Question

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

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

Answer 1

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

Putting $u=-12\text{cm}$ and $f=+20\text{cm}$ in the lens formula
$\frac{1}{v}-\frac{1}{u}=\frac{1}{f}$
$\frac{1}{v}-\frac{1}{-12}=\frac{1}{20}$
$\frac{1}{v}=\frac{1}{20}-\frac{1}{12}$
$\frac{1}{v}=\frac{12-20}{20\times 12}=\frac{1}{-30}$
$v=-30\text{cm}$,

i.e., the image is formed at a distance of $30\text{cm}$ from the lens on the same side as the object. The distance of this image from the mirror $=30+10=40\text{cm}$. Therefore, the final image is formed behind the mirror at a distance of $40\text{cm}$ from it. Hence the correct answer is (c).