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 intensity. From this position a rotation of 30⁰ shows that the two beams have same intensity. The ratio of intensities 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

For the beam $A : I'_{A} = I_{A} \cos^{2} (30 °)$
For the beam B $I'_{B} = I_{B} \cos^{2} (90 ° - 30 °) = I_{B} \sin^{2} (30 °)$
$\Rightarrow \frac{I_{A}}{I_{B}} = \frac{\sin^{2} 30 °}{\cos^{2} 30 °} = \tan^{2} (30 °) = \frac{1}{3}$

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