132 Dr . Brewster on the laws which regulate the 
similar triangles ABH,AEF,we have AH or BG : HB :: EF : Rad.; 
and HB = consequently CL = HB and the angle BAN 
= CAK. But EAB + BAN = 90°, hence EAB CAK = 90°. 
Cor. The complement of the polarising angle is equal to the 
angle of refraction. 
Prop. v. 
When a ray of light is polarised hy reflexion, the reflected ray 
forms a right angle with the refracted ray. 
Since the angles DAM, BAN, CAK (Fig. 1.) are equal to 
one another, the angle DAC is equal to the right angle 
MAK : hence the reflected ray AD forms a right angle with 
the refracted ray AC. 
Prop. vi. 
If light were polarised simply by the action of the reflecting force, 
the polarising angle would be 45*. 
For when the refracting force is infinitely small, the pola- 
rising angle is 45 0 . The reflecting force is also infinitely 
small in this case, but any diminution of the reflecting force, 
however great, does not alter the direction of the reflected 
ray with respect to the incident ray, or the position of any 
point or side of a ray with regard to the direction of its motion. 
It may also be remarked that 45 0 is the only angle of reflexion 
at which any point or side of a ray makes a revolution of 90° 
relative to the direction of its motion. See Prop. VIII, and 
Cor. 2, of the same Proposition. 
