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(B) $1$. When unpolarised light of intensity $I_0$ passes through the first polaroid,the intensity of the transmitted light becomes $I_1 = \frac{I_0}{

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$\frac{I_0}{8}(\sin 2 	heta)^2$

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(B) $1$. When unpolarised light of intensity $I_0$ passes through the first polaroid,the intensity of the transmitted light becomes $I_1 = \frac{I_0}{2}$.$2$. The first and second polaroids are crossed (angle between axes is $90^\circ$),so no light passes through the second polaroid initially.$3$. $A$ third polaroid is placed between them at an angle $	heta$ with the first polaroid. The angle between the third and the second polaroid is $(90^\circ - 	heta)$.$4$. Intensity after the third polaroid: $I_2 = I_1 \cos^2 	heta = \frac{I_0}{2} \cos^2 	heta$.$5$. Intensity after the second (last) polaroid using Malus' Law: $I_3 = I_2 \cos^2(90^\circ - 	heta) = I_2 \sin^2 	heta$.$6$. Substituting $I_2$: $I_3 = (\frac{I_0}{2} \cos^2 	heta) \sin^2 	heta = \frac{I_0}{2} (\sin 	heta \cos 	heta)^2 = \frac{I_0}{2} (\frac{\sin 2 	heta}{2})^2 = \frac{I_0}{8} \sin^2 2 	heta$.

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