You are standing 18 m in front of a flat mirror. How far behind is your image?

Question

What is the magnification of your image?

Answer 1

Flat mirrors are equivalent to curved mirrors with infinite focal lengths. So we can just plug it into the mirror equation:

1/ (focal length) = 1/ (object distance) + 1/ (image distance)

1/ (infinite focal length ) = 1 / (18cm object distance ) + 1/ (image distance)

0 = 1/(object dist ) + 1/ (image distance)

So from this last line, we can clearly see that the image distance is equal to the negative of the object distance - that means it is 18cm behind the mirror.

The magnification, which is the image distance divided by the object distance, is 1. It is often easiest to draw a ray diagram to determine whether it is inverted or upright, but in this case with a regular mirror you can just think about it - flat mirrors show upright images.