Question

An image is formed at a distance of $100cm$ from the glass surface when light from point source in air falls on a spherical glass surface with refractive index $\mathrm{1.5.}$ The distance of the light source from the glass surface is $100cm$. The radius of curvature is

• A. 20 cm
• B. 40 cm
• C. 30 cm
• D. 50 cm

Answer 1

Answer: (A)

The refraction formula is
$\frac{{\mu }_2}{V}-\frac{{\mu }_1}{u}=\frac{{\mu }_2-{\mu }_1}{R}$
where, $R=$ radius of curvature
Given, $u=100cm;v=100cm$
${\mu }_2=1.5,{\mu }_1(\text{ air })=1$
$\Rightarrow \frac{1.5}{100}+\frac{1}{100}=\frac{1.5-1}{R}\Rightarrow \frac{2.5}{100}=\frac{0.5}{R}$
$R=\frac{0.5\times 100}{2.5}\Rightarrow R=20cm$