Question

An image is formed at a distance of $100 \,cm$ 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 $100\, cm$. 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, $u=100 \,cm ; v=100 \,cm$
$\mu_{2}=1.5, \mu_{1}(\text { air })=1$
$\Rightarrow \frac{1.5}{100}+\frac{1}{100}=\frac{1.5-1}{R} \Rightarrow \frac{2.5}{100}=\frac{0.5}{R}$
$R=\frac{0.5 \times 100}{2.5} \Rightarrow R=20\, cm$