Three identical polaroid sheets $P_1, P_2, P_3$ are oriented so that pass axis of $P_2$ and $P_3$ are inclined to $P_1$ at 60° and 90° respetively. A monochromatic source of intensity $I_0$ is used to pass through $P_1$, $P_2, P_3$. Intensities after passing through $P_1, P_2, P_3$ will be respectively :
(A) $I_0, \frac{I_0}{2}, \frac{I_0}{8}$
(B) $\frac{I_0}{2}, \frac{I_0}{8}, \frac{I_0}{32}$
(C) $\frac{I_0}{2}, \frac{I_0}{8}, \frac{3 I_0}{32}$
(D) $I_0, \frac{I_0}{2}$, zero
Choose the correct answer from the options given below :
Answer & explanation
Correct answer: option 1
Intensity of light after passing through $P_1$ is $I_1 = \frac{I_0}{2}$
Intensity after passing through $P_2$ is $I_2 = I_1 cos^2\theta = \frac{I_0}{2} cos^260^o = \frac{I_0}{8}$
Angle between $P_2$ and $P_3$ is $30^o$
Intensity after passing through $P_3$ is $I_3 = I_2 cos^2\theta = \frac{I_0}{8} cos^230^o = \frac{3I_0}{32}$