Unpolarized light of intensity I passes through an ideal polarizer A. Another identical polarizer B is placed behind A. The intensity of light beyond B is found to be $\frac{I}{2}$ . Now another identical polarizer C is placed between A and B. The intensity beyond B is now found to be $\frac{I}{8}$ . The angle between polarizer A and C is.

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$0^{0}$

$45^{0}$

$60^{0}$

$30^{0}$

answer is C.

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Detailed Solution

Polarizers A and B are oriented with parallel pass axis. Suppose polarizer C is at angle $θ$ with A then it also makes an angle $θ$ with B.Using malus law , $I_{C} = \frac{I}{2} \cos^{2} θ$

And $I_{B} = I_{C} \cos^{2} θ = \frac{I}{2} \cos^{4} θ$

$\frac{I}{8} = \frac{I}{2} \cos^{4} θ (∴ I_{B} = \frac{I}{8})$

$\cos^{4} θ = \frac{1}{4} \Rightarrow \cos θ = \frac{1}{\sqrt{2}} \Rightarrow θ = 45^{0}$

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