Question

The plane side of a thin plano-convex lens with radius of curvature $20cm$ is silvered to obtain a concave mirror. An object is located at a distance of 25 cm in front of this mirror. The distance of the image from the mirror is

• A. $100cm$
• B. $100/11cm$
• C. $6.25cm$
• D. $100/9cm$

Answer 1

The correct option is A $100cm$

Given radius of curvature $R_1=20cm$ and $R_2=\infty$and

object distance $u=-25cm$

We know,

$\frac{1}{f_l}=(\mu -1)[\frac{1}{R_1}-\frac{1}{R_2}]$-----------(A)

where $\mu =1.5$= refractive index

Thus A becomes,

$\frac{1}{f_l}=0.5[\frac{1}{20}-\frac{1}{\infty }]$

$f_l=40$cm and $f_m=\frac{1}{\infty }=0$ here $f_l$ and $f_m$ are focal length of lens and mirror respectively.

Again,

$P_C=2P_L+P_M=\frac{2}{40}+0=\frac{1}{20}$

Thus focal length $f=20$.

Now from mirror formula we get,

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

$v=\frac{-20\times 25}{25-20}=-100$