Light from a point source in air falls on a spherical glass surface ($n=1.5$ and radius of curvature

Question

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

Professor PC Thomas Classes · Answer

We use the relation $\frac{n_{2}}{v}-\frac{n_{1}}{u}=\frac{n_{2}-n_{1}}{R}$. Here $u=-100$ cm, $R=+20$ cm, $n_{1}=1$, and $n_{2}=1.5$. Substituting the values, we have $\frac{1.5}{v}+\frac{1}{100}=\frac{0.5}{20}$, which yields $v=+100$ cm.