A beam of natural light falls on a system of 5 polaroids, which are arranged in succession such that the pass axis of each polaroid is turned through `60^(@)` with respect to the precending one. The friction of the incident light intensity that passes through the system is :

Options

A. `(1)/(64)`
B. `(1)/(32)`
C. `(1)/(256)`
D. `(1)/(512)`

Answer

D

Explanation

Let `I_(0)` be the intensity of incident light. Then the intensity of light from the `1^(st)` polaroid is `I_(1)=(I_(0))/(2)`
Intensity of light from the `2^(nd)` polaroid is
`I_(2)=I_(1)cos^(2)60^(@)=(I_(0))/(2)((1)/(2))^(2)=(I_(0))/(8)`
Intensity of light from the `3^(rd)` polaroid is
`I_(3)=I_(2)cos^(2)60^(@)=(I_(0))/(8)((1)/(2))^(2)=(I_(0))/(32)`
Intensity of light from the `4^(th)` polaroid is
`I_(4)=I_(3)cos^(2)60^(@)=(I_(0))/(32)((1)/(2))^(2)=(I_(0))/(128)`
Intensity of light from `5^(th)` polaroid is
`I_(5)=I_(4)cos^(2)60^(@)=(I_(0))/(128)((1)/(2))^(2)=(I_(0))/(512)`
Therefore, the fraction of the incident light that passes through the system is
`(I_(5))/(I_(0))=(1)/(512)`