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 5.60 ft from the mirror on the left wall and 13.9 ft from the mirror on the right wall.

A. First Image= 11.2ft

B. Second Image?

C. Third Image?

Answer 1

The first image is the first reflection from the left-hand mirror. The reflection is as far behind the mirror as the person is in front of the mirror. So the distance to reflection 1

5.6ft + 5.6ft= 11.2 ft.

The second reflection is the reflection in the right mirror and again reflected by the left mirror. The reflection in the right mirror is 11.2 ft behind that mirror, which is 33.4 ft from left mirror. It will therefore appear 33.4 ft behind the left mirror.

The second reflection is then 5.60+33.4 = 39 ft from the person.

The third reflection is the reflection in the right-hand mirror of the first reflection in the left-hand mirror. That is 27.8 ft from the right-hand mirror, so it appears 27.8 ft behind the right-hand mirror. It is 44.6 ft from the left mirror and so appears 44.6 ft behind the left mirror, and 50.2 ft from the person.

therefor A = 11.2ft B = 39ft C = 50.2ft

--C--------------B-------------------A------------M1----------P-------------------M2--------------B--------------------------B'------------------

5.6ft 5.6ft 13.9ft 13.9 25.1