Question

A plane mirror is moved towards a stationary observer with a speed of 4 ms${}^{-1}$. The speed with which his image will move towards him?

• A. 2 ms${}^{-1}$
• B. 4 ms${}^{-1}$
• C. 8 ms${}^{-1}$
• D. the image will stay at rest

Answer 1

The correct option is C 8 ms${}^{-1}$

Let say the object is placed at origin.

Let the say the distance of object from mirror is $x$.

So the distance of image from mirror is $x$.

And distance between object and image is $2x$

Now in 1 sec mirror moved by $4m$.

The distance of object from mirror is $x-4$.

Distance of image from mirror is $(x-4)$

Distance between object and image is $x-4+x-4=2x-8$

Initially they were separated by 2x distance and now $2x-8$

So distance traveled by image in 1 sec is $=2x-(2x-8)=8$

Speed of image is $8m/s$