Q. The polaroid P_{1} , P_{2} & P_{3} are arranged coaxially. The angle between P_{1} and P_{2} is 37°. The angle between P_{2} and P_{3} is , if intensity of emerging light is one quarter of intensity of unpolarized light

(a) θ = cos^{-1} (5/4)

(b) θ = cos^{-1} (4/5)

(c) θ = cos^{-1} (4/(5√2))

(d) θ = cos^{-1} (5/(4√2))

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Ans: (d)

Sol: Let I

_{0}= Intensity of unpolarised lightAccording to Malus’s Law

$\large I_2 = \frac{I_0}{2}cos^2 37^o $

$\large I_2 = \frac{I_0}{2}(4/5)^2 = \frac{8 I_0}{25}$

$\large I_3 = I_2cos^2\theta $

$\large \frac{I_0}{4} = \frac{8 I_0}{25}cos^2 \theta $

$\large cos^2 \theta = \frac{25}{32} $

$\large cos\theta = \frac{5}{4\sqrt{2}} $