1912-13.] The Scattering of Light. 2 77 
The table below gives corresponding values of 0 and p, calculated from 
(3), on the assumption that //. = 1*5. 
e 
0 
11 
3f 
5 
7i 
10 
121 
15 
17| 
20 
25 
30 
V 
•oooo 
•04365 
•08736 
•1312 
•1752 
•2641 
•3545 
•4470 
•5421 
•6404 
•7427 
•9622 
1-207 
In order to find a mathematical expression for the intensity of the light, 
scattered by an equivalent cavity, as a function of the angle of scatter, it is 
convenient to regard the matter thus.* Let it be supposed that the rays 
of the beam of light incident perpendicularly on the plate are separated 
into bundles by an infinite number of imaginary tubes forming a system of 
coaxial cylinders parallel to the direction of the light. If these tubes 
accompany the rays through the plate, and if after transmission the same 
bundles as before are to be found within the same tubes, we must further 
suppose that on the far side of the plate the tubes diverge in the form of 
a family of hollow coaxial cones, having their common axis perpendicular 
to the plate, as shown in fig. 8, in which, for greater clearness, only a few 
of the tubes are drawn. With the help of such an imaginary arrangement 
it can easily be seen that the light-intensity i, measured at any the same 
constant distance from the plate, and normally to rays which make an 
angle 0 with the axis, is equal to lex dx/ (sin OdO), where k is a constant 
* We shall ignore the reduction of intensity in the transmitted light due to reflection 
losses, because in all the cases considered it is so very nearly the same. On making a 
calculation by means of Fresnel’s formula, it appears that when a beam of light falls 
normally on the interface separating two media of refractive indices 1 and 1 -5 respectively, 
96 ’00 per cent, of the light energy is transmitted ; and even when the obliquity of the 
beam has reached 30° to the normal, the percentage of energy transmitted is still as great 
as 95-85. 
