Question

A person walks into a room that has, on opposite walls, two plane mirrors producing multiple images. Find the distances from the person to the first three images seen in the left-hand mirror, when the person is 9.00 ft from the mirror on the left wall and 10.0 ft from the mirror on the right wall.

first image	ft
second image	ft
third image	ft

Answer 1

For plane mirrors focal length is infinity, image and object distances are same.

Left mirror is at 9 ft from person., object distance u =9 ft to the right side of left mirror , image distance v=9 ft   is formed to the left side of left mirror.

First image is formed at d₁=9 ft+9 ft =18 ft from the person.

This image serves as an object to right mirror which is at a distance of 10 ft from person.

Now object distance is u=18 ft + 10 ft =28 ft to the left side of right mirror ,, the right mirror forms an image at a distance of v = 28 ft to the right side of right mirror.

Second image thus formed is at d₂ =28 ft + 10 ft = 38 ft from the person.

This serves as object to left mirror at a object distance u=38 ft + 9 ft =47 ft to the right side of left mirror.

The left mirror forms its image at a distance of v= 47 ft to the left of left mirror.

Third image thus formed is at d₃ =47 ft +9 ft= 56 ft from the person.

Answer :

First image : 18 ft

Second image :38 ft

Third image : 56 ft