Question

A rotating disc is held in front of a plane mirror in two different orientations which are (i) angular momentum parallel to the mirror and (ii) angular momentum perpendicular to the mirror. Which of the following schematic figures correctly describes the angular momentum (solid arrow) and its mirror image (shown by dashed arrows) in the two orientations ?

• A.
• B.
• C.
• D.

Answer 1

The Correct Option is B

To solve the problem of determining the correct schematic representation of angular momentum and its mirror image, we need to understand how angular momentum vectors are affected by reflection in a plane mirror.

Concept Explanation:

When a vector is reflected in a plane mirror, its component perpendicular to the mirror gets inverted, while the components parallel to the mirror remain unchanged. This applies to any vector, including the angular momentum vector.

Case Analysis:

1. Angular Momentum Parallel to the Mirror:
   • If the angular momentum vector is parallel to the mirror, its mirror image will also be parallel and in the same direction as there is no perpendicular component to invert.
2. Angular Momentum Perpendicular to the Mirror:
   • If the angular momentum vector is perpendicular to the mirror, its mirror image will point in the opposite direction because the perpendicular component is inverted.

Solution with Justification:

Given these principles, when evaluating the provided options, we determine the correct reflection outcomes for each orientation:

• For the angular momentum vector parallel to the mirror, the solid and dashed arrows should be aligned.
• For the angular momentum vector perpendicular to the mirror, the dashed arrow should be pointing in the opposite direction of the solid arrow.

The option that accurately reflects this behavior is the second option:

This image correctly illustrates that in the first scenario (parallel), both arrows (solid and dashed) are parallel, and in the second scenario (perpendicular), the dashed arrow is in the opposite direction of the solid arrow. Therefore, the correct answer is Option 2.