Question

Light from a point source in air falls on a convex spherical glass surface ( refractive index = 1.5, radius of curvature = 20 cm). The distance of light source from the glass surface is 100 cm. At what position is the image formed ?

Answer 1

Given,

Refractive index, $\mu =1.5$

Radius of curvature, $R=20cm$

Object distance, $u=100cm$

Image distance, $v=$?

We know

$\frac{{\mu }_2}{v}-\frac{{\mu }_1}{u}=\frac{{\mu }_2-{\mu }_1}{R}$

${\mu }_2=1.5$

${\mu }_1=1$

$\Rightarrow$ $\frac{1.5}{v}+\frac{1}{100}=\frac{1.5-1}{20}$

$\Rightarrow$ $\frac{1.5}{v}=\frac{0.5}{20}-\frac{1}{100}$

$\Rightarrow$ $\frac{1.5}{v}=\frac{3}{200}$

$\Rightarrow$ $v=\frac{200}{3}\times 1.5$

$v=100cm$