Four polaroids are placed such that the optic axis of each is inclined at an angle of `30^(@)` with the optic axis of the preceding one. If unpolarised light of intensity I_(0) falls on the first polaroid, the light transmitted from the fourth is

Options

A. `I_(0)`
B. `I_(0)//16`
C. `0.21 I_(0)`
D. none

Answer

C

Explanation

After first, `I_(1)=I_(0)/2`
After second, `I_(2)=I_(1) cos^(2) 30^(@)=I_(0)/2xx3/4=(3I_(0))/8`
After third, `I_(3)=I_(2) cos^(2) 30^(@)=(3I_(0))/8xx3/4=(9I_(0))/32`
After fourth, `I_(3) cos^(2) 30^(@)=(9I_(0))/32xx3/4=27/128I_(0)=0.21I_(0)`