Question

The angle of a prism is A. 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 silvered surface.The refractive index $\mu$, of the prism is :

• A. $2sinA$
• B. $2cosA$
• C. $\frac{1}{2}cosA$
• D. $tanA$

Answer 1

Answer: (B)

$2cosA$

To retrace its path light rays should fall normally on the reflecting surface. So
$r_2=0$

$\Rightarrow r_1=A-r_2\Rightarrow r_1=A$

Now applying snell rule between incident ray and refracted ray.

$\left(1\right)sin\left(2A\right)=nsin\left(A\right)\Rightarrow 2sinAcosA=nsinA$

$\Rightarrow n=2cosA$