AIIMS 2006 Physics Polarization MCQ Question

To understand the variation of the electric field vector with time for circularly polarized light, we need to delve into the concept of circular polarization and how it manifests graphically.

Circular Polarization Explained

Circularly polarized light consists of two perpendicular electric field vectors that are out of phase by 90 degrees (or $\frac{\pi}{2}$ radians). This means that as one component reaches its maximum value, the other is at zero, and vice versa. The combination of these two components results in the electric field vector tracing out a circular path in the plane perpendicular to the direction of propagation.

Mathematical Representation

The electric field vector $\vec{E}$ for circularly polarized light can be expressed as:

1. For a right-handed circularly polarized light: $\vec{E}(t) = E_0 \hat{x} \cos(\omega t) + E_0 \hat{y} \sin(\omega t)$

2. For a left-handed circularly polarized light: $\vec{E}(t) = E_0 \hat{x} \cos(\omega t) - E_0 \hat{y} \sin(\omega t)$

In both cases, $\hat{x}$ and $\hat{y}$ are unit vectors in the x and y directions, respectively, $E_0$ is the amplitude of the electric field, and $\omega$ is the angular frequency.

Analyzing the Diagrams

Given the options (a), (b), (c), and (d), we need to identify which diagram correctly depicts the behavior of the electric field vector over time for a circularly polarized light.

• Option B (the correct answer): This diagram should show the electric field vector rotating in a circular motion as time progresses. The vector will appear to move through both the x and y axes, continuously changing direction while maintaining a constant magnitude.

Why Other Options are Incorrect

• Option A: If this diagram shows the electric field vector oscillating back and forth in a straight line (either in the x-direction or y-direction), it represents linearly polarized light, not circularly polarized light.

• Option C: This diagram might show two separate oscillating vectors, each varying in amplitude but not combining to form a circular motion. This is also indicative of linear polarization or possibly elliptical polarization, not circular.

• Option D: If this diagram depicts a constant electric field magnitude without any circular motion or proper phase relationship, it would be incorrect as it does not represent any form of polarization.

Conclusion

The correct answer is B because it accurately illustrates the circular motion of the electric field vector, demonstrating the characteristics of circularly polarized light. The other options do not represent this behavior and thus are incorrect.

Understanding these differences is crucial for visualizing and analyzing light polarization in various optical applications.