Question

An object is placed at a distance of $10$ cm (in a medium of ) from the pole of a spherical refracting surface bounding a medium of $1.5$ if the image formed is virtual and at a distance of $40$ cm then the spherical surface is-

calculate the Radius of curvature :

Answer 1

Given object distance $u=10cm$ and image distance $v=40cm$ and refracting index of medium $n_2=1.5$ and

refracting index of air $n_1=1$

We know

$\frac{n_2}{v}-\frac{n_1}{u}=(n_2-n_1)R$ where R= radius of curvature.

Considering for concave lens,

$\frac{-1.5}{40}-\frac{1}{-10}=(1.5-1)R$

$\frac{-1.5+4}{40}=0.5R$

$R=0.125$cm