Question

To find refractive index of a liquid by using a convex lens and a plane mirror with readings

Answer 1

Let $f_1$ be the focal length of convex lens.
$f_2$ be the focal length of liquid lens. [ liquid is also worked as a lens due to refraction phenomenon ]

and Let F be the focal length of combination of convex lens and liquid lens.

use formula, $\frac{1}{F}=\frac{1}{f_1}+\frac{1}{f_2}$

so, from here, $\frac{1}{f_2}=\frac{1}{F}-\frac{1}{f_1}$.... (1)

if the focal length of combination and focal length of convex lens are given , refractive index of the liquid can be calculated.

liquid lens formed is a plano-convex lens [ it is because one side of liquid is plane mirror and other side is convex lens ] so, radius of curvature of liquid lens , $R_1$ = R [ R is the radius of curvature of convex lens ]
and $R_2=\infty$

now, $\frac{1}{f_2}=(\mu-1)\left(\frac{1}{R_1}-\frac{1}{R_2}\right)$

so, $\frac{1}{f_2}=(\mu-1)\left(\frac{1}{R}-\frac{1}{\infty}\right)$

or, $\frac{1}{f_2}=\frac{(\mu-1)}{R}$

or, $\mu=1+\frac{R}{f_2}$

so, putting the value of $f_2$ and R we can get the refractive index of given liquid.