Two polaroids are placed in the path of unpolarized beam of intensity `I_(0)` such that no light is emitted from the second polarid. If a third polaroid whose polarization axis makes an angle `theta` with the polarization axis of first polaroid, is placed between these two polariods then the intensity of light emerging from the last polaroid will be

Options

A. (a) `(I_0/8)sin^2 2theta`
B. (b) `(I_0/4)sin^2 2theta`
C. (c) `(I_0/2)cos^4theta`
D. (d) `I_0cos^4theta`

Answer

A

Explanation

No light is emitted from the second polaroid, so `P_1` and `P_2` are perpendicular to each other

Let the initial intensity of light is `I_0`. So intensity of light after transmission from first polaroid`=I_0/2`.
Intensity of light emitted from `P_3, I_1=I_0/2cos^2theta`
Intensity of light transmitted from last polaroid, i.e., from `P_2=I_1cos^2(90^@-theta)=I_0/2 cos^2theta.sin^2theta`
`=I_0/8(2sinthetacostheta)^2=I_0/8sin^2 2theta`