Question

What is the refractive index of the material of a plano-convex lens, if the radius of curvature of the convex surface is $10cm$ and focal length of the lens is $30cm$?

• A. $\frac{4}{3}$
• B. $\frac{3}{2}$
• C. $2$
• D. $3$

Answer 1

The correct option is A $\frac{4}{3}$

Applying lens maker’s formula for a plano-convex lens,



$\frac{1}{f}=(\mu -1)(\frac{1}{R_1}-\frac{1}{R_2})$
where $\mu =\frac{{\mu }_L}{{\mu }_M}={\mu }_L$
(because here the medium is air, so ${\mu }_M=1$)
$\therefore \frac{1}{+30}=(\mu -1)(\frac{1}{+10}-\frac{1}{\infty })$
$\Rightarrow \mu -1=\frac{1}{3}\Rightarrow \mu =\frac{4}{3}$