Question

A beam of diameter d is incident on a glass hemisphere as shown in figure. If the radius of curvature of the hemisphere is very large in comparison to d, then diameter of the beam at the base of the hemisphere will be

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

Answer 1

The correct option is A

$\frac{3d}{4}$

Refraction at the curved surface $\frac{{\mu }_2}{v}-\frac{{\mu }_1}{u}=\frac{{\mu }_2-{\mu }_1}{R}$
$P{P}^1$ is very small

$\frac{P^1}{P^{1}D}=\frac{BC}{CD}A{P}^1=d,P^{1}D=v$