A beam of unpolarized light of intensity I_0 is passed through a polaroid A and then through another polaroid

Q: A beam of unpolarized light of intensity I0 is passed through a polaroid A and then through another polaroid B which is oriented so that it principal plane makes an angle of 45° relative to that of A . The intensity of emergent light is

(a) I0

(b) I0/2

(c) I0/4

(d) I0/8

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Ans: (c)
Sol: Here, polaroid A polarizes light.

Intensity of polarized light from A= I0/2

According to law of Malus ,

Intensity of light emerging from B,

$\displaystyle I_B = \frac{I_0}{2}cos^2 45^o $

$\displaystyle I_B = \frac{I_0}{2}(\frac{1}{\sqrt{2}})^2 $

$\displaystyle I_B = \frac{I_0}{4} $