i %6 Dr. Brewster on the laws which regulate the 
Prop. xi. 
When a ray of light is polarised by reflexion from the second 
surface of transparent bodies , the refected ray will form a right 
angle with the refracted ray. 
Let AB, Fig. 3, be a ray incident at the first surface 
MN, AD the ray polarised at that surface, AC the ray inci- 
dent at the second surface PQ, and CM the ray polarised at 
that surface ; then if CF be the refracted ray, the angle 
MCF is a right angle. By Prop. V, DA£ is a right angle, 
and on account of the parallelism of MN, PC, and BA, CF, 
the angle FCP is equal to DAM, but MCP is equal to 
MAC, hence the whole MCF is equal to the whole DAC, 
or a right angle. 
Cor. 1 . The ray CM, reflected by the second surface, is at 
right angles to the ray AB incident on the first surface. 
Cor. 2. The internal reflected ray CM forms with the 
external reflected ray AD, an angle equal to the angle of 
deviation CAO. 
Cor. 3. The ray CF emerging from the second surface 
forms with the first reflected ray, AD an angle equal to the 
complement of the angle of deviation. 
Prop. xii. 
When a ray of light is incident at the polarising angle , upon the 
second surface of transparent bodies, it receives such a change in 
its direction from the action of the refracting force, that the 
real angle of incidence, at which it is refected and polarised, 
is 45 0 
By the very same reasoning which was used in Prop. XI, 
