The refractive index of the material of a prism is √2 and its refracting angle is 30°. One of the two refracting surfaces of the prism is made a mirror inwards by silver coating. A beam of monochromatic light entering from the other face will retrace its path, if its angle of incidence on the prism is:
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Question

The refractive index of the material of a prism is √2 and its refracting angle is 30°. One of the two refracting surfaces of the prism is made a mirror inwards by silver coating. A beam of monochromatic light entering from the other face will retrace its path, if its angle of incidence on the prism is:

Options

G1 Physics · Accepted Answer

Step 1: To retrace the incident path after reflection, the ray must hit the silvered face normally. Step 2: This makes the internal refraction angle at the entrance face r = A = 30°. Step 3: Snell’s law sin i = μ sin r = √2 × (1/2) = 1/√2. Thus i = 45°. Final answer: (B) 45°.