Question:
A light ray incidents on a prism PQR ($PQ=QR$) and travels as shown in the figure. The minimum refractive index of the referred prism is:
A light ray incidents on a prism PQR ($PQ=QR$) and travels as shown in the figure. The minimum refractive index of the referred prism is:
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Total internal reflection occurs when the light travels from a denser to a rarer medium at an angle greater than the critical angle.
Updated On: Jun 11, 2026
- $\sqrt{3}$
- $3/\sqrt{2}$
- $1/\sqrt{2}$
- $\sqrt{2}$
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The Correct Option is D
Solution and Explanation
Step 1: Concept
For total internal reflection to occur at the second face of the prism, the angle of incidence must exceed the critical angle.
Step 2: Analysis
Since $PQ=QR$, the base angles are $45^\circ$, and the prism angle $A = 90^\circ$. For the ray to undergo TIR at the second face, $\sin(C) \leq \sin(45^\circ) = 1/\sqrt{2}$. Since $\sin(C) = 1/\mu$, we need $\mu \geq \sqrt{2}$.
Step 3: Conclusion
The minimum refractive index is $\sqrt{2}$.
Final Answer: (D)
For total internal reflection to occur at the second face of the prism, the angle of incidence must exceed the critical angle.
Step 2: Analysis
Since $PQ=QR$, the base angles are $45^\circ$, and the prism angle $A = 90^\circ$. For the ray to undergo TIR at the second face, $\sin(C) \leq \sin(45^\circ) = 1/\sqrt{2}$. Since $\sin(C) = 1/\mu$, we need $\mu \geq \sqrt{2}$.
Step 3: Conclusion
The minimum refractive index is $\sqrt{2}$.
Final Answer: (D)
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