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A polaroid examines two adjacent plane polarised beams A and B whose planes of polarisation are mutually perpendicular. In the first position of the analyser, beam B shows zero intensty. From this position a rotation of 30° shows that the two beams have same intensity. The ratio of intensties of the two beams I_A and I_B will be

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3 : 1

$1 : \sqrt{3}$

1 : 3

$\sqrt{3} : 1$

answer is A.

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Detailed Solution

Initially beam A is parallel and beam B is perpendicular to the amalyer.
Later $I_{A^{1}} = I_{A} \cos^{2} 30; I_{B^{1}} = I_{B} \cos^{2} 60 .$
Given $I_{A^{1}} = I_{B^{1}}, then I_{A} : I_{B} = 1 : 3$

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