Question

A glass slab has concave surface of radius of curvature 2.0 cm. The glass has refractive index of 1.5. If a point object is placed on axis in air at a distance of 18 cm from concave face, find the position and nature of the image.

Answer 1

Given,

$R=2cm$

$n_1=1$

$n_2=1.5$

$u=18cm$

$v=?$

Refraction through spherical end face

From medium 1 to 2 of refractive index $n_1$ and $n_2$

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

$\frac{1.5}{v}-\frac{1}{-18}=\frac{1.5-1}{2}$

$\frac{1.5}{v}=\frac{0.5}{2}+\frac{1}{-18}$

$\frac{1.5}{v}=\frac{0.5}{2}-\frac{1}{18}$

$\frac{1.5}{v}=\frac{4.5-1}{18}=\frac{3.5}{18}$

$v=1.5\times \frac{18}{3.5}=7.7$