The angle of prism is A. One of its refracting surfaces is silvered. Light rays falling at angle of incidence 2A on the first surface are retraced after suffering reflection at the silvered surface. The refractive index μ of the prism is:
Options

Question

The angle of prism is A. One of its refracting surfaces is silvered. Light rays falling at angle of incidence 2A on the first surface are retraced after suffering reflection at the silvered surface. The refractive index μ of the prism is:

Options

G1 Physics · Accepted Answer

Step 1: The ray must reach the silvered face normally to retrace. Therefore internal angle at entrance r₁ = A. Step 2: Snell’s law μ = sin i/sin r₁ = sin(2A)/sin A. Step 3: Use sin 2A = 2 sin A cos A. Final answer: (B) μ = 2 cos A.