Question

The curved face of a plano-convex lens is silvered. If $\mu$ be the refractive index and r the radius of curvature of this curvature 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

Answer: (A)

$\frac{r}{\mu }$

let the distance of object for which the arrangement forms image at infinity be $x$

and the ray from $x$ refracts at the plane surface which causes a shift in position of $x$ the new object distance for mirror is $u=x\mu$ ; $f=\frac{r}{2}$ ;$v=\infty$

$\frac{1}{v}+\frac{1}{u}=\frac{1}{f}$

$0+\frac{-1}{x\mu }=\frac{-2}{r}$

$x=\frac{r}{2\mu }$

focal length is $\frac{r}{2\mu }$

$radius=2f=\frac{r}{\mu }$

option $A$ is correct