Patricia Dent, age 15, of South Charleston, West Virginia, for her question:
Why is the reflection in a spoon upside down?
A spoon is a very unflattering mirror, no matter which way you look at it. The curved outside of the bowl reflects a miniature face, right side up but with a bulging nose and receding cheeks. The curved inside reflects a skinny, upside down image with the chin where the forehead should be.
Mirrored reflections are full of tricky angles. The truest kind is a flat or plane mirror that reflects a properly proportioned copy of the image. But even this appears to be reversed and in a mirror image your right hand seems to be where your left hand is. fiat when a mirror is curved, all kinds of strange distortions happen to the reflected image. A well polished spoon is a mirror with two curved surfaces. The outside of the bowl is a convex mirror, the inside is a concave mirror. And it is the concave mirror that turns a reflected image upside down.
Let's start with the simplest plane mirror and see why it reflects as it does. It depends, on light and rays of light travel traight lines. They carry with them pictures of the scenery. When you stand before a mirror, the rays carrying your image strike the shiny surface and bounce back. They strike the mirror and reflect at definite angles. The angle of incidence that strikes the d mirror always equals the angle of reflection that bounces back.
Rays from the left side of your face reflect from the left side of your mirror. The left and right sides appear reversed but otherwise the image is a reasonable likeness. That is, if the mirror is smooth and flat. If there is a bump in the glass, some of the angles of incidence strike a curved surface and their angles of reflection do not harmonize with the rest of the reflection. You see a bumpy image with surprising distortions.
A concave mirror is curved like the inside of a sphere. The completed sphere would have a center. We call it the center of curvature. It is, of course, in front of the concave surface. We cannot see it, but this center of curvature is the point that turns the image upside down. Rays striking, the shiny surface are reflected in lines that angle towards each other. They meet at a point halfway between the center of the mirror and the center of curvature.. There they cross and keep going. The rays reflected from your forehead change places with those reflected from your chin. Your mirrored image is upside down.
A spoon is a concave oval and its tapering sides add to the distortions. The angles of incidence are reflected to make the image narrower than it should be and your central features appear to bulge. The upside down image, however, appears only when you are outside the center of curvature. If you were small enough to poke your face inside the spoon, between the bowl and the center of curvature, your image would be right side up with a few bulging distortions around the edges.
The concave bowl of a spoon is a small, steep sided scoop. A round and very gentle sloped concave mirror is part of a very large sphere. Its center of curvature is a long way from the shiny surface. When you look in this mirror, the point where the reflecting rays meet and cross over is behind your head. You see your face right side up and because the mirror slopes inward in a gentle scoop, your image is enlarged.