Question

A plane mirror is approaching you at $10{\text{cm s}}^{-1}$. Your image shall approach you with a speed of:

• A. $10{\text{cm s}}^{-1}$
• B. $5{\text{cm s}}^{-1}$
• C. $20{\text{cm s}}^{-1}$
• D. $40{\text{cm s}}^{-1}$

Answer 1

The correct option is C $20{\text{cm s}}^{-1}$

Given:
Speed of mirror, $v_m=10{\text{cm s}}^{-1}$

Initially,
Let the distance between the object and the mirror be $x$.
For a plane mirror, object distance is equal to the image distance.

Distance between object and image:
$s_o=2x$

After time t,
Distance between the mirror and the object,
$u=x-v_{m}t$
Distance between object and image after time t:
$s_t=2x-2v_{m}t$

Distance travelled by image in time $t$ is:
$d=s_o-s_t$
$d=2v_{m}t$

Speed of the image,
$v_i=\frac{d}{t}=2v_m$
$v_i=20{\text{cm s}}^{-1}$