Q. A car is fitted with a convex side view mirror of focal length 20 cm. A second car 2.8 m behind the first car is overtaking the first car is a relative speed of 15 m/s. The speed of the image of the second car as seen in the mirror of the first one is
A) $\frac{1}{15}m/s$
B) 10 m/s
C) 15 m/s
D) $\frac{1}{10}m/s$
Explanation
(a) $\frac{1}{u} + \frac{1}{v} = \frac{1}{f}$
$\Rightarrow - \frac{1}{u^{2}}\frac{du}{dt} - \frac{1}{v^{2}}\frac{dv}{dt} = 0$
$\Rightarrow \frac{dv}{dt} = \ - \frac{{\ v}^{2}}{u^{2}}\left( \frac{du}{dt} \right)$
But $\frac{v}{u} = \frac{f}{u\ - \ f}$
$\therefore\frac{dv}{dt} = \ - \left( \frac{f}{u\ - \ f} \right)^{2}\left( \frac{du}{dt} \right)$
$= \left( \frac{0.2}{- 2.8 - 0.2} \right)^{2} \times 15 = \frac{1}{15}ms^{- 1}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.