Question

The plane of polarisation of a plane-polarised light rotates by $60^\circ$ after passing through a wave plate. The pass-axis of the wave plate is at an angle $\alpha$ with respect to the plane of polarisation of the incident light. The wave plate and $\alpha$ are

• A. $\lambda/4,\; 60^\circ$
• B. $\lambda/2,\; 30^\circ$
• C. $\lambda/2,\; 120^\circ$
• D. $\lambda/4,\; 30^\circ$

Hint:

A half-wave plate rotates the plane of polarisation by twice the angle between the incident polarisation and its fast axis.

Answer 1

The Correct Option is B

Step 1: Understand the effect of a half-wave plate.
A half-wave ($\lambda/2$) plate rotates the plane of polarisation by an amount equal to $2\alpha$, where $\alpha$ is the angle between the incident polarisation and the fast axis.

Step 2: Use the given rotation.
Given rotation = $60^\circ$, therefore $2\alpha = 60^\circ \;\Rightarrow\; \alpha = 30^\circ$.

Step 3: Exclude quarter-wave plates.
A quarter-wave ($\lambda/4$) plate changes linear polarisation to elliptical or circular, not simply rotate it; hence $\lambda/4$ plates cannot produce pure rotation.

Step 4: Conclusion.
Thus, the correct wave plate is a $\lambda/2$ plate and $\alpha = 30^\circ$.