Unpolarized light of intensity 24 W/m² passes through three polarizers such that the transmission axis of the last polarizer is crossed with the first. Let (a) $α$ be the angle between the transmission axes of first two polarizers, such that intensity of final emerging light is 2.25 W/m² (b) $β$ be the angle between the transmission axes of first two polarizers, such that the intensity of final emerging light is maximum. The values of $α$ and $β$ are:

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45°, 30°

45°, 60°

30°, 60°

30°, 45°

answer is C.

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Detailed Solution

Let the angle between the transmission axes of first two polarizes is $θ$ . Then angle between second and third polarizers will be 90 - $θ$ . From Malus law:
$I = \frac{I_{0}}{2} \cos^{2} {θcos}^{2} (90 - θ) = \frac{I_{0}}{8} \sin^{2} (2 θ)$
From the given data:
$2.25 = \frac{24}{8} \sin^{2} 2 θ => \sin^{2} 2 θ = \frac{8 X 2.25}{24} = \frac{3}{4} =>= 30^{\circ}$