An unpolarizing beam of light is incident on a group of four palarizing sheets, which are arranaged in such a way that the characteristic direction of each polarizing sheet makes an angle of `30^(@)` with that of the preceding sheet. What fraction of incident unpolarized light is transmitted ?

Options

A. 27/54
B. 27/81
C. 27/128
D. 27/112

Answer

C

Explanation

Intensity of light transmitted by first polariser
`= I_(1) = (I_(0))/(2)`
`:. I_(2) = (I_(0))/(2) cos^(2) theta = (I_(0))/(2) cos^(2) 30 = (3I_(0))/(8)`
`:. I_(3) = (3I_(0))/(8) cos^(2) theta = (3I_(0))/(8) xx (3)/(4) = (9I_(0))/(32)`
`:. I_(4) = (9I_(0))/(32) cos^(2) theta = (9I_(0))/(32) xx (3)/(4)`
`(I_(4))/(I_(0)) = (27)/(128)`