Question

The radius of the glass is 15 cm. A beam of parallel light strikes the sphere, which converges at point 30 cm behind the spherical surface. Find refractive index of glass.

Answer 1

Diameter of sphere $=15cm$

$\Rightarrow$ radius $=\frac{15}{2}=7.5cm$

$n_1=1$

$n_2=?$

$u=+30cm$

$v=30-15=+15cm$

$(n_1=ref.indexofair{n}_2=ref.indexofsphere)$

$\frac{n_2}{v}-\frac{n_1}{u}=\frac{n_2-n_1}{R}$

$\Rightarrow \frac{n_2}{15}-\frac{1}{30}=\frac{1.5-1}{\frac{15}{2}}$

$\Rightarrow \frac{2n_2-1}{30}=\frac{\left(0.5\right)2}{15}$

$\Rightarrow 2n_2-1=\frac{\left(1\right)30}{15}=2$

$\Rightarrow 2n_2=3$

$\Rightarrow n_2=\frac{3}{2}$

$\therefore$ refractive index of the sphere $=\frac{3}{2}$