Two beams A and B, of plane polarized light with mutually perpendicular planes of polarization are seen through a polaroid. From the position when the beam a has maximum intensity (and beam B has zero ntensity), a rotation of polaroid through `30^circ` 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)` equals:

Options

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

Answer

B

Explanation

As `I_(A)` and `I_(B)` are initial intensitieas, therefore, on rotation of polaroid through `30^(@)`,
`I'_(A) = I_(A) cos^(2) 30^(@)`
and `I'_(B) = I_(B) cos^(2) 60^(@)`
`:. 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)) = (1)/(3)`