1905-6.] Obtaining the Half -Shade Field in Polarimelers. 523 
On recombining the two components, the new direction of light 
vibration is OP', giving an angle of rotation of POP'. The 
magnitude of this angle depends on the angle of inclination Q 0 Y 
of the plate : and on the direction of the light vibration (defined by 
the angle POX say). As regards the effect of the first of these, it is 
clear that if the angle be made less than the angle of polarisation, 
then the component along 0 Y will suffer loss as well as the 
component along O X (though, as may easily be shown, always 
to a less degree), and the angle POP' will be diminished. As 
regards the effect of the second factor, it appears from the 
diagram that P 0 P' is a maximum when P 0 X is in the neighbour- 
hood of 45°,* and that POP' gradually declines to zero as 
POX proceeds towards either 0° or 90°. To obtain the value 
of the maximum rotation let 
QOY = 57°i P 0 X = 45°, and OS = l; 
then if p be the fraction of the light energy polarised in the 
plane of incidence which is reflected from the front surface of 
the plate, by Fresnel’s formula, 
p = sin 2 (£-?•) = sin 2 [57|°-(90 o -57J°)] 
p = sin 2 25° = 0 1786. 
But the same fraction of the incident light is reflected from the 
back surface as from the front, hence the amplitude after trans- 
mission through both surfaces is given by 
OS'= 1— p = 0*821. 
|tan P' 0 Y = 0 S' ; 
P0P' = 45°-39i o = 5i°. 
* More exactly 42° ‘ 2 . 
But 
therefore 
