A beam of natural light falls on a system of 6 polaroids, which are arranged in succession such that each polaroid is turned through `30^@` with respect to the preceding one. The percentage of incident intensity that passes through the system will be

Options

A. 1
B. 0.5
C. 0.3
D. 0.12

Answer

D

Explanation

If n polaroids are arranged in succession such that each is turned through `theta` with respect to preceding then the intensity of `n^(th)` polaroid is
`I_(n) = (I_(0))/(2) (cos^(2) theta)^(n-1)`
`I_(6) = (I_(0))/(2) (cos^(2) 30)^(5) = (I_(0))/(2) xx (3)/(4)xx (3)/(4)xx (3)/(4)xx (3)/(4)xx (3)/(4)`
`(I_(6))/(I_(0)) = (243)/(2048) = 0.1186 ~~ 12%`