Question:
The angle of a prism is \( A \). One of its refracting surface is silvered. If light rays falling at an angle of incidence \( 2A \) on the first surface returns back through the same path after reflection from silvered surface. The refractive index \( \mu \) of the prism is
The angle of a prism is \( A \). One of its refracting surface is silvered. If light rays falling at an angle of incidence \( 2A \) on the first surface returns back through the same path after reflection from silvered surface. The refractive index \( \mu \) of the prism is
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Ray retracing path in prism \(\Rightarrow\) internal incidence at reflecting surface is \(0^\circ\).
Updated On: Apr 22, 2026
- \( 2\sin A \)
- \( 2\cos A \)
- \( \frac{1}{2\cos A} \)
- \( \tan A \)
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The Correct Option is B
Solution and Explanation
Concept:
For ray to retrace path after reflection $\longrightarrow$ it must strike second face normally.
Step 1: Condition at second face.
Angle of incidence at second face = \( 0^\circ \) Thus, inside prism: \[ r_2 = 0 \Rightarrow r_1 = A \]
Step 2: Apply Snell's law at first surface.
\[ \mu = \frac{\sin i}{\sin r} = \frac{\sin 2A}{\sin A} \]
Step 3: Simplify.
\[ \mu = \frac{2\sin A \cos A}{\sin A} = 2\cos A \]
Step 1: Condition at second face.
Angle of incidence at second face = \( 0^\circ \) Thus, inside prism: \[ r_2 = 0 \Rightarrow r_1 = A \]
Step 2: Apply Snell's law at first surface.
\[ \mu = \frac{\sin i}{\sin r} = \frac{\sin 2A}{\sin A} \]
Step 3: Simplify.
\[ \mu = \frac{2\sin A \cos A}{\sin A} = 2\cos A \]
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