If a plane mirror is approaching you at a speed of \( 10\,\mathrm{m\,s^{-1}} \), the speed with which your image approaches you is
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → \( 20\,\mathrm{m\,s^{-1}} \)
A plane mirror is a spherical mirror of infinite radius of curvature, so \( f\to\infty \). The mirror equation \( 1/v+1/u=1/f \) then gives the image position directly.
\( \begin{aligned} \frac{1}{v}+\frac{1}{u} &= \frac{1}{f} \\ &= 0 \end{aligned} \)
\( \Rightarrow\; v=-u \)
So the image is as far behind the mirror as the object is in front of it. If you are at a distance \( d \) from the mirror, your image is \( d \) behind it, and the distance between you and your image is \( 2d \).
As the mirror approaches you, \( d \) decreases at \( 10\,\mathrm{m\,s^{-1}} \). The distance \( 2d \) to your image therefore decreases twice as fast:
\( \begin{aligned} \text{speed of the image} &= 2\times\frac{\Delta d}{\Delta t} \\ &= 2\times10\,\mathrm{m\,s^{-1}} \\ &= 20\,\mathrm{m\,s^{-1}} \end{aligned} \)