Question

An object, a convex lens of focal length $20\text{cm}$ and a plane mirror are arranged as shown in the figure. How far behind the mirror is the image after refraction from lens and reflection from mirror is formed?

• A. $30\text{cm}$
• B. $20\text{cm}$
• C. $40\text{cm}$
• D. $50\text{cm}$

Answer 1

The correct option is C $40\text{cm}$

Given data for lens:

object distance, $u_1=-12\text{cm}$
focal length, $f_1=20\text{cm}$
Let, the image is formed at distance $v_1$.

Applying lens formula for first refraction,

$\frac{1}{v_1}-\frac{1}{u_1}=\frac{1}{f_1}$

Substituting the values given in the problem,

$\Rightarrow \frac{1}{v_1}-\frac{1}{(-12)}=\frac{1}{20}$

$\Rightarrow \frac{1}{v_1}=-\frac{1}{30}$

$\Rightarrow v_1=-30\text{cm}$

This image will act as an object for the plane mirror.

For first reflection at plane mirror:

Object distance,
$u_2=-(30+10)=-40\text{cm}$

Thus, image distance, $v_2=-\left(u_2\right)=-(-40)\text{cm}=40\text{cm}$


Hence, option (c) is correct answer.