An image is formed at a distance of $100 \mathrm{~cm}$ from the glass surface when light from point source…
An image is formed at a distance of $100 \mathrm{~cm}$ from the glass surface when light from point source in air falls on a spherical glass surface with refractive index 1.5. The distance of the light source from the glass surface is $100 \mathrm{~cm}$. The radius of curvature is
$20\ cm$
$40\ cm$
$30\ cm$
$50\ cm$
Solution
The refraction formula is
$\frac{\mu_2}{v}-\frac{\mu_1}{u}=\frac{\mu_2-\mu_1}{R}$
$\begin{aligned} & \mu_2=1.5, \mu_1 \text { (air) }=1, u=-100 \mathrm{~cm}, v=100 \mathrm{~cm} \\ & \Rightarrow \frac{1.5}{100}+\frac{1}{100}=\frac{1.5-1}{R} \Rightarrow \frac{25}{100}=\frac{0.5}{R} \Rightarrow R=20 \mathrm{~cm}\end{aligned}$
