii of the bows, 83 ; the undulatory theory fails to explain them, 84 ; the artificial iris seen in a drop of water, how to try the experiment, 85 ; the first to the tenth iris formed by a cylinder of glass, 87 ; darkness at the caustic .... 87

ON THE INTERFERENCE OF POLARIZED LIGHT 88

M. Arago discovers the interference from thin plates of crystals, the laws of the interference of polarized light of MM. Arago and Fresnel, 88 ; how to try the experiment, 89 ; selenite plates and wedges, 90 ; selenite designs, unannealed glass, gelatinous bodies unequally dried, &c., 91 ; extemporary experiment by heating to redness and then chilling a piece of glass, macled crystals, 92 ; plates of uniaxal crystals cut perpendicular to the axis, how used in experiments, 93 ; how the interference arises, 94 ; phenomena exhibited by them, 95 ; when circularly polarized light is used, 96 ; quartz a peculiar uniaxal crystal, 96 ; M. Biot's theory of rotatory polarization, M. Fresnel's theory, Mr. Airy's extension of it, phenomena shown by quartz near the optic axis, 97; experiments described, M. Jamin employs the compensator, the spirals shown by quartz when the light is circularly polarized or analyzed, 98; how to prepare a plate of quartz for experiment, right-handed and left-handed crystals, liquids which have properties like quartz near the axis, 99 ; experiments with these liquids, the compensator described, 100; description of M. Duboscq Soleil's large polariscope, 101-2; interference by biaxal crystals, how to prepare a plate of nitre, 103 ; figures exhibited by it, figure when the axes are much separated, 104 ; the light circularly polarized or analyzed, 105; the polarizing microscope, how constructed, its uses 106

ON INTERFERENCE WITH LARGE RETARDATION 106

The arrangement in MM. Fizeau and Foucault's experiments 107

Vlll CONTENTS.

CHAPTER IV. Page

ON PHOSPHORESCENCE AND PHOTOMETRY 108

Definition of phosphorescence, bodies which shine in the dark after exposure to the light of the sun, observations upon the subject, 108 ; epipolic dispersion, Brewster's observation with tincture of chlorophyle, internal dispersion, Stokes's experiments, the chemical rays of the solar spectrum rendered luminous, method of experiments, 109; dichroism, 110; photometry, instruments for it, 111; the author's improved photometer, 112; method of experiments, 113; table of the reflective powers of crown, plate and flint-glass, 114 ; reflective powers of polished speculum metal and steel, 115; the connexion of the specific heats of bodies with their reflective powers, 115; photometry by comparison with the reflexion of glass, the light reflected by diamond, mica, Iceland spar, rock-crystal, amethyst, emerald, and glass of antimony, 116; description of an improved comparative photometer, 117 ; its applications 118

ERRATA.

Page 37, line 22, for latter read former. „ „ 23, „ former „ latter.

THE SCIENCE

or

THE NATURAL PROPERTIES OF LIGHT.

Introduction

WHEN we first endeavour to form an opinion as to what light is, we recur to the opposite, darkness, or privation of light, and see that light must arise from some luminous origin or shining surface, either directly or indirectly. But considering light to originate in some self-luminous surface, we recollect that there are many which give out light; such as names of different kinds, incandescent substances, as burning charcoal, metals, and earths at high temperatures, phosphorescent substances at low temperatures, the glow-worm and many insects from animal life, the electric light, &c., besides the heavenly bodies whose existence is only known to us by the light they give out. With such variety of origins we might well despair of forming any conclusive opinion upon the nature of light ; as we ascend however from the more evident properties which it presents, to others which are less so, and from these again to others which are more and more intimately connected with its essential constitution, we arrive at the means of judging of its nature, in a far higher degree than can be appreciated by those who have not followed that course of examination. We are thus led to form hypotheses of the nature of light in order to explain the

B

Z PHYSICAL OPTICS.

phenomena it presents; these hypotheses ought not to be accepted, however, longer than they suffice to that end.

We call a shining surface self-luminous when the light originates there; but the light from it falling on the surfaces of bodies renders them visible also ; visibility meaning the property of being perceived by the eye. In this manner opaque bodies acquire a property similar to luminous origins, and it is thus that the planets shining by the light they receive from the sun, are only distinguished from the fixed stars by their motion in the heavens, or by their exhibiting determinate discs when seen in telescopes. Here we meet with the property of the reflexion of light. It is sometimes regular, as when the light falls on a polished surface, like that of water or mercury, the facets of many crystals, polished mirrors, &c. ; but in others and the more common cases it is irregular, as when it falls on the rough surfaces of bodies. These latter are visible by the eye in a great variety of positions, by means of this irregularly reflected or dispersed light coming from them ; the former only when the eye is so situated as to receive the regularly reflected light, supposing them to furnish no dispersed light, which, however, is never absolutely the case.

When light has been reflected, it has generally received new properties, and in some cases it is entirely polarized; on the other hand, if polarized before reflexion at a surface, the dispersed light is found to have lost its property of polarization, and to have become depolarized by reflexion.

The law of the reflexion of light at polished surfaces is so simple, that it has been known from ancient times. When an elastic ball is thrown against a hard surface, it rebounds from the surface at an an- ""\n gle nearly equal to that with which it impinged ; the perpendicular drawn to

the surface at the point of impinging, the original direction of the ball and its direction after rebounding lying all in the same plane. If the ball were perfectly elastic, the angles would be

REFRACTION OF LIGHT.

exactly equal. In the figure, let SA be the direction of motion of the ball before striking the hard plane at A, and let AR be the direction in which it rebounds, draw also AN a perpendicular to the hard surface at A. Then the angles SAN and NAR are in the same plane, and the angle SAN equals the angle NAR. It is found that the same law holds with respect to the reflexion of light.

Definition 1. A ray of light is the smallest portion of a beam of light which we can imagine to exist separately, and it is represented by a straight line SA, which is its direction whilst in the same medium. In the same way the line AR represents the

Fig. 2.

reflected ray corresponding to the ray SA, which is called the incident ray.

When CAB (fig. 2) is the surface of a transparent medium such as water, a portion of the light enters the medium and is turned out of the original course SAS' towards the perpendicular line NAN' ; this breaking of its course into a new direction AT, is called the refraction of light. The line AT represents the refracted ray.

Def. 2. The angle SAN is called the angle of incidence.

Def. 3. „ NAR „ angle of reflexion.

Def. 4. „ TAN' „ angle of refraction.

That a ray of light is refracted on passing from one medium to another of a different density, is shown by an easy experiment. Attach a coin with wax to the bottom of a cup as at a in fig. 3, place the eye at such a position e that the coin is hidden by the edge of the cup ; if now an assistant pours water into the cup to some height c dj the coin will appear over the edge as at «', and the visual rays must have followed the broken course abe to reach the eye ; the refraction at b on

B 2

PHYSICAL OPTICS.

Fig. 4.

passing from water into air being from the perpendicular to the surface. It is found that the course of a ray would be the same whichever way it passed, that is, a ray would pass from e to a along the path eba.

It was only in late times that the law of the refraction of light was discovered by Snellius"*, as follows.

In figure 4, SA, AR, AT representing the incident, the reflected and the refracted rays respectively as in fig. 2, measure off a distance A« on the incident ray SA, and an equal distance Kb on the refracted ray AT ; draw perpendiculars am, bn on the perpendicular line to the surface NAN' ; then the ratio which ma bears to bn is the same whether the angles SAN, TAN' be great or small ; or otherwise the

fraction -j— is constantly of

the same value for all angles of incidence and refraction. This, with the condition that the angles SAN and TAN' are in the same plane, is called the law of the sines when we use trigonometry, or the law of Snellius. If we put the Greek letter //, for

the constant value of the above ratio, we have -, - equal to p,

bn

which indicating by its value the degree of refraction, we call it the index of refraction.

Now as the refracting medium becomes more dense, the value

of fji or -7— becomes greater. It is about ^- when light passes

3 from air into water, about ~ when it passes from air into glass,

and about ^ when it passes from air into diamond. Inflammable substances, however, refract more in proportion to their density

Huygens' ' Opera Reliqua,' vol. ii. page 2.

COLOURS IN LIGHT.

than others, which led Newton to believe what has since been proved, that the diamond was inflammable.

The law of the reflexion of light is thus enunciated. The incident ray, the reflected ray, and the perpendicular to the reflecting surface at the point of incidence, lie all in the same plane ; and the angle of reflexion equals the angle of incidence.

The law of the refraction of light is thus stated. The incident ray, the refracted ray, and the perpendicular to the refracting surface at the point of incidence, lie all in the same plane ; and

Cma\ —j-\ to

the sine of the angle of refraction.

Sir Isaac Newton's great optical discovery was this, — that white light consists of all the colours of the solar spectrum ; and that they are only separated from the other colours when we see them, and are not white light (considered simple light) which has been changed to coloured light by some means. He found that the differently coloured rays are differently refracted*, red being the least, violet the most refracted, and the refraction increasing from the red rays, through orange, yellow, green, blue, indigo to the violet rays. From this property, a ray of white light which is made up of all shades of colour is spread into a fanlike form when it enters a refracting medium oblique-

Fig. 5.

ly. In figure 5 this is

shown by taking SAS' for

the original direction of

the ray, and the angle S'Ar

the deviation for the red,

the angle S'Av that for the

violet ray. This constitutes the chromatic or coloured dispersion

of light.

When we say that white light consists of all shades passing through red, orange, yellow, green, blue, indigo to violet, it is

* Newton's ' Opticks,' Prop. I. Theor. I. — " Lights which differ in colour, differ also in degrees of refrangibility."

not meant to say that the solar spectrum shows a continuous shading of tints through these colours. About the year 1814, M. Fraunhofer, using the fine prisms of the manufactory at Munich, with which he was connected, discovered that the pure solar spectrum contains numerous black lines across it which are the places of deficient tints. The figure below, copied of one-fourth the size of M. Fraunhofer's* engraving, will serve to show the places of some of these fixed lines of the solar spectrum of Fraunhofer.

Red. Orange.Yell. Green.

Blue.

Indigo.

Violet.

A triangular chandelier drop, which can be purchased at a small price at many glass shops, will serve for an optical prism for common use, to form a solar spectrum, by allowing the sun's light to shine through it upon a distant sheet of white paper ; or to look through when we want to analyse lights, colours, and dyes ; but to see Fraunhofer*s fixed lines we must have a good prism. When the prisms of pure glass, with flat and accurately polished sides, are not at hand, a hollow prism formed with pieces of well and flatly polished plate glass, cemented together with japanners' gold size (which can be purchased at the artists' colour shops), and filled with water or alcohol, may be well employed. The prism need not be more than a cubic inch in bulk, and should be used in Fraunhofer' s manner, by placing it on a support attached on the object end of a small telescope.

In fig. 6, E being the eye end, and o the object end of a small telescope, let ABC be a support of wood, which will slide on the end o, and abc the prism, attached with wax or otherwise to the support ; a line of light, as de, is to be looked at through the telescope and prism, when the chromatic spectrum will be seen in the field of view.

THE SOLAR SPECTHUM.

The precautions requiring to be attended to, in order to have the spectrum pure, and the fixed lines distinct, are these : first,

Fig. 6.

the line of light de must be narrow, such as light thrown through a slit between two knife-edges which are set parallel, and j^th to Tty oth of an inch apart, and it must be parallel to the refracting edge of the prism ; secondly, the prism must be set so that the light makes the same angle with the first surface of the prism, when it falls upon it, as it does with the second surface when it leaves it, or in figure 7 the angle of incidence at A must equal the angle of emergence at B. The angle of deviation CaD is about half the angle Fig. 7.

of the prism for glass, and about one-third of it for water, when the angle of the

prism is not large. When ^

sunlight is examined, it will

be necessary to have a mir- ,s''

ror to throw the light into a &''

darkened room through an opening in a window-shutter, and

the telescope should be as distant as possible, being set to the

focus to show the line of light distinctly, before the prism is set

in its place j and after that is done, the telescope and prism

must be turned round to the requisite angle of deviation, so that

the beam on emergence from the prism may pass up the tube of

the telescope. When artificial lights are examined they must be

placed behind the narrow slit, and the fixed lines will be found

PHYSICAL OPTICS.

to differ very greatly from those in sunlight, and from each other. The double line D, where light is wanting in sunlight, is the brightest part in oil-flames, and it is the entire light when a spirit-lamp (alcohol) has a little common salt put on the wick. This last-named lamp is the one used in delicate optical experiments where it is necessary to have a homogeneous light, or light of one tint only.

When we come to consider how the laws of reflexion and refraction of light may arise physically, it is convenient to consider the motion of a ray as made up of two motions, one parallel, and the other perpendicular to the surface on which the light is incident.

When a body moves with a certain velocity in a direction AC (fig. 8), if we take the length AC to represent the velocity, then it is shown in mechanical treatises that F- g

the same velocity would have arisen if two velocities represented by AN and AM, the sides of the parallelogram of which AC is the diagonal, had been

simultaneously given to the body. Then

the two velocities are said to be compounded into one. The reciprocal of this is also true, that a velocity in any direction may be considered decomposed into two others represented by the sides of a parallelogram, of which the diagonal represents the given velocity. The sides of the parallelogram may be at right angles, or at any other angle to each other.

Applying this parallelogram of velocities to rays of light, we see that the motion of the ray parallel to the reflecting surface is not changed in reflexion, but that the motion perpendicular to the surface is reversed, the ray being throw a back perpendicularly with the velocity with which it was perpendicularly incident, that is, supposing the reflected ray to move with the velocity of the incident ray.

For measuring off the distances Ac, A.d, and Ab (fig. 9) equal to each other, then describe parallelograms with these lines for diagonals, and with their sides parallel and perpendicular to the surface BAC, we shall have the parallel velocities am and md equal, and the perpendicular velocity mA of the incident ray

VELOCITY OF LIGHT.

Fig. 9.

equal, but opposite to the perpendicular velocity Am of the reflected ray.

If we suppose the parallel velocity in the refracted ray to be unchanged as it is in the reflected ray, we must find a point b' in AT, such that b'n1 equals am or md} and then the perpendicular velocity An' must be greater than Am, and the whole velocity represented by Ab1 must be increased also. Now this would imply an attraction perpendicular to the refracting surface, for the refracted ray increasing its velocity, and a repulsion throwing back the reflected ray, but leaving its velocity in its own direction, the same as in the incident ray.

Newton and other philosophers have supposed light to move quicker* in dense media than in a vacuum from a perpendicular attractive force. Huygens had, however, previously supposed the velocity to be slower f in dense media. Some of Newton's experiments enabled Dr. Young J to show that light really moves slower in dense refracting media according to Huy gens' s view ; and this has been confirmed by very different experiments made by M. Fresnel§ and the author ||. Huygens's supposition was this, that the velocity of light in a vacuum was to the velocity in the refracting medium as the line am to the line bn (fig. 4) ; and also in fig. 9 if we take Ab equal to Aa. Then the velocities

have the ratio ^, which is the refractive index //,, and constant. on

Take in fig. 9 a point b11, such that the ratio -^ equals p, the refracted light will have traversed the space Ab", whilst the

* Newton's ' Opticks/ pp. 69 and 245.

t Huygens's 'Traite de la Lumiere,' p. 34.

£ Philosophical Transactions for 1802.

§ Annales de Chimie et de Physique for 1815, vol. i. p. 239.

|| Philosophical Magazine for 1833, vol. iii. p. 333.

reflected light has passed over the space Ad. From this foundation Huygens showed that the law of the sines must arise as a natural consequence, provided light arises from waves in an aethereal medium, in the same manner as sound arises from waves in the air ; and that a wave may be considered as formed by a series of small waves, into which the original light was broken in falling upon the refracting surface. This was the first proposal of the undulatory theory of light. DesCartes had previously proposed a vibratory theory, but had not advanced to an undulatory theory. Dr. Hooke, in his ( Micrographia/ not only adopts an undulatory theory, but first advances the doctrine of interference in light. In order that these vibrations and undulations or waves may exist, it is required that there should be an elastic medium suitable for their transmission ; and it has been generally called the luminiferous aether. It is supposed to pervade all space, and to be either of different density or of different elasticity within dense bodies to what it is without them, so as to travel through them with diminished velocity.

A similar supposition of the original wave being broken into small waves at the surface of the dense medium, enabled Huygens to explain the reflexion of light, on the undulatory theory.

We shall find further on, that this un- -p- JQ

dulatory theory of light cannot be the true theory, yet it has led to the discovery of some of the most important properties of light ; and the student should understand its nature and results. Suppose a stone thrown into still water at a place such as the center of the fig. 10, there will arise a series of circular waves around this point, the water rising and falling successively at the center and other points of the surface ; and the waves spread in circles outwards, but become less and less deep as they are further from the center. Each point on the surface of the water has thus a vibratory motion ascending and descending, and so gives rise to an undulatory or wave motion upon the surface. The waves diverging from the center, spread at right angles to the nearly upward and downward motion of the vibrations. These latter are from this called transversal vibrations.

UNDULATORY THEORY. 11

In the undulatory theory of light, the direction in which a wave within the hypothetical aether comes to any point is direct from the center or luminous origin, and corresponds to what is termed a ray of light ; therefore in general, though not always, the ray direction is the perpendicular to the wave.