Question

A point object is placed at a distance of $10\text{cm}$ and its real image is formed at a distance of $20\text{cm}$ from a concave mirror. If the object is moved by $0.1\text{cm}$ towards the mirror the image will shift by (nearly)

• A. $0.4\text{cm}$ away from the mirror
• B. $0.8\text{cm}$ away from the mirror
• C. $0.4\text{cm}$ towards the mirror
• D. $0.8\text{cm}$ towards the mirror

Answer 1

The correct option is A $0.4\text{cm}$ away from the mirror

From the relation,
$\frac{1}{v}+\frac{1}{u}=\frac{1}{f}$
By differentiation mirror formula we have,
$\frac{-dv}{v^2}-\frac{du}{u^2}=0$
$dv=\frac{v^2}{u^2}(-du)$
From given data,
$\Rightarrow dv={\left(\frac{20}{10}\right)}^2\left(0.1\right)=0.4\text{cm}$

As the change in the final distance is positive so the image will shift away from the mirror.

Why this question? Caution: We can use differential formula only for small changes in object position