Question

An object is present on the principal axis of a concave mirror at a distance $60\text{cm}$ from it. The focal length of the mirror is $40\text{cm}$. If the object starts moving with $4\text{cm/s}$ along the principal axis towards the mirror, then:

• A. Image starts moving with $8\text{cm/s}$ away from the mirror.
• B. Image starts moving with $8\text{cm/s}$ towards the mirror.
• C. Image starts moving with $16\text{cm/s}$ away from the mirror.
• D. Image starts moving with $16\text{cm/s}$ towards the mirror.

Answer 1

The correct option is C Image starts moving with $16\text{cm/s}$ away from the mirror.

Given that,
Distance of object from mirror $\left(u\right)=-60\text{cm}$
Focal length of the mirror $\left(f\right)=-40\text{cm}$
Velocity of the object towards mirror $\left(V_O\right)=4\text{cm/s}$


By using mirror formula,
$\frac{1}{v}+\frac{1}{u}=\frac{1}{f}$

$\Rightarrow \frac{1}{v}=\frac{1}{-40}-\frac{1}{-60}$

$\Rightarrow v=-120\text{cm}$

Using formula of magnification,
$m=-\frac{v}{u}=-\frac{-120}{-60}$
$\Rightarrow m=-2$

Now, velocity of image along P.A is given by,

Velocity of image $=-m^2\times$ Velocity of object
$\Rightarrow V_I=-(m{)}^2\times V_O$
$\Rightarrow V_I=-(-2{)}^2\times 4\text{cm/s}$
$\Rightarrow V_I=-16\text{cm/s}$
Since, the image is formed on the left side of the mirror $(v=-ve)$ and the image is moving in the left direction $(V_I=-ve)$, we can say that velocity of the image is away from the mirror.
Hence, option $\left(c\right)$ is the correct answer.