Question

A linearly polarized light falls on a quarter-wave plate and the emerging light is found to be elliptically polarized. The angle between the fast axis of the quarter-wave plate and the plane of polarization of the incident light can be:

• A. \( 30^\circ \)
• B. \( 45^\circ \)
• C. \( 90^\circ \)
• D. \( 180^\circ \)

Hint:

A quarter-wave plate converts linearly polarized light to circular or elliptical, depending on the incident angle with the fast axis. \( 45^\circ \) gives equal components and maximum ellipticity.

Answer 1

The Correct Option is A

Step 1: Behavior of a quarter-wave plate.
A quarter-wave plate introduces a phase difference of \( \pi/2 \) between the components of light along its fast and slow axes.
Step 2: Condition for elliptical polarization.
If the incident light’s electric field makes an angle \( \theta \) with the fast axis, its components along fast and slow axes are different. When the amplitudes differ, the resulting polarization becomes elliptical.
Step 3: Condition for circular polarization.
For circular polarization, the amplitudes must be equal (\( \theta = 45^\circ \)) and the phase difference must be \( \pi/2 \). Thus, any deviation from \( 45^\circ \) results in elliptical polarization, but for an exact quarter-wave plate and linearly polarized input, elliptical polarization occurs precisely at \( 45^\circ \).
Step 4: Final Answer.
The correct angle is \( 45^\circ. \)