Question

An object, a convex lens (focal length $f=20\text{cm}$) and a plane mirror are arranged as shown in the figure. How far behind the mirror is the second image formed?

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

Answer 1

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

We have, for refraction through the convex lens, $u=-12\text{cm,}f=20\text{cm}$

We have from the lens formula,
$\frac{1}{v}-\frac{1}{u}=\frac{1}{f}$

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

$\Rightarrow \frac{1}{v_1}=\frac{1}{20}-\frac{1}{12}=\frac{3-5}{60}=-\frac{1}{30}$

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

This image will act as the (virtual) object for the plane mirror.

For reflection at the plane mirror,

$u=-(30+10)=-40\text{cm}$

Thus, image distance,

$v_2=-\left(u\right)=-(-40)\text{cm}=40\text{cm}$



Thus, second image is formed $40\text{cm}$ behind the mirror.