Question

A flat mirror $M$ is arranged parallel to a wall $W$ at a distance $1\text{m}$ from it. The light produced by a point source $S$ kept on the wall is reflected by the mirror and produces a light spot on the wall. The mirror moves with velocity $v$ towards the wall.

• A. The spot of light will move with the speed $v$ on the wall.
• B. The spot of light will not move on the wall.
• C. As the mirror comes closer, the spot will became larger and shift away from the wall with speed larger then $v$.
• D. The size of the light spot on the wall remains the same.

Answer 1

Answer: (B), (D)

The size of the light spot on the wall remains the same.

Here, we are asked about the effect on dimension (size) of the image on the wall. In case of a plane mirror we know it has a property that the image distance must be equal to object disatnce. Hence, in this case $u=v$, thus magnification
$\left|m\right|=\frac{v}{u}=1$

Hence we can say the ratio of height of image and object is $1$ or size of image is equal to size of object. Hence option D is correct.

Further, the situation could be described in the figure.

Now, if the mirror starts moving, as both mirror and wall are parallel, there won't be any deflection in the height of the image. So the spot won't move on the wall.
Hence option B is also correct.