The intensity of transmitted light when a polaroid sheet is placed between two crossed polaroids suc

Question

The intensity of transmitted light when a polaroid sheet is placed between two crossed polaroids such that its pass axis makes an angle of $30^{\circ}$ with the polarization axis of the first polaroid is (where $I_0$ is the intensity of polarised light immediately after passing through the first polaroid)

Professor PC Thomas Classes · Answer

(a) : Let the intensity after the first polaroid be $I_1 = I_0$. The second (middle) polaroid is at an angle $	heta_1 = 30^{\circ}$ to the first. By Malus's Law, the transmitted intensity is $I_2 = I_0 \cos^2(30^{\circ}) = I_0 \left(\frac{\sqrt{3}}{2}ight)^2 = \frac{3I_0}{4}$. The third polaroid is completely crossed with respect to the first, meaning its angle with the middle polaroid is $	heta_2 = 90^{\circ} - 30^{\circ} = 60^{\circ}$. The final transmitted intensity is $I_3 = I_2 \cos^2(60^{\circ}) = \left(\frac{3I_0}{4}ight) \left(\frac{1}{2}ight)^2 = \frac{3I_0}{16}$.