Question

A given ray of light suffers minimum deviation in an equilateral prism \( P \). Additional prisms \( Q \) and \( R \) of identical shape and of the same material as \( P \) are now added as shown in the figure. The ray will now suffer:
\includegraphics[width=0.5\linewidth]{31.png}

• A. Greater deviation
• B. No deviation
• C. Same deviation as before
• D. Total internal reflection

Hint:

For prisms in an optical system:
- Identical prisms arranged symmetrically do not alter the deviation.
- The principle of reversibility ensures that light retraces its path under symmetrical conditions.
- Minimum deviation occurs when the internal refraction angle is equal at both interfaces.

Answer 1

The Correct Option is C

Step 1: Understanding minimum deviation
- A ray suffers minimum deviation in a prism when it is symmetrically refracted through it.
- The angle of deviation \( D_{\min} \) in an equilateral prism is given by:
\[ D_{\min} = 2i - A \] where \( A \) is the prism angle and \( i \) is the angle of incidence in the minimum deviation condition.
Step 2: Effect of additional prisms
- Since the additional prisms Q and R are identical and arranged symmetrically, their combined effect cancels out any additional deviation.
- The light undergoes opposite deviations at each interface, resulting in no net change in the final deviation.
Step 3: Conclusion
- Since the overall deviation remains unchanged, the correct answer is:
\[ Same deviation as before. \]