Question

A luminous point object is moving along the principal axis of a concave mirror of focal length 12 cm towards it. When its distance from mirror is 20 cm its velocity is 4 cm/s. The velocity of the image in cm/s at that instant is :

• A. 6, towards the mirror
• B. 6, away from the mirror
• C. 9, away from the mirror
• D. 9, towards the mirror

Answer 1

The correct option is C 9, away from the mirror

Using the mirror formula,

$\frac{1}{f}=\frac{1}{v}+\frac{1}{u}$

Now, $f=-12$

$u=-20$

$u^{\prime }=4$

Now, $v=-30$

Differentiating the mirror formula,
we get

$\frac{u^{\prime }}{u^2}=\frac{-v^{\prime }}{v^2}$

Substituting the values obtained

$v^{\prime }=\frac{-4\times 900}{400}$

Hence, the velocity of the image is $9$ cm/sec away from the mirror