A beam of unpolarised light of intensity $I_0$ is passed through a polaroid $A$, then through anothe

Question

A beam of unpolarised light of intensity $I_0$ is passed through a polaroid $A$, then through another polaroid $B$ oriented at $30^{\circ}$ relative to $A$, and finally through a third polaroid $C$ oriented at $60^{\circ}$ relative to $B$. The intensity of the emergent light is

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(a) : When unpolarised light passes through the first polaroid $A$, its intensity is halved, becoming $I_1 = \frac{I_0}{2}$. Passing through $B$ (oriented at $	heta_1 = 30^{\circ}$ to $A$), by Malus's law the intensity becomes: $I_2 = I_1 \cos^2(30^{\circ}) = \left(\frac{I_0}{2}ight) \left(\frac{\sqrt{3}}{2}ight)^2 = \frac{3I_0}{8}$. Passing through $C$ (oriented at $	heta_2 = 60^{\circ}$ to $B$), the final emergent intensity is $I_3 = I_2 \cos^2(60^{\circ}) = \left(\frac{3I_0}{8}ight) \left(\frac{1}{2}ight)^2 = \frac{3I_0}{32}$.