Question

An object is placed at a distance of $40\text{cm}$ from a concave mirror of focal length $15\text{cm}$. If the object is displaced through a distance of $20\text{cm}$ towards the mirror, by how much distance the image is displaced?

• A. $84\text{cm}$
• B. $48\text{cm}$
• C. $36\text{cm}$
• D. $64\text{cm}$

Answer 1

The correct option is C $36\text{cm}$

Given:
$u=-40\text{cm};f=-15\text{cm}$

Using mirror formula,

$\frac{1}{f}=\frac{1}{u}+\frac{1}{v}\Rightarrow v=\frac{uf}{u-f}$

Substituting the values we get,

$v=\frac{(-40)(-15)}{(-40)-(-15)}=-24\text{cm}$

On displacement of the object towards the mirror,
$u^{\prime }=20-40=-20\text{cm}$

$\therefore v^{\prime }=\frac{u^{\prime }f}{u^{\prime }-f}=\frac{(-20)(-15)}{(-20)-(-15)}=-60\text{cm}$

$\therefore$ Distance by which image is displaced :
$\Delta v=|(-60)-(-24)|=36\text{cm}$

Hence, option (c) is the correct answer.