On the diffraction of light incident at nearly the critical angle on the boundary between two media

When a parallel pencil of monochromatic light falls at nearly the critical angle on the plane boundary between two media of differing refractive index, and emerges in the rarer medium in a direction almost parallel to the surface of separation, the aperture of the emergent pencil becomes greatly restricted. A study of the diffraction phenomena observed in this limiting case of oblique emergence seems of interest, especially in view of the fact that in the Lummer-Gehrcke interference spectroscope we have an actual case of importance in which such obliquely emergent pencils determined the observed phenomena. Some preliminary work on this subject was carried out by Prof. C. V. Raman, and at his suggestion the author of the present paper undertook a detailed experimental investigation of the case with a view to establishing its principal features. So far as the writer is aware, though the theory of the parallel-plate interferometer in its essentials is well known, the special character of the diffraction phenomena observed with pencils very obliquely refracted at a plane surface had not been discussed previously. It is proposed in the present paper to describe the results obtained by the writer, some of the observations (to be mentioned below) having special reference to the theory of the Lummer-Gehrcke plate. 2.Experimental Methods and Results . The general features of the case may be observed on an ordinary spectrometer. It is well known that an ordinary prismatic spectroscope may be so adjusted as to give very large dispersions, by putting the prism on the table of the instrument in such a position that the light incident on the first face, after passing through it, falls at nearly the critical angle of incidence on the second face and emerges nearly grazing the surface. The lines in the spectrum then appear very widely separated, and also strongly curved, owing to the fact that pencils of light from different points on the slit of the collimator do not all pass through the principal plane of the prism. In his investigation of the optical power of spectroscopes, Lord Rayleigh has remarked that the resolving power of the prism in the position referred to above is no greater than at other positions. The width of the beam emerging from the prism tends to zero as the grazing position is approached, and the spectrum lines are much widened by diffraction. This sets off the effect of the increased dispersion on the resolving power. Owing to the great dispersion and the enfeeblement of the light in oblique transmission, a very powerful source of monochromatic light is necessary for satisfactory observation of the diffraction phenomena. A Westinghouse quartz silica lamp is most suitable, though visual observations may also easily be made with a glass Cooper-Hewitt mercury-vapour lamp. Observations are made on the green line of the spectrum. In order to secure an extended diffraction-pattern, it is advantageous to use something less than the full aperture of the prism to start with, cutting it down by one or more slits having their edges parallel to the slit of the collimator. The position of the slits is a matter of indifference, so long as the aperture of the beam is cut down before it emerges or just as it emerges from the second surface of the prism, and notafter it has emerged. The simplest arrangement is to limit the aperture of the beam by a slit or slits immediately before entry into the prism. Another arrangement would be to use a hollow prism, filled with liquid, and to put the slit or slits inside the prism, so as to limit the aperture of the beam just before incidence on the second face. A third arrangement is to use a glass prism the aperture of the second face of which has been reduced by grinding down to the desired width with parallel edges. All the arrangements give identical results.