Unpolarized light of intensity 32 W `m^(-2)` passes through three polarizers such that transmission axis of first is crossed with third. If intensity of emerging light is 2 W `m^(-2)`, what is the angle of transmission axis between the first two polarizers?

Options

A. `30^(@)`
B. `45^(@)`
C. `22.5^(@)`
D. `60^(@)`

Answer

C

Explanation

Let `theta` be angle between the axis of the first two polarisers then obviously `(90^(@)-theta)` is the angle between `2^(nd)` and `3^(rd)` polarisers.
` :.I=(I_(0))/(2)"cos"^(2)theta "cos"^(2)(90-theta)`
or `2=(32)/(2)"cos"^(2)theta "cos"^(2)(90-theta)=16"cos"^(2)theta "sin"^(2)theta`
`(2sin theta cos theta)^(2)=(1)/(2) " or " sin^(2)2theta=(1)/(2) :. sin2theta=(1)/(sqrt(2))`
` :. 2theta=45^(@) " or "theta=22.5^(@ )`