Question

A given ray of light suffers minimum deviation in an equilateral prism P. Additional prisms Q and R of identical shape and of same material as that of P are now combined as shown in the figure. The ray will now suffer

• A. greater deviation
• B. no deviation
• C. same deviation as before
• D. total internal reflection

Hint:

When you see an even number of identical prisms alternating (up-down-up-down), the net deviation is zero. When you have an odd number (like 3 here), the net deviation is usually that of a single prism.

Answer 1

The Correct Option is C

Step 1: Understanding the Concept:
When a ray of light passes through a prism, it suffers a certain deviation. If an identical prism is placed adjacent to it but in an inverted orientation, the inverted prism will produce an equal and opposite deviation, effectively cancelling the deviation of the first prism.
Step 2: Key Formula or Approach:
The total deviation produced by a combination of thin prisms is the algebraic sum of the individual deviations: \[ \delta_{\text{total}} = \delta_1 + \delta_2 + \delta_3 + \dots \] For identical prisms oriented alternately (upright, inverted, upright), the deviations alternate in sign: $+\delta, -\delta, +\delta$.
Step 3: Detailed Explanation:
Let the deviation produced by the first upright prism P be $\delta$.
Since the second prism Q is identical to P but placed inverted, it will produce a deviation of $-\delta$ (equal in magnitude but opposite in direction).
The third prism R is identical to P and is placed upright, so it will produce a deviation of $+\delta$.
The total deviation $\delta_{\text{total}}$ of the ray after passing through the combination of the three prisms is: \[ \delta_{\text{total}} = \delta_{\text{P}} + \delta_{\text{Q}} + \delta_{\text{R}} \] \[ \delta_{\text{total}} = \delta + (-\delta) + \delta = \delta \] Thus, the total deviation of the ray after passing through all three prisms is exactly the same as the deviation produced by the single prism P alone.
Step 4: Final Answer:
The ray will suffer the same deviation as before. The correct option is (C).