DR. T. R. MERTON AND PROF. J. W. NICHOLSON ON 
266 
The ordinary theory of the Lummer Gehrcke plate is, as stated above, well known 
so far as monochromatic radiation is concerned. If light falls on the plate, as in the 
figure (fig. 4), and if a and /3 are the rays respectively reflected once, and refracted 
twice and reflected once, their path difference is D =2 fid cos r where /x is the index 
of the plate for the particular wave-length, r is the angle of refraction, and d is the 
thickness of the plate. When the complete system of multiple reflections is considered, 
Fig. 4. 
and the interfering rays are focussed on a screen S, the intensity corresponding to the 
angle of refraction r is 
4 Ct J T Sill" (tt DA) 
(l —t) J + 4t Sin 2 (7T D/X) 
where X is the wave-length, a 2 is the intensity of the incident light, and r is the 
square of the internal reflection coefficient of amplitude, such that, for light polarized 
parallel to the plane of incidence, by Fresnel’s formula 
r = tan 2 (< —r)J tan 2 ((-hr), 
but for light polarized perpendicular to this plane, 
t = sin 2 (i —r)/sin 2 (/+r). 
Maxima occur on the screen when I) — l- n\ if n is an odd integer, and minima when 
n is even. 
As regards the nature of these maxima and minima, a full discussion may be found, 
for example, in Geiircke’s treatise.* It is not difficult to show that in order to obtain 
very sharp maxima nearly grazing incidence must be employed, so that r is nearly 
unity, and this is adopted in the present experiments. 
When we pass from this ordinary theory to the problem now in hand, difficulties 
begin to appear. In the first place, D = 2 ,u d cos r is not actually a constant, 
although it may be nearly so for several successive maxima if the order is high. The 
successive separations of the maxima are therefore not identical, and there is also a 
variation in their intensities. This effect could be calculated, but owing to the 
* ‘ Anwendung der Interferenzen,’ Braunschweig, 1916. 
