Question

The plane face of a plano-convex lens is silvered. If $\mu$ be the refractive index and r the radius of curvature of the curved surface, then the system behaves like a concave mirror of radius

• A. $\frac{r}{\mu }$
• B. $\frac{r}{\mu -1}$
• C. $r\mu$
• D. $r(\mu -1)$

Answer 1

The correct option is B $\frac{r}{\mu -1}$

Consider a parallel beam of light incident on the convex surface of the lens.

$\frac{\mu }{v_1}-\frac{1}{-\infty }=\frac{\mu -1}{r}$

$v_1=\frac{\mu r}{\mu -1}$

This image gets reflected from the mirror to form an image at a distance $\frac{\mu r}{\mu -1}$ to the left of the lens.

Refraction again takes from convex surface,

$\frac{1}{v_2}-\frac{\mu }{\frac{\mu r}{\mu -1}}=\frac{1-\mu }{-r}$

$\frac{1}{v_2}=\frac{2(\mu -1)}{r}$ to the left of the lens.

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

Hence, $R=\frac{r}{\mu -1}$