Question

A point object is placed midway between two plane mirrors a distance apart. The plane mirrors form an infinite number of images due to multiple reflections. The distance between nth order images formed in the two mirrors is
${\text{A}}{\text{. }}na \\\ {\text{B}}{\text{. 2}}na \\\ {\text{C}}{\text{. 0}}{\text{.5}}na \\\ {\text{D}}{\text{. }}{n^2}a \\\$

Answer 1

The object is placed midway between two plane mirrors which means it is at equal distance from each mirror. The images formed by the plane mirror are at the same distance from the mirror as the object from the mirror.

Complete step-by-step answer:
We are given that an object is placed midway between two plane mirrors a distance apart.
When we have two plane mirrors placed parallel to each other as shown in the figure and an object is kept between these mirrors, then light from the object is incident normally on the mirror.

The number of images formed is equal to the number of reflections taking place. Since in our case, we have innumerable number of reflections taking place between two mirrors, the number of images formed is infinite.
As we know that the images formed in a plane mirror are at the same distance from the mirror as the object from the mirror. The object given is at equal distance from each mirror and all the infinite images will also be at equal distance from adjacent images.
Now the distance between the mirrors is a and based on the above reasoning, the distance between the nth images in either mirrors will be na.
So, the correct answer is “Option A”.

Additional Information: The reflection of light by a plane mirror follows all the laws of reflection which are given as
1. The incident ray of light, the reflected ray of light and the normal to the plane of the mirror, all lie in the same plane.
2. The angle of incidence of light is always equal to the angle at which the light gets reflected.

Note: The number of images formed by two parallel mirrors does not depend on the distance between the mirrors. Only the distance of image from the mirror changes with the change in the distance of the object from the mirror.