You are sitting in a parked car and you notice a boy running towards…

The correct answer is Option (3) → The boy will appear to be running towards the car and his speed will appear to be continuously increasing

The side view mirror of a car is a convex mirror. Its image is virtual and erect, and the image moves only a small distance when the object moves far away, but more and more as the object comes closer.

With the object at distance \( x \) in front of a convex mirror of focal length \( f \), the mirror equation puts the image at distance \( fx/(x + f) \) behind it. Differentiating:

    \( \displaystyle v_{\mathrm{image}} = \left(\frac{f}{x + f}\right)^{2} v_{\mathrm{boy}} \)

As the boy approaches, \( x \) falls, so the factor \( (f/(x + f))^{2} \) grows. The image always approaches, and its speed keeps increasing, even though the boy's speed is constant.

NCERT (2026-27):
The Mirror Equation – “… Although the jogger has been moving with a constant speed, the speed of his/her image appears to increase substantially as he/she moves closer to the mirror. This phenomenon can be noticed by any person sitting in a stationary car or a bus. In case of moving vehicles, a similar phenomenon could be observed if the vehicle in the rear is moving closer with a constant speed.”