Question

An object is present on the principal axis of a concave mirror at a distance of $30\text{cm}$ from it. The focal length of the mirror is $20\text{cm}$. If the object starts moving with velocity $2\text{cm/s}$ perpendicular to the principal axis, then:

• A. Image moves with $4\text{cm/s}$ below the principal axis.
• B. Image moves with $8\text{cm/s}$ above the principal axis.
• C. Image moves with $8\text{cm/s}$ below the principal axis.
• D. Image moves with $4\text{cm/s}$ above the principal axis.

Answer 1

The correct option is A Image moves with $4\text{cm/s}$ below the principal axis.

Given that
$u=-30\text{cm};f=-20\text{cm};V_o=2\text{cm/s}$
where $V_o\to$ speed of object

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

$\Rightarrow \frac{1}{v}=\frac{1}{f}-\frac{1}{u}=\frac{1}{-20}-\frac{1}{-30}$

$\Rightarrow v=-60\text{cm}$

Magnification of the mirror is
$m=\frac{-v}{u}=\frac{-(-60)}{-30}$
$\Rightarrow m=-2$

Velocity of image perpendicular to principal axis
$=m\times V_o$
$=-2\times 2=-4\text{cm/s}$
Negative sign indicates velocity in downward direction i.e below the principal axis.