Question

Behind a thin converging lens having both the surface
of the same radius 10cm, a plane mirror has been
placed. The image of an object at a distance 40 cm
from the lens is formed at same position. What is the
refractive index of lens ?​

Answer 1

Given :

Radius of the lens = 10 cm

Distance of image from the object = 40 cm

To Find :

The refractive index of the lens = ?

Solution :

• As the image distance is also 40 cm, the focal length of the lens becomes 40 cm as the object distance and image distance is same.

• We have the relation

           $\frac{1}{f} = (\mu-1)(\frac{1}{R_{1} } -\frac{1}{R_{2} } )$

          $\frac{1}{40} =(\mu-1)(\frac{1}{10} +\frac{1}{10} )$

          $\frac{1}{40} =(\mu-1)\frac{2}{10}$

          $\mu=\frac{9}{8}$

  The refractive index of the lens is 9/8