140 Dr. Brewster on the laws which regulate the 
Prop. xiv. 
JVhen a pencil of light is incident upon the separating surface of 
two media having different indices of refraction m m' , it will 
be polarised at an angle whose tangent is equal to the quotient 
of the greater index of refraction divided by the lesser , or —• 
This Proposition is a necessary consequence of the general 
law, and is also deduced from direct experiment. 
If we call A the angle whose tangent is equal to then the 
corresponding angle at which the pencil is incident from air 
upon the first surface of the upper medium, or a — sin. A y.m. 
In the case of water and glass, where m is equal to 1.525, 
and in' to 1.336, we have the polarising angle at the surface 
of separation, or A = 48° 47', and sin. Axw'= 1.0048, conse- 
quently a is greater than 90°. Hence it follows, that when a 
ray of light is incident upon a parallel plate of water lying 
upon a plate of glass, there is no angle of incidence upon the 
first surface of the water at which the ray will suffer polari- 
sation at the separating surface of the two media. The pola- 
risation of the incident pencil increases from o° to 90°, and is 
nearly complete at 90 0 . 
When m is equal to 1.508, which is sometimes the case, 
then sin. A x ml = 1.000, and « = 90° exactly. 
This conclusion was so unexpected that I immediately en- 
deavoured to confirm it by experiment. The result was 
exactly conformable to the law : the polarisation of the pencil 
became more and more perfect from o° to 9 o° of incidence. 
Between 8o° and 90° the change was scarcely perceptible, 
owing to the slow variation of the sines, for when the pencil is 
