Two beams, A and B of plane polarised light with mutually perpendicular plane of polarisation are seen through a polaroid. From the position when the beam A has maximum intensity (and beam B has zero intensity) a rotation of polaroid through `30^(@)` makes the two beams appear equally bright. If the initial intensities of the two beams are `I_(A) and I_(B)` respectively, then `(I_(A))/(I_(B))=.....`

Options

A. `(3)/(2)`
B. 1
C. `(1)/(3)`
D. 3

Answer

C

Explanation

Let the maximum intensities of beam A and beam B are `I_(A) and I_(B)` respectively. Both beams have same intensity now B polaroid rotates by `30^(@)`
`:.I_(A)cos^(2)30^(@)=I_(B)cos^(2)60^(@)`
`:.(I_(A))/(I_(B))=(cos^(2)60^(@))/(cos^(2)30^(@))=(((1)/(2))^(2))/(((sqrt(3))/(2))^(2))`
`:. (I_(A))/(I_(B))=(1)/(3)`