138 Dr. Brewster on the laws which regulate the 
In order to ascertain the relation between the polarising 
angle at the second surface of transparent bodies, and the 
angle at which they reflect the whole of the incident pencil, 
let us make. 
The index of refraction = m 
Sine of the angle of total reflexion ~ 
Cotangent of the polarising angle m 
Tangent of the polarising angle ~ 
Since the sine of any angle is always less than the tangent, 
the polarising angle whose tangent is will always be less 
than the angle of total reflexion whose sine is The angle 
of polarisation, therefore, must fall without the limit of total 
reflexion, but it will gradually approach to that limit as the 
refractive power increases. When the pencil, however, is 
incident within the sphere of total reflexion, the quantity 
of polarised light is so near its maximum, that the experi- 
ments can be conducted with almost the same result, as if the 
polarising angle had exceeded the angle of total reflexion. 
The only consequence of the difference between the two 
angles is, that the depolarised image is inferior in point of 
intensity to the other image. 
The following measures tor flint glass with a refractive 
power of 1 .600, and of diamond with a refractive power of 
2.80, will show the relations between these two angles. 
o , 
Polarising angle for the second surface of flint glass 32 o 
Angle at which total reflexion commences - 38 45 
S°45' 
Difference 
