A Virtual Image

(a) An image formed by a mirror.

We can understand a mirror image using a ray diagram. The figure shows several light rays, a, that originated by diffuse reflection at the person's nose. They bounce off the mirror, producing new rays, b. To anyone whose eye is in the right position to get one of these rays, they appear to have come from a behind the mirror, c, where they would have originated from a single point. This point is where the tip of the imageperson's nose appears to be. A similar analysis applies to every other point on the person's face, so it looks as though there was an entire face behind the mirror. The customary way of describing the situation requires some explanation:

Customary description in physics: There is an image of the face behind the mirror.

Translation: The pattern of rays coming from the mirror is exactly the same as it would be if there was a face behind the mirror. Nothing is really behind the mirror.

This is referred to as a virtual image, because the rays do not actually cross at the point behind the mirror. They only appear to have originated there.

Self-Check

Imagine that the person in figure (a) moves his face down quite a bit - a couple of feet in real life, or a few inches on this scale drawing. Draw a new ray diagram. Will there still be an image? If so, where is it visible from?

Answer

You should have found from your ray diagram that an image is still formed, and it has simply moved down the same distance as the real face. However, this new image would only be visible from high up, and the person can no longer see his own image. If you couldn't draw a ray diagram that seemed to result in an image, the problem was probably that you didn't choose any rays that happened to go away from the face in the right direction to hit the mirror.

The geometry of specular reflection tells us that rays a and b are at equal angles to the normal (the imaginary perpendicular line piercing the mirror at the point of reflection). This means that ray b's imaginary continuation, c, forms the same angle with the mirror as ray a. Since each ray of type c forms the same angles with the mirror as its partner of type a, we see that the distance of the image from the mirror is the same as the actual face from the mirror, and lies directly across from it. The image therefore appears to be the same size as the actual face.

Discussion Questions

A	The figure shows an object that is off to one side of a mirror. Draw a ray diagram. Is an image formed? If so, where is it, and from which directions would it be visible?