Chapter 23, Problem 3Q

To determine

To discuss:

That a plane mirror appears to reverse left and right not reverse up and downand that the front to back is also reversed and also to discuss what happens if, while standing, you look up vertically at a horizontal mirror on the ceiling.

Answer to Problem 3Q

Solution:

The mirror actually doesn’t reverse right and left, either, just as it doesn’t reverse up and down.The directions left and right are simply relative and swap once you turn 180 degrees. Also, if the mirror is held over the head, it would "reverse" vertically, and not horizontally.

Explanation of Solution

The image formation in a plain mirror:

The image formed by a plane mirror is always virtual (meaning that the light rays do not actually come from the image), upright, and of the same shape and size as the object it is reflecting. However, the image is a laterally-inverted "mirror image" of the object.

Lateral inversionmeans the apparent reversal of the mirror image's left and right when compared with the object. "Lateral" just means "sideways".... Consider your own mirror image. You don't easily perceive your front and back as reversed even though that is what happens when you face a mirror.

When the mirror is vertical to the object:

With the mirror vertical, the vertical status of the image is preserved, top is still top. If you move your right hand, the "mirror hand" that moves is still on your right side. There's no reversal in that sense. However, your right hand is perceived as the left hand of your image. The perceived reversal of intrinsic left and right is "lateral inversion". We often perceive these left-right mirror reversals. So, that's why mirror reversals are called "lateral inversion", even though that's not usually what the mirror does directly.

When the mirror is horizontal to the object:

If the mirror is held over the head, it would "reverse" vertically, and not horizontally.