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This was an experiment I saw in my son's workbook. It said to mark out the top of your forehead and the bottom of your chin on a mirror using a whiteboard marker. Then slowly move backwards, and investigate what happens to the size of the reflection subjective to the two marks made. It actually got me quite flabbergasted. I always thought the reflection would get smaller as you moved away from the mirror.
Why is this?
The mirror gets proportionally smaller.
The explanation is the similarity of triangles. The eye and the marks on the mirror form a triangle, while the eye and the two points on the image form another triangle. The two triangles are similar, with ratio 1/2, no matter the distance.
The reason you might think the reflection gets smaller it that you most often see mirrors sitting above the bathroom sink; when you back away you see more of yourself (but you know the mirror is the same size) so you think the reflection has shrunk. It's hard to remember that half your mirror starts out full of the reflected image of your sink.
The answer is neither smaller, as is the common assumption, nor the same, as in the answer Cristi Stoica gave (although her logic gets us closer to the actual solution). In fact, as an observer pulls away from a flat mirror, his image actually gets larger! The reason for this is that the observer (like the rest of us) is not a simple 2-dimensional line, but a 3-dimensional solid.
If instead of drawing the observer as a line, we draw him as a circle, it becomes pretty easy to see that as the observer pulls back, the sight lines (tangents) from the eye to the edge of the reflected image "roll back" along the edge of the observer's body. The size of the image at the mirror's surface gets bigger (albeit not by an easily observable amount after a short distance).
At distance d=0 from the mirror, the reflected image size = 0 (you never get that in real life, because your nose keeps your eyes from getting right up to the mirror's surface.
At distance d=infinity, the reflected image size is one-half the subject's height.
