A beam of natural light falls on a system or `N = 6` Nicolprisms whose transmission planes are turned each through an angle `varphi = 30^(@)` with respect to that of the foregoing prism. What fraction of luminous flux passes through this system ?

Explanation

Let `I_(0) =` intensity of the incident beam.
Then the intensity of the beam transmitted through the first Nicol prism is
`I_(1) = (1)/(2)I_(0)`
and through the `2^(nd)` prism is
`I_(2) = ((1)/(2)I_(0))cos^(2)varphi`
Through the `N^(th)` prism it will be
`I_(N) - I_(N-1) cos^(2) varphi`
`= (1)/(2)I_(0)cos^(2(N - 1)) varphi`
hence fraction transmitted
`= (I_(N))/(I_(0)) = eta = (1)/(2)cos^((2N-1)) varphi = 0.12` for `N = 6`.
and `varphi = 30^(@)`