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PHOTOMETRY (from Gr. (Pews, xarrbs, l...

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Originally appearing in Volume V21, Page 530 of the 1911 Encyclopedia Britannica.
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PHOTOMETRY (from Gr. (Pews, xarrbs, light, µerpov, a measure), the art and science of comparing the intensities or illuminating powers of two or more sources of light. As in all scientific measurements, its methods are attempts to give quantitative accuracy to the crude comparisons made by the eye itself. The necessity for this accuracy in practical affairs of life has arisen because of the great development of artificial lighting in recent times. The eye soon learns to associate with any particular source of light a quality of brightness or power of illumination which diminishes with increase of distance of the source from the eye or from the surface illuminated. This quality depends upon an intrinsic property of the source of light itself, generally known as its " candle power." The aim of photometry is to measure this candle power; and whatever be the experimental means adopted the eye must in all cases be the final judge. In the photometric comparison of artificial lights, which frequently vary both in size and colour, direct observation of the sources themselves does not yield satisfactory results. It is found to be much better to compare the illuminations produced on dead white surfaces from which no regular reflection takes place, or through colourless translucent material uniformly illuminated by the light placed on the further side. By such processes there is always loss of light, and we must be certain that the various coloured constituents of the light are reduced in the same proportion. This necessary condition is practically satisfied by the use of white diffusing screens. Two principles of radiation underlie many photometric applications, namely, the inverse square distance law, and J. H. Lambert's " cosine law." Both can be established /averse on theoretical grounds, certain conditions being Square fulfilled. But as these conditions are never abso- Distance lutely satisfied, the applicability of the two laws Law. must in the end be tested by experiment. Since we find that within the errors of observation four candles, placed together at a distance of 2 ft. from a diffusing screen, produce the same illumination as one candle at a distance of 1 ft., we may regard the inverse square distance law as satisfied. Thus if two lights of intensities A and B produce equal illuminations on a screen when their distances from the screen are respectively a and b, we at once write down the relation between the two intensities in the form A : B=a2 : b2. The theoretical basis of the law follows at once from the universally accepted view that light is energy radiating outwards in all directions from the source. If we assume that there is no loss of energy in the transmitting medium, then the whole amount of radiant energy passing in one second across any closed surface completely surrounding the source of light 'must be the same whatever the size or form of the surface. Imagine for simplicity a point source of light, or its equivalent, a uniformly radiating spherical surface with the point at its centre, and draw round this point a spherical surface of unit radius. Across this surface there will pass a definite amount of radiant energy, in other words a definite total luminous flux, E, which will be the same for all concentric spherical surfaces. Since the area of a spherical surface of radius r is 41r r2, the flux which crosses unit area is E/4 7r r2. This quantity is the " illumination." It is measured in terms of the unit called. the lux, which is defined as the illumination produced by a light of unit intensity on a perfectly white surface at a distance of 1 ft. In the great majority of photometers the illuminations are compared, and the intensities are deduced by applying the law of the squared distances. Lambert's cosine law has to do with the way in which a luminous surface sends off its radiations in various directions. It is a matter of common observation that the disk of the sun appears equally bright all over the surface. Careful measurements show that this is not strictly true; but it is sufficiently near the truth to suggest that under certain definable conditions the law 1 would hold accurately. Again, when a glowing surface is viewed through a small hole in an opaque plate, the brightness is very approximately independent of the angular position of the incandescent surface. This is the same phenomenon as the first mentioned, and shows that the more oblique, and therefore larger, element of surface sends the same amount of radiation through the hole. Hence the amount per unit surface sent off Lambert's Cosine Law. at a given angle with the normal must be less than that sent off in the direction of the normal in the inverse ratio of the areas of the corresponding normal and oblique elements; that is, as the cosine of the given angle to unity. For most practical purposes, and so long as the obliquity is not great, Lambert's law may be assumed to hold. In almost all accurate methods of photometry the aim is to bring the illuminating powers of the two sources to equality. This may be effected by altering the distance of either light from the illuminated surface. Or we may use polarized light and diminish the intensity of the stronger beam by suitable rotation of a Nicol prism, a method particularly useful in spectrophotometers. The same result may also be effected by inter-posing absorbent disks, the precise absorbing powers of which must, however, be known with great accuracy. Another useful method is that first described by H. Fox Talbot in 1834, and used with effect by Professor William Swan (1849), and more recently by Sir W. de W. Abney. Talbot's law is thus enunciated by H. von Helmholtz: " When any part of the retina is excited by regularly periodic intermittent light, and when the period is sufficiently short, the resulting impression will be continuous, and will be the same as that which would be produced if the whole light were distributed uniformly throughout the whole period." Talbot deduced the principle from the well-known experiment in which a continuous luminous line is produced by rapid rotation of a luminous point. If the principle be granted, it is obvious that any mechanism by which a ray of light is obstructed in a regularly rhythmic manner during definite intervals t', separated by intervals t, during which the light is allowed to pass, will have the effect of reducing the apparent brightness of the ray in the ratio t/(t + t'). This is frequently accomplished by placing in the ray a rotating disk perforated by radial sectors, the so-called Talbot disk. If photometric results are to be of general value it is essential to have a unit in which to express all other intensities. For example, electric lights are classified according to Standards of Light. their " candle-power." The candle, in terms of whose brightness the brightness of other sources of light is to be expressed, must, of course, fulfil the conditions demanded of all standards. It must give under definite and easily realizable conditions a definite and constant luminous effect, and it must be easily reproducible. The earlier attempts to get a candle of constant brightness were not very satisfactory. The British standard is a sperm candle which weighs Ib, and loses in burning 120 grains per hour. It is found that these conditions are not sufficient to determine the luminous power of the candle, since the length and shape of the wick, the height of the flame, and the composition, temperature and humidity of the atmosphere all have an effect upon its brightness. The same is true of other similar sources of light—for example, the German standard candle, which is made of paraffin, has a diameter of 2 cm., and has its wick cut until the flame is 5 cm. high, but which with all precautions suffers continual altera- tions in brightness. For ordinary practical purposes, however, these candles are steady enough. Other kinds of flame have also been used as a standard source of light. The oldest of these is the French Carcel lamp, which is provided with a cylindrical Argand burner, and gives the standard brightness. Vernon- when 42 grammes of colza oil are consumed per hour. Harcourt The supply and draught are regulated by clockwork. Pentane A. G. Vernon-Harcourt's pentane standard, in which standard. a mixture of gaseous pentane and air is burnt so as to maintain a flame 2'5 in. high at ordinary barometric pressure, gives good results, and is readily adjustable to suit varied con- ditions. Several forms of this standard have been constructed, one of the most important being the ro candle-power pentane lamp, in which air saturated with pentane vapour is burnt in a specially-designed burner resembling an Argand burner. For photometric purposes a definite length of the lower part of the flame is used, the upper part being hidden within an opaque tube. The amyl-acetate lamp designed by H. von Hefner-Alteneck has been elaborately studied by the German authorities, and at present is probably more used than any other flame for photometry. It is of simple construction, and gives the standard brightness when it burns with a flame 4 cms. in height in still air of humidity o.88% and free of carbon dioxide. The presence of carbon dioxide and increase in the humidity have a marked effect in diminishing the brilliancy of the flame. If the vapour pressure is e and the barometric pressure p, the strength of the flame, when all other conditions are fulfilled, is given by the formula r'049 — 5' 5c/(p — e) One disadvantage for photometric purposes is the reddish colour of the flame as compared with the whiter artificial lights in general use. For an interesting account of the various experimental investigations into the properties of the Hefner flame see E. L. Nichols, Standards of Light," Transactions of the International Electrical Congress, vol. ii. (St Louis, 1904).1904). Angstrom's determination of the radiation of the flame in absolute energy units is also of special interest. Attempts have been made, but hitherto with limited success, to construct a convenient standard with acetylene flame. Could a satisfactory burner be devised, so that a steady brilliancy could be easily maintained, acetylene would, because of its intense white light, soon displace all other flames as standards. J. Violle has proposed to use as standard the light emitted by a square centimetre of surface of platinum at its melting point, but there are obvious practical difficulties in the way of realizing this suggested standard. J. E. Mlle's Petavel, who carefully examined the necessary condi- Platinum tions for producing it (Prot. Roy. Soc. 1899), finds Standard. that the platinum must be chemically pure, that the crucible must be made of pure lime, that the fusion must be by means of the oxy-hydrogen blow-pipe, that the gases must be thoroughly mixed in the proportion of 4 volumes of hydrogen to 3 of oxygen, and that the hydrogen must contain no hydro-carbons. Under these cohditions the variation in the light emitted by the molten platinum would probably not exceed 1%. O. Lummer and F. Kurlbaum have proposed as a standard a strip of platinum foil 25 mm. wide and •015 mm. thick brought to incandescence by an electric current of about 8o amperes. The temperature is gradually increased until 1lo-th of the total radiation is transmitted through a water trough 2 cm. in width. This ratio is determined by means of a bolometer, and so long as it is adjusted to - th the light is practically constant. For comparative photometric work the incandescent. electric light is very convenient, having the one great advantage over candles and flames that it is not affected by atmospheric changes. But it does not satisfy the requirements of a primary standard. It ages with use, and when run at constant voltage gradually loses in brilliancy, partly because of changes in the filament itself, partly because of the deposit of carbon on the interior of the bulb. Professor J. A. Fleming has shown that very good results can be obtained if carbon filaments carefully selected Fleming's and run in ordinary bulbs for a definite time at a Incandeslittle above their normal voltage are remounted centLamp in large clear glass bulbs 6 or 8 in. in diameter. Standard. If used sparingly, and never above their marked voltage, these large incandescent bulbs have been found to remain constant for years, and therefore to be eminently suitable as secondary standards. In his Handbook for the Electrical Laboratory and Testing Room (vol. ii.) Fleming concludes that the best primary standards are the Violle incandescent platinum and the Vernon-Harcourt pentane one-candle flame; and that the most convenient practical standards are the Hefner lamp, the ten-candle pentane lamp, and the Fleming large bulb incandescent electric lamp. Comparisons of the intensities of these various standards do not give quite concordant results. Thus three different authorities have estimated the 10-candle pentane lamp as being equal to 10.75, 11.0, 11.4 Hefner lamps. A specially constructed instrument or piece of apparatus for comparing light intensities or illuminations is called a Talbot's Law. Hefner Lamp. photometer. The earlier forms of photometers were very simple and not capable of giving very precise results. The principles of Photo construction are, however, the same in all the recog- meters. nized forms down to the most elaborate of recent inventions. Two of the earliest forms were described by P. Bouguer and W. Ritchie. The Ritchie wedge constitutes the basis of many varieties of type. The two lights to be Rltchte's compared illuminate the sides of the wedge, which wedge,. is placed between them, so that the eye set in front of the wedge sees the two sides illuminated each by one of the lights. The edge should be as sharp as possible so that the two illuminated surfaces are in close contact. The illuminations are made equal either by shifting the wedge along the line joining the lights or by moving one of the lights nearer to or farther from the wedge as may be required. The lights given out by the sources are then as the squares of the distances from Rumford's the matched parts of the surfaces. Count Rumford Photo-* suggested the comparison of the intensity of the meter. shadows of the same object thrown side by side on a screen by the two lights to be compared. In this case the shadow due to one source is lit up by the other alone; and here again the amounts of light given out by the sources are as the squares of their distances from the screen when the shadows are equally intense. The shadow-casting object should be near the screen, so as to avoid penumbra as much as possible; yet not too near, so that the shadows may not overlap. R. Bunsen suggested the very simple expedient of making a grease-spot on white paper for photometric purposes. When Bunsen's the paper is equally illuminated from both sides Photo- the grease-spot cannot be seen except by very meter. close inspection. In using this photometer, the sources are placed in one line with the grease-spot, which lies between them and can be moved towards one or other. To make the most accurate determinations with this arrangement the adjustment should first be made from the side on which one source lies, then the screen turned round and the adjustment made from the side of the other source—in both cases, therefore, from the same side of the paper screen. Take the mean of these positions (which are usually very close together), and the amounts of light are as the squares of the distances of the sources from this point. The efficiency of the Bunsen photometer has been improved by using two inclined mirrors so that the eye views both sides of the paper simultaneously. Sir Charles Wheatstone suggested a hollow glass bead, silvered internally, and made to describe very rapidly a closed path, for Wheat- use as a photometer. When it is placed between two stone'sPho- sources we see two parallel curves of reflected light, rometen one due to each source. Make these, by trial, equally bright; and the amounts of light from the sources are, again, as the squares of the distances. William Swan's prism photometer, invented in 1859, is a beautiful application of the principle embodied in Bunsen's grease-spot photo-Swan's meter (see Trans. Roy. Soc. Ed. vol. xxi.). The essential Swan part of the instrument is fundamentally the same as Double pm that described by O. Lummer and E. Brodhun in 1889. It consists of two equal right-angled isosceles glass prisms placed with their diagonal faces together so as to form a cube (fig. I), and cemented together by a small patch of Canada balsam, which spreads out into a circle when the prisms are pressed together. In the figure, which represents a central section of the bi-prism, the Canada balsam is represented by the letter N. The , light from two illuminated surfaces, PQ, RS, is allowed to fall perpendicularly on the faces AB, 0 AD. In each case that part of the light falling internally on the portion of the diagonal face which is not backed with the Canada balsam is totally reflected. On the other hand, the light which falls on the portion backed by the 4 P Canada balsam is almost wholly transmitted. Thus an eye placedin the position qtp receives light from both sources, the surface RS supplying nearly all the light that seems to come from the patch N, and the surface PQ supplying all the light which seems to come from the region immediately surrounding N. The patch N will in general be visible; but it will quite disappear when the luminosity of the ray Tt, which traverses the Canada balsam, is exactly equal to the luminosity of the rays Pp, Qq, which have come after total reflection from the surface PQ. This condition of in-visibility of N is arrived at by adjusting the positions of the sources of light which illuminate the surfaces PQ, RS. The brightnesses of the two sources will then be as the squares of their distances from their respective screens. The essential part of Lummer and Brodhun's photometer is a combination of prisms very similar to Swan's. In its most improved form the bi-prism or " optical cube " has one 4umnd of its component prisms cut in a peculiar manner. Brodmhuern'as The diagonal face is partly cut away, so that the central photometer. part only of this face can be brought into contact with the diagonal face of the other prism. The Canada balsam is dispensed with, the surfaces being pressed closely together so that no layer of air is left between them. In order to make the instrument convenient for use with an optical bench, Lummer and Brodhun make the illuminated surfaces which are to be compared the opposite sides of an opaque screen set in the continuation of the diagonal (CA) of the bi-prism, the rays being brought by reflection from symmetrically situated mirrors so as to enter the sides AB and AD perpendicularly. An important modification, due also to Lummer and Brodhun, is the following: By means of a sand-blast a portion, which may be called r, is removed from one half of the diagonal face of the one prism, and from the other half of the same prism there is removed in like manner all but a part 1 corresponding to the part r. The portions which have not been removed are pressed close to the diagonal face of the other prism, and become the parts through which light is freely transmitted. On the other hand, the light which enters the second prism and falls on the portions of surface backed by the layers of air filling the cut-out parts is totally reflected. The general result is the production of two similar luminous patches 1 and r, each of which is surrounded by a field of the same intensity as the other patch. When the photometric match is made the whole region will be uniformly bright. But, by insertion of strips of glass so as to weaken equally the intensity in the surrounding fields, the match will be obtained when these fields are made of equal intensity and when at the same time the two patches differ equally in intensity from them. Under these conditions the eye is able to judge more certainly as to the equality of intensity of the two patches, and an untrained observer is able to effect a comparison with an accuracy which is impossible with most forms of photometer. J. Joly's diffusion photometer consists of two equal rectangulat parallelepipeds of a translucent substance like paraffin separated by a thin opaque disk. It is set between the sources Joly,s of light to be compared in such a way that each paraffin photometer block is illuminated by one only of the sources, and is adjusted until the two blocks appear to be of the same brightness. The method is made more sensitive by mounting the photometer on an elastic vibrator so as to render it capable of a slight to-and-fro oscillation about a mean position. A form of photometer which is well adapted for measuring the illumination in a region is that due to L. Weber. It consists of a horizontal tube across one end of which is fitted another Weber's tube at right angles. This second tube can be rotated Photometer. into any position perpendicular to the horizontal tube. Where the axes of the two tubes meet is placed in the later forms of the instrument one of Lummer and Brodhun's modified Swan cubes. At the other end of the horizontal tube a standard flame is set illuminating a piece of ground glass which may be moved to any convenient position in the tube. The eye looks along the cross tube, at the farther end of which is placed another piece of ground glass illuminated from the outside. The illuminations of the two pieces of ground glass as viewed through the photometer double prism are brought fo equality, either by shift of the ground glass to or from the standard light, or by means of two Nicol prisms placed in the cross tube. One advantage of the instrument is its portability. The photometry of incandescent electric lamps has led to several special modifications and devices. The candle power varies distinctly in different horizontal directions, !mans and one measurement in any particular direction descent is not sufficient. Sometimes the lamp is rotated Etect'ac about three times a second about a vertical axis and Lamp. an average value thus obtained. But there is always a risk of the filament breaking; and in all cases the effect of centrifugal force must alter the form of the filament and therefore the distances of the different parts from the screen. Accuracy demands either the measurement of the radiation intensity in a number of directions all round the lamp, or one combined R TS measurement of as many rays as can be conveniently combined. One of the best methods of effecting this is by means of Matthews's C. P. Matthews's integrating photometer. By the Integrating use of twelve mirrors arranged in a semicircle whose Photometer.diameter coincides with the axis of the lamp, twelve rays are caught and reflected outward to a second set of twelve mirrors which throw the rays on to the surface of a photometric screen. This combined effect is balanced by the illumination produced by a standard lamp on the other side of the screen (see Trans. Amer. Inst. Elect. Eng., 1902, vol. xix.). So long as the lights to be compared are of the same or nearly the same tint, the photometric match obtained by different Netero- observers is practically the same. If, however, they chromatic are of distinctly different colours, not only do dif-Photometry.ferent observers obtain different results but those obtained by the same observer at different times are not always in agreement. Helmholtz was of opinion that photo-metric comparison of the intensities of different coloured lights possessed no real intrinsic value. There can be little doubt that in a rigorous sense this is true. Nevertheless it is possible under certain conditions to effect a comparison which has some practical value. For example, when the intensities of two differently coloured lights differ considerably there is no difficulty in judging which is the stronger. By making the one light pass through a fairly large range of brightness we may easily assign limits outside which the intensities are undoubtedly different. After some experience these limits get close; and many experimenters find it possible, by taking proper precautions, not only to effect a match, but to effect practically the Abney's same match time after time. According to Abney, expert• whose memoirs on colour photometry (Phil. Trans., ments. 1886, 1892) form a most important contribution to the subject, the observer in making his judgment as to the equality of luminosity of two patches of colour placed side by side must not begin to think about it, but must let the eye act as unconsciously as possible. His method was to compare the coloured patch with white light given by a particular standard and cut down to the proper intensity by use of a Talbot's rotating sector, which could be adjusted by means of a suitable mechanism while it was rotating. At the same time, although the eye may be able to effect a definite matching of two patches of colour of a particular luminosity, it has been long known that a change in the luminosity will destroy the apparent equality. This depends upon a physiological property of the retina discovered by J. E. Purkinje in 1825 (see below, Celestial Photometry). In virtue of this property the blue and violet end of the spectrum is more stimulating to the eye than the red end when the general luminosity is low, whereas at high luminosities the red gains relatively in brightness until it becomes more stimulating than the blue. Unless therefore account is taken in some definite measurable manner of the absolute brightness, there must always be some uncertainty in the photometric comparison of the intensities of differently coloured sources of light. Instead, however, of trying to effect a photometric match in any of the ways which have been found sufficient when the sources are of the same or nearly the same tint, we may effect important practical comparisons in what is called heterochromatic photometry by an appeal to other physiological properties of the eye. For example, the power of clearly discriminating patterns in differently coloured lights of various intensities is obviously of great practical importance; and this power of detailed discrimination may be made the basis of a method of photometry. According to this method two lights Discrimina- are arranged so as to illuminate two exactly similar 'Ion Photo-patterns of lines drawn, for example, on the sides meter. of a Ritchie wedge, and their distances are adjusted until the patterns are seen equally distinct on the two sides. Application of the usual distance law will then give the relation between the two lights. A discrimination photometer constructed on this principle has been designed by J. A. Fleming. Its results do not agree with the indications of an ordinaryluminosity photometer; for it is found that the eye can discriminate detail better with yellow than with blue light of the same apparent luminous intensity. Another and very promising method of photometry depends upon the duration of luminous impressions on the retina. J. A. F. Plateau observed in 1829 that the blending into Flicker a homogeneous impression of a pattern of alternatePhotometry, sectors of black and some other colour marked on a disk when that disk was rotated occurred for rates of rotation which depended on the colour used. A form of experiment suggested in Professor O. N. Rood's Modern Chromatics seems to have been first carried out by E. L. Nichols (Amer. Journ. of Science, 1881). A black disk with four narrow open sectors was rotated in front of the slit of a spectroscope. When the rotation was not too quick the yellow part of the spectrum appeared as a succession of flashes of light separated by intervals of darkness of appreciable length, whereas towards both the red and violet ends no apparent interruption in the steady luminosity could be observed. As the rate of rotation increased the part of the spectrum in which flickering appeared contracted to a smaller length extending on each side of the yellow, and finally with sufficiently rapid alternation the yellow itself became steady. This seems to show that the retinal image persists for a shorter time with yellow light than with light of any other colour; for with it the intervals of darkness must be shorter before a continuous impression can be obtained. Now yellow is the most luminous part of the spectrum as it affects the normal human eye; and E. S. Ferry (Amer. Journ. of Science,1892) has shown that the duration of luminous impression is mostly, if not entirely, determined by the luminosity of the ray. Hence the determination of the minimum rate of intermittence at which a particular colour of light becomes continuous may be regarded as a measure of the luminosity, the slower rate corresponding to the lower luminosity. Although in the experiment just described the red part of the ordinary solar spectrum becomes continuous for a slower rate of intermittence than the yellow part, yet we have simply to make a red ray as luminous as the yellow ray to find that they become continuous for the same rate of intermittence. It is, however, highly improbable that the duration of impression depends only on the luminosity of the light and not to some extent upon the wave-length. There are indeed phenomena which require for their explanation the assumption that the duration of luminous impression does depend on the colour as well as on the brightness. Nevertheless the luminosity is by far the more important factor, as shown by Ogden N. Rood's experiments. He found (Amer. Journ. of Science, 1893) that, when a disk whose halves , Ex. differ in tint but not in luminosity is rotated rather Roods periments. s slowly, the eye of the observer sees no flickering such as is at once apparent when the halves differ slightly in luminosity. Rood himself suggested various forms of photo-meter based on this principle. In his latest form (Amer. Journ. of Science, Sept. 1899) the differently coloured beams of light which are to be compared photometrically are made to illuminate the two surfaces of a Ritchie wedge set facing the eye. Between the wedge and the eye is placed a cylindrical concave lens, which can be set in oscillation by means of a motor in such a way that first the one illuminated surface of the wedge and then the other is presented to the eye in sufficiently rapid alternation. The one source of light is kept fixed, while the other is moved about until the sensation of flicker disappears. From work with this form of instrument Rood concluded that " the accuracy attainable with the flicker photometer, as at present constructed, and using light of different colours almost spectral in hue, is about the same as with ordinary photometers using plain white light, or light of exactly the same colour. Various modifications of Rood's forms have been constructed from time to time by different experimenters. Thesimmanee Simmance and Abady flicker photometer is an ingeniousandAbady's and yet mechanically simple method by which (as it photometer. were) the wedge itself is made to oscillate so as to throw on the eye in rapid succession, first the one side and then the other. The rim of a wheel of white material is bevelled in a peculiar manner. The sharp edge, which passes slightly obliquely across the rim from One side of the wheel to the other and back again, is the meeting of two exactly similar conical surfaces facing different ways and having their axes parallel to, but on opposite sides of, the axis of rotation of the wheel. As the wheel rotates with its rim facing the eye, the intersection of the two surfaces crosses and recrosses the line of vision during each revolution. Hence first the one illuminated side and then the other are presented to the eye in rapid alternation. The inventors of this instrument claim that their instrument can gauge accurately and easily the relative intensities of two lights, whether of the same or of different colour (Phil. Mag., 1904). There is no doubt that results obtained by different observers with a flicker photometer are in better agreement than with any other form of photometer. The comparative ease with which the balance is obtained even when the tints are markedly different shows that its action depends upon a visual distinction which the eye can readily appreciate, and this distinction is mainly one of brightness. The spectrophotometer is an instrument which enables us to make photometric comparisons between the similarly coloured spectra. portions of the spectra of two different sources of photometry. light, or of two parts of the same original source after they have passed through different absorbing media. When it is desired to compare the intensities of the spectra from two different sources a convenient form is the one described by E. L. Nichols. A direct visior_ spectroscope mounted upon a carriage travels along a track between the two sources. In front of the slit two right-angled triangular prisms are set so that the light from each source enters the one side of one prism perpendicularly and is totally reflected into the spectroscope. The two spectra are then seen side by side. Attention being fixed on some chosen narrow portion, say, in the green, the instrument is moved along the track between the sources until the two portions appear of the same intensity. The process is then repeated until the whole spectrum has been explored. In Lummer and Brodhun's form of spectrophotometer the rays to be compared pass in perpendicular lines through the modified Brace's Swan double prism, and then together side by side Bpctro- through a spectroscope. By means of a simple modifi- photometer. cation in the form of the two prisms, Professor D. B. Brace (Phil. Mag., 1899) made the combined prism serve to produce the spectra as well as to effect the desired comparison. In this arrangement the compound prism ABC (fig. 2) is made up of two equal right-angled prisms S ADB and ADC placed with their longer sides in contact, so that the whole forms an equilateral prism with three polished faces. Part of the interface AD is silvered, the silvering forming a narrow central strip running parallel to AD. Along the rest of the interface the two prisms are cemented together with Canada balsam or other material having as nearly as index as the glass. When two rays R S enter symmetrically from opposite sides of the base of the compound prism as shown in the diagram, the ray R will pass through the prism except where the silver strip intercepts it, and will form a part of a spectrum visible to the eye placed at R', while to the same eye there will be visible the similarly dispersed ray SS' reflected from the silvered surface. Thus two systems of incident parallel rays of white light will form on emergence two spectra with corresponding rays exactly parallel. With these and other forms of instrument the aim of the experimenter is to make the two spectra of equal intensity by a method which enables him to compare the original intensities of the sources. In most cases the relative intensities of the portions of the spectra being compared cannot conveniently be altered by varying the distances of the sources. Recourse is therefore generally had to one of the other methods already mentioned, such as the use of polarizing prisms or of rotating sectors. Under certain conditions K. Vierordt's method of allowing the two rays to pass through slits of different width leads to good results, but too great confidence cannot be placed upon it. In other types of spectrophotometer, such as those associated with the names of H. Trannin, A. Crova, H. Wild, G. Hiifner, J. Konigsberger, A. Konig, F. F. Martens and others, the equalization in brightness of two rays is effected by using polarized light, which can be cut down at pleasure by rotation of a Nicol prism. For example, in the Konig-Martens instrument the two rays which are to be compared enter the upper and lower halves of adivided slit. After passing through a lens they pass in succession through (I) a dispersing prism, (2) a Wollaston prism, (3) a biprism, and are finally focused where the eight spectra so produced can be viewed by the eye. Of these only two Kon1g" are made use of, the others being cut out. These two Martens's are polarized in perpendicular planes, so that if be- Spectro" tween the spectrum images and the eye a Nicol prism photometer. is introduced the intensities of any two narrow corresponding portions of the two spectra can be readily equalized. In terms of the angle of rotation of the Nicol the relative intensities of the original rays can be calculated. An important application of the spectrophotometer is to measure the absorptive powers and extinction coefficients of transparent substances for the differently coloured rays of light. By appropriate means the intensities of chosen corresponding parts of the two contiguous spectra are made equal—in other words, a match is established. Into the path of the rays of one of the spectra the absorbent substance is then introduced, and a match is again established. A measure of the loss of luminosity due to the interposition of the absorbent substance is thus obtained. To facilitate experiments of this nature Dr J. R. Milne has devised a spectrophotometer which presents some novelties of construction (see Proceedings of the Optical Convention, 1905, vol. i.). The light from a bright flame is suitably Mi1ne's projected by a lens so as to illuminate a small hole in the Spectroend of the collimator. The rays from this point-source photometer. are made parallel by the collimator, and then pass, partly through the absorbing medium, partly through the space above it. These two parts of the original beam are transmitted through a dispersing prism and then fall upon a screen with two similar rectangular openings, the upper one allowing the unabsorbed part of the beam to pass, the lower that part which has been transmitted through the absorbing medium. The objective of the observing telescope converges the rays suitably upon a Wollaston prism, so that two spectra are seen side by side, having their light polarized in perpendicular planes. A Nicol prism is placed between the Wollaston prism and the eye-piece of the telescope, and by its rotation in the manner already described the intensities of any two corresponding portions of the two spectra can be brought to equality. By careful attention to all necessary details Milne shows that his instrument satisfies the requirements of a good spectrophotometer; for (1) the rays through the absorbing medium can be made strictly parallel; (2) the two spectra can be brought with ease accurately edge to edge without any diffraction effects; (3) the plane of the delimiting screen can be made conjugate to the retina of the observer's eye; (4) not only do the two spectra touch accurately along their common edge, but the two fans of rays which proceed from every point of the common edge lie in one and the same plane; (5) the eye is called upon to judge the relative intensities not of two narrow slits but of two broad uniformly illuminated areas. Milne also points out that this instrument can be used as a spectropolarimeter. E. L. Nichols considers that spectrophotometers which depend for their action upon the' properties of polarized light are necessarily open to serious objections, such as: selective absorption in the calcspar, altering the relative intensities of the constituents in the original rays; selective losses by reflection of polarized rays at the various optical surfaces; and the necessarily imperfect performance of all forms of polarizing media. To eliminate these defects as far as possible great care in construction and arrangement is needed, otherwise corrections must be applied.. . , It is evident that if the successive parts of two spectra are compared photometrically we may by a process of summation obtain a comparison of the total luminosities of the lights which form the spectra. This process is far too tedious to be of any practical value, but sufficiently accurate results may in certain cases be obtained by comparison of two or more particular parts of the spectra, for example, strips in the red, green and blue. Similar in principle is the method suggested by J. Mace de Lepinay, who matches his lights by looking first through a red glass of a particular tint and then through a chosen green. If R and G represent the corresponding ratios of the intensities, the required comparison is calculated from the formula 1 + 0.208 R (1 — GR) . A. Crova, one of the earliest workers in this subject, effects the photometric comparison of differently coloured lights by matching those monochromatic rays from the two sources which have the same ratio of intensities as the whole collected rays that make up the lights. Careful experiment alone can determine this particular ray, but were it once ascertained for the various sources of light in use the method would have the merits of rapidity and accuracy sufficient for practical needs. Spectrophotometric observations are necessary to determine the position in the spectrum of the particular mono-chromatic ray, but when it has been determined a coloured glass may be made which allows light in the neighbourhood of this ray to pass, and the photometric comparison may then be effected by looking through this glass. This article has been confined strictly to the methods of visual photometry, with very little reference to the results. Comparison of intensities of radiation by photographic means or by methods depending on the effects of heat introduces considerations quite distinct from those which lie at the basis of photometry in its usual signification. (C. G. K.)
End of Article: PHOTOMETRY (from Gr. (Pews, xarrbs, light, µerpov, a measure)
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