Question

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

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

Answer 1

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

For objects at infinity image will be formed at:

$\frac{3/2}{V}=\frac{1/2}{R}$

$⟹V=3R$

From similar triangles $ABC$ and $ADE$

$\frac{D^{\prime }}{2R}=\frac{D}{3R}$

$⟹D^{\prime }=\frac{2}{3}D$