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 $50 ^ { \circ }$. Polarizer $B$ is set so that the beam intensity is zero at the observer. What are the two possible axis angle settings (less than $180 ^ { \circ }$ ) of polarizer B?

Question

Quizplus · Accepted Answer

EFor the beam intensity to be zero at the observer, polarizer B must be oriented such that no light passing through it can pass through polarizer C. This can happen in two scenarios: when polarizer B is perpendicular to polarizer A (making the light polarized horizontally and thus unable to pass through polarizer C set at $50 ^ { \circ }$), or when polarizer B is set in such a way that the light it passes is perpendicular to polarizer C. The first scenario gives us $90 ^ { \circ }$ since it's perpendicular to polarizer A set at $0 ^ { \circ }$. For the second scenario, if polarizer C is at $50 ^ { \circ }$, to make the light perpendicular to it, polarizer B must be set at $50 ^ { \circ } + 90 ^ { \circ } = 140 ^ { \circ }$ or at a setting that results in light that cannot pass through C, which is also achieved by setting B to $90 ^ { \circ }$ directly. Thus, the correct answers are $90 ^ { \circ }$ and $140 ^ { \circ }$ (A), and also considering the perpendicular orientation to achieve zero intensity, $90 ^ { \circ }$ and $130 ^ { \circ }$ (E) due to a misunderstanding in the explanation process. However, the correct physical interpretation strictly leads to $90 ^ { \circ }$ and $140 ^ { \circ }$ as the angles that would result in zero intensity at the observer, making A the correct choice based on the principles of polarization. The inclusion of E was an error in the explanation process, as the correct interpretation of the physics involved does not support $130 ^ { \circ }$ as a valid answer.

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