The following items are positioned in sequence: A source of a beam of natural light of intensity $I _ { 0 }$, three ideal polarizers A, B, and C; and an observer. Polarizer axis angles are measured clockwise from the vertical, as viewed by the observer. The axis angle of polarizer $A$ is set at $0 ^ { \circ }$ (vertical), and the axis angle of polarizer $C$ is set at $50 ^ { \circ }$. The axis angle of polarizer $B$ is set at $120 ^ { \circ }$. What is ratio of the intensity of the beam at the observer to the intensity $I _ { 0 }$ of the source?
A) $0.015$
B) $0.035$
C) $0.020$
D) $0.025$
E) $0.030$

Question

Quizplus · Accepted Answer

The intensity of the beam at the observer is given by:$$I = I_0 \cos^2 \theta_A \cos^2 \theta_B \cos^2 \theta_C$$where $\theta_A$, $\theta_B$, and $\theta_C$ are the angles of the polarizer axes.In this case, $\theta_A = 0^\circ$, $\theta_B = 120^\circ$, and $\theta_C = 50^\circ$. Therefore,$$I = I_0 \cos^2 0^\circ \cos^2 120^\circ \cos^2 50^\circ = I_0 (1)(0)(0.643) = 0.0256I_0$$Therefore, the ratio of the intensity of the beam at the observer to the intensity of the source is 0.0256, which is closest to choice A, 0.025.

The Following Items Are Positioned in Sequence: a Source of a Beam