A system is created by adjusting the five polaroids to touch each other. The polaroid rotates one by one about its axis to `60^(@)`. Then intensity of emergent light emitted from the last polaroid will be the ...... part of intensity of incident light.

Options

A. `(I_(0))/(64)`
B. `(I_(0))/(32)`
C. `(I_(0))/(256)`
D. `(I_(0))/(512)`

Answer

D

Explanation

Suppose the intensity of light on polaroid is `I_(0)`.
The intensity of light emergent from polaroid is,
`I_(1)=(I_(0))/(2)`
The intensity of light emergent from second polaroid is
`I_(2)=(I_(0))/(2)cos^(2)60^(@)`
`=(I_(0))/(8) " " [ :. 60^(@)=(1)/(2)]`
The intensity of light emergent from third polaroid is,
`I_(3)=(I_(0))/(8)cos^(2)60^(@)`
`=(I_(0))/(32) " "[ :. cos60^(@)=(1)/(2)]`
The intensity of light emergent from fourth polaroid is,
`I_(4)=(I_(0))/(32)cos^(2)60^(@)=(I_(0))/(128)`
The intensity of light emergent from fifth polaroid is
`I_(5)=(I_(0))/(128)cos^(2)60^(@)=(I_(0))/(512)`
By short method:
`I_(5)=(I_(0))/(2)(cos^(2)60^(@))^(4)=(I_(0))/(2)((1)/(4))^(4)=(I_(0))/(512)`