Question

Two plane mirrors are placed parallel to each other at a distance $$L$$apart. A point object O placed between them, at a distance$$L/3$$ from one mirror. Both mirrors form multiple images. The distance between any two images cannot be
A. $${\displaystyle \frac{3L}{2}}$$
B. $${\displaystyle \frac{2L}{3}}$$
C. $$2L$$
D. $$L$$

Answer 1

Hint Make different images using both mirrors and check distance between different images as both are plane mirrors and distance of image will be equal to distance of object from mirror and through this calculate distance of different images from mirror.

Complete step by step answer As in the given question we are given in the question with distances between the mirrors as, $$L$$
And object is at a distance of $$L/3$$from any one of the mirror and we have to find distance between any two images that cannot be there,
So assuming the mirror placed nearer to left, so first image will be near to left and it will far from right and now we will take image from second mirror and distance between the images will become
$$d={\displaystyle \frac{L}{3}}+L+{\displaystyle \frac{2L}{3}}$$
$$d=2L$$
And now again by taking images from mirrors of the images that we have created, hence we will have two images on left of left mirror and two images on the right of right mirror in which we will get distance between the images at left as, $${\displaystyle \frac{2L}{3}}$$
And by this method we will calculate the distance between images which will get as,
$$L$$
Therefore the distance between images will not be equal to $${\displaystyle \frac{3L}{2}}$$
And we can also see that there will be a pattern of distances between images in which we will never have
$$2$$ in the denominator.

Note In this question the easiest method to check distances between the images will be by making a diagram of two mirrors and objects at a given distance and can check positions of different images.