Question

A narrow beam of light of diameter D falls on a hemispherical glass sphere of radius R (R >>> D) and refractive index $\frac{3}{2}$. Diameter of beam on the base of hemisphere is.

• A. $\frac{D}{2}$
• B. $\frac{D}{3}$
• C. $\frac{2D}{3}$
• D. $\frac{3}{4}D$

Answer 1

The correct option is C $\frac{2D}{3}$

$\frac{\mu }{v}-\frac{1}{\infty }=\frac{\mu -1}{R}\Rightarrow \frac{3}{2v}=\frac{1}{2R}\Rightarrow v=3R$

$\theta =\frac{D}{3R}=\frac{d}{2R}\Rightarrow d=\frac{2D}{3}$