Light from a point source in the air falls on a spherical glass surface ($\mu =1.5$ and radius of curvature $20cm$). The distance of the light source from the glass surface is $100cm$. The position where the image is formed is :

The correct option is B $100cm$
Given: Light from a point source in the air falls on a spherical glass surface ($\mu =1.5$ and radius of curvature 20 cm). The distance of the light source from the glass surface is 100 cm.

To find the position where the image is formed

Solution:

As per the given criteria,

Refractive index of air, ${\mu }_1=1$

Refractive index of glass, ${\mu }_2=1.5$

Radius of curvature, $R=20cm$

Object distance, $u=-100cm$

Substituting the above values in the following formula, we get:

$\frac{{\mu }_2}{v}-\frac{{\mu }_1}{u}=\frac{{\mu }_2-{\mu }_1}{R}⟹\frac{1.5}{v}-\frac{1}{(-100)}=\frac{1.5-1}{20}⟹\frac{1.5}{v}=\frac{0.5}{20}-\frac{1}{100}⟹\frac{1.5}{v}=\frac{2.5-1}{100}⟹v=\frac{1.5\times 100}{1.5}⟹v=100cm$

Hence the image is formed at 100cm in the denser medium.