surface. As the film is slightly inclined the photograph when developed is crossed by alternately bright and dark bands, the dark bands being due to the deposit of silver at the places where the amplitude was near its maximum. Plate II. Fig. 5 is a reproduction of one of Wiener's photographs. The light incident on the film was decomposed in this case into its homogeneous constituents by a prism, and the result gives a picture of the separate effects of the different wavelengths. The vertical bands represent the spectrum of the electric arc used. The carbon bands will be noticed, and the H and K calcium lines show faintly, but each of these lines and bands is seen to be crossed obliquely by a series of bands which are due to the variations in amplitude of the stationary vibration. The inclination of the two systems of bands to each other is due to the inclination of the refracting edge of the prism decomposing the light to the edge of the wedge formed by the photographic film and the reflecting plate.

Drude and Nernst having succeeded in obtaining sufficiently thin fluorescent films, observed the stationary vibrations by their fluorescent effect.

Lippmann's Colour Photography is based on the formation of thin layers of reduced silver deposited within a photographic film, the layers being half a wave-length apart. They are formed by the stationary vibration of waves of light reflected from a surface of mercury over which the sensitive film has been extended. When viewed in reflected light, the colours of thin plates are seen, and that colour shows a maximum of intensity which has a wave-length equal to twice the distance between the layers. We therefore see in the reflected light chiefly the colour belonging to the wave which originally had formed the stationary vibration. The possibility of reproducing natural colours by photography in this fashion, had already occurred to Wm Zenker*, and to Lord Rayleight. The experimental realization due to Lippmann is, however, a very considerable experimental achievement.

44. Applications. We may divide the principal applications of the interference phenomena which have been described, into two classes. In the first, the difference in phase of two portions of the same wavefront which have traversed two media, is used to measure the difference in optical length of the path, and hence the difference in refractive index. Instruments used for this purpose have been called interference refractometers. Fresnel, already, in conjunction with Arago, used the principle of interference to measure the difference in the refractive index between dry and moist air. Two parallel tubes, filled with the gases to be examined, were placed in the path of a plane wave-front

*Lehrbuch der Photochromie.

+ Collected Works, Vol. III. p. 13.

:

which traversed the tubes longitudinally the displacement in the bands observed when dry air was replaced by moist air served as a measure of the difference in refractive index. Jamin carried out important measurements in an apparatus in which use was made of Brewster's interference bands. Fig. 50 represents Jamin's apparatus.

One of the plates of glass PB is fixed, while the other CD is movable round a vertical axis by means of the screw Q and a horizontal axis by means of the screw O. If the plates are exactly parallel, the illumination over the whole field is uniform. If now the second plate be slightly tilted round a horizontal axis, horizontal bands appear which come closer and closer together as the inclination increases. Rotation round the vertical axis does not change the distance between the bands, but shifts the whole system of bands up and down. If two tubes, which may be exhausted or filled with different gases, be introduced into the path of the interfering rays, the position of the bands depends on the relative retardation of the two rays. Starting e.g. with air at atmospheric pressure, and the central band being adjusted so as to pass through the centre of the field, a partial exhaustion of one of the tubes displaces the bands; the displacement being measured by means of a "Compensator." This compensator, in Jamin's apparatus, consisted of two plates of glass (Fig. 51) capable of being rotated round a horizontal axis AB, and placed at such a distance from each other that each plate receives the light which has passed through one of the tubes. Rotation round the horizontal axis alters the thickness of glass traversed. The alteration being different for the two plates a measurable retardation of one set of rays, as compared with the other, is produced. If the central band, having been displaced by the change of pressure in the tube, is brought back by the compensator to its original position, the difference in refractive dex between the air under partial exhaustion and the air at atmo

A

Fig. 51.

spheric pressure, can be measured. Different gases may be compared in a similar manner.

Lord Rayleigh's form of Refractometer more nearly approaches the original instrument of Fresuel and Arago.

L

C

Light coming from a fine slit and rendered parallel by a collimator lens C of 3 cms. aperture passes through two brass tubes side by side, and soldered together. These tubes, 20 cms. long and

Fig. 52.

6 mms. in bore, are closed at the ends by plates of worked glass, so connected as to obstruct as little as possible the passage of light immediately over the tubes. The light having passed through the tubes enters two slits and is brought to a focus F by means of a lens. The optical arrangement is practically identical with that which gives Young's fringes (Art. 32). The fringes are observed by means of an eyepiece. To secure better illumination and sufficient magnifying power, the eyepiece is cylindrical, so as only to magnify in a horizontal direction. It is made of a short length of glass rod, 4 mm. in diameter. There are two systems of bands, one formed by light which has traversed the gases within the tubes, the other by light which passes above them. If different gases are to be compared with each other, as regards their refracting power, their pressure is adjusted until the system of bands formed by light which has passed through the tubes is coincident with the system formed by the light which has passed above the tubes; the retardation in the two tubes is then the same. If the experiment be repeated at a different pressure, then the ratio of the changes of pressure for each gas is the inverse ratio of the refractivities (-1) of the gases.

Other refractometers have been constructed, chiefly with a view to separating the path of the interfering rays laterally as much as possible, so as to leave more room for the tubes or other apparatus to be introduced into the path of the rays. It is sufficient to refer to the apparatus of Zehnder*. It should be noticed, however, that the lateral separation of the rays is by no means always an advantage. One of the experimental difficulties in delicate optical measurements consists in keeping the temperature sufficiently constant, or at any rate, not to introduce a difference in temperature into the two optical paths. The nearer these are together, the easier will equality of temperature be secured. Where a separation of rays is necessary or advisable for other reasons, Michelson's arrangement, which has already been described, will probably be found to be the most advantageous. The applications which Michelson has made with this

*Ztsch. f. Instrumentenkunde, 1891, p. 275.

instrument to the investigation of the constitution of nearly homogeneous radiation will be referred to in Chapter XIV.

An appliance, useful in many optical measurements, is the "bi-plate" which serves either to separate or to bring together two parallel beams of light. It consists of two plane parallel plates of glass cemented together at an angle. Their action is sufficiently illustrated by of Fig. 53.

In the applications of the phenomena of interference which have been dealt with so far, the problems are of a purely optical nature. We turn now to the second class of applications in which optical methods are used for linear

Fig. 53.

measurement.

Fizeau has used Newton's rings to examine the coefficients of expansion of certain substances. The body to be examined, cut e.g. into the form of a cube, is placed on a plate which, by means of screws passing through it, supports a lens. The upper surface of the cube is polished. If the lens be adjusted so as to leave a small air space between it and the cube, Newton's rings may be observed. If the whole arrangement is raised in temperature, a change takes place in the rings which depends on the altered distance, between the upper surface of the cube and the lens. Knowing the effect of temperature on the refractive index of air and the coefficient of dilatation of the other part of the apparatus, that of the cube may be deduced. Fizeau has measured in this manner, the expansion of crystals in different directions. For a more detailed account of the apparatus and method of obtaining the result from the observed displacements of Newton's rings, Mascart's Optics, vol. 1, p. 503, may be consulted.

Perfectly flat surfaces are sometimes required in optical investigations, and it is a matter of great difficulty to work them so as to satisfy optical tests. Not the least of the difficulties consists in testing the surface when it is nearly flat, so as to discover where its faults are and how they may be corrected. Lord Rayleigh* uses for this purpose the interference bands seen between a horizontal surface of water and the carefully levelled surface which is to be examined. The latter surface is supported horizontally at a distance of about one or two millimetres below that of the water. By the aid of screws the glass surface is brought into approximate parallelism with the water. When the surface is perfectly flat, the interference bands are straight, while a curvature of the bands always implies a curvature of the surface. In the paper referred to it is shown

*Collected Works, vol. iv. p. 202.

how to interpret the curvature of the surface by means of that of the bands. The chief difficulty in applying the method consists in securing perfect steadiness, so as to avoid the effects of the tremor of the water surface.

An important application of interference bands has been made by Michelson*, who was able to obtain a direct comparison between the standard of length, and the wave-length.

45. Historical. Christian Huygens, (born April 14, 1629, at Haag in Holland, died June 8, 1695,) is the founder of the undulatory theory of light. His treatise on light appeared in 1690, and contains the explanation of the reflexion and refraction of light by means of the principle which now bears his name. He also demonstrated how double refraction could be explained by means of wave-surfaces having two sheets, and in particular showed how, in Iceland Spar, a wavesurface consisting of a sphere and spheroid accounted for the laws of refraction of both rays.

Sir Isaac Newton (born Jan. 5, 1643, in Lincolnshire, died March 21, 1727) did not look with favour on the undulatory theory of light. He was misled by the apparent difference in the behaviour of waves of sound which, after passing through an opening, spread out in all directions, and the rays of light which pass in nearly straight lines. This seemed a formidable difficulty, and Huygens' attempts at explaining the apparently rectilinear propagation of light were not clear or convincing. While there is no doubt that Newton's great authority kept back the progress of the undulatory theory for more than a century, this is more than compensated by the fact that the science of Optics owes the scientific foundation of its experimental investigation in great part to him. His experiments on the prismatic decomposition of white light do not fall within the range of this volume, but the phenomena of Newton's rings have been referred to. Newton discovered that the radii of bright or dark rings was determined by the thickness of the layer of air interposed, and found the correct law connecting the diameters of successive rings.

Thomas Young, born June 13, 1773, at Milverton (Somerset), studied medicine in London, Edinburgh and Göttingen. He was Professor of Physics at the Royal Institution in London between 1801 and 1804, but gave up his position in order to devote himself to the practice of medicine. He died on May 10, 1829. To Young belongs the merit of having been the first to state clearly the principle of the superposition of waves and to show how interference may be explained by means of it. Owing to the historical importance of this

* Travaux et Mémoires du Bureau International des Poids et Mesures x1. (1895).