Question

The angle of a prism is A and one of its refracting surfaces is silvered. Light rays falling at an angle of incidence 2A on the first surface returns back through the same path after suffering reflection at the second (silvered) surface. The refractive index of the material of the prism is,

• A. 2 sin A
• B. 2 cos A
• C. $\frac{1}{2}$ cos A
• D. tan A

Answer 1

The correct option is B 2 cos A


$\alpha ={90}^{\circ }-A$
Hence r = A
$\mu =\frac{sini}{sinr}=\frac{sin2A}{sinA}$
$\Rightarrow \mu =\frac{2sinAcosA}{sinA}=2cosA$