Question

One end of a cylindrical glass rod ends in a hemispherical surface of radius $R=20mm$. Find the image distance (in mm) of a point object on the axis of the rod, $80mm$ to the left of the vertex. The rod is in air.

• A. 120

Answer 1

The correct option is A 120
Given:
${\mu }_1=1$
${\mu }_2=1.5$
$R=+20mm$
$u=-80mm$

Equation of refraction of light at curved surfaces is given as:
$\frac{{\mu }_2}{v}-\frac{{\mu }_1}{u}=\frac{{\mu }_2-{\mu }_1}{R}$
$\frac{1.5}{v}-\frac{1}{-80}=\frac{1.5-1}{20}$
$v^{\prime }=+120mm$
The image is formed at distance of $120mm$ and is hence, real.