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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? |
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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.
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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. |
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