A beam of unpolarised light is passed first through tourmaline crystan A and then through another tourmaline crystal B oriented so that its principal plane is parallel to that of A. The intensity of the emergent light is I. If A now rotated by `45^(@)` in a plane perpendicular to the direction of the incident ray, the intensity of the emergent light will be

Options

A. `2I_(0)`
B. `I_(0)//2`
C. `I_(0)//4`
D. `I_(0)//sqrt2`

Answer

C

Explanation

Case I Since, ray emergent from `C_(2)` has intensity.

`l=l_(1)/2cos^(2)theta=l_(1)/2cos^(2)0^(0)=l_(1)/2`
`or" "l_(1)/2=l_(0)rArrl_(1)=2l_(0)`
Case II

Intensity of emergent ray `=l_(0)cos^(2)60^(0)=l_(0)(1/2)^(2)=l_(0)/4`