A narrow beam of natural light falls on a set of `N` thick plane-parallel glass plates at the Brewster angle. Find:
(a) the degree `P` of polarization of the transmitted beam,
(b) what `P` is equal to when `N = 1, 2, 5,` and 10.

Explanation

When natural light is incident on a glass plate at Brewster's angle, the transmitted light has
`I'_(||) = I_(0)//2` and `I''_(bot) = (16n^(4))/((n^(2) + 1)^(4))I_(0)//2 = alpha^(4)I_(0)//2`
where `I_(0)` is the incident intensity
After passsing through the `2^(nd)` plate we find
`I''''_(||) = (1)/(2)I_(0)` and `I''''_(||) = (alpha^(4))^(2) (1)/(2)I_(0)`
Thus after `N `plates `I_(||)^(trans) = (1)/(2)I_(0)`
`I_(bot)^(trans) = alpha.^(4N)(1)/(2)I_(0)`
Hence `P = (1 - alpha^(4N))/(1 + alpha^(4N))` where `alpha = (2n)/(1+n^(2))`
(b) `alpha^(4) = 0.726` for `n = (3)/(2)`.
Thus `P(N = 1) = 0.158, P(N =2) = 0.310`
`P(N = 5) = 0.663, P(N = 10) = 0.922`.