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 7.00 ft from the mirror on the left wall and 6.00 ft from the mirror on the right wall.

first image: ft

second image: ft

third image: ft

Answer 1

1st image

By direct reflection

Distance = 7 ft

2nd image

1st Ray reflect from right side mirror and then come for left side mirror.

So image of right side mirror acts as object for left side mirror. So distance of object = 7+6+6 = 19 ft

So 2nd image distance = 19 ft

Now for 3rd image

3rd image form when Ray 1st reflect from left side then right side and then again from left side.

So 1st image of left side acts as object for right side

So distance of object = 7+7+6 = 20 ft

So image distance for right side mirror = 20 ft

Now Ray reflect from left side mirror so image of right side mirror acts as object for left side.

So distance of object = 20+6+7 = 33 ft

So distance of 3rd image = 33 ft

So distance of images from person

1st image = 7+7 = 14 ft

2nd image = 20+7 = 27 ft

3rd image = 33+7 = 40 ft