Saturday, September 20, 2008

Depth Perception, part II

The goal is to understand why a mirror allows depth perception, but a television or painting does not. In the first part of the answer, I demonstrated that depth perception relies on seeing the same object with two eyes. Eyes detect to angle to the object, but the two eyes will detect different angles. The bigger the difference between these angles, the closer the object.

Here's a diagram of a television and a mirror. A pair of eyes looks at each, and sees a purple ball.

Notice that for the television, the light rays converge at the screen. But the light rays bounce off the mirror in different places, converging only at the ball.

Although the ball is actually in front of the mirror, there's a problem. The light you detect is the light right at your eyes. You can't detect the light's entire path. So if you want to reconstruct the path of the light to see where light beams intersect, you just have to guess. That's what your brain does, and it simply guesses that the light doesn't bend or bounce or anything like that. It just goes back straight to the source. So the situation for the mirror is that the light actually travels the solid line, but your brain thinks it travels the dotted line.

An object can appear to have a depth well back behind the mirror. Objects on a television screen will always appear to be right at the television screen, since that's where the lines leading to those objects converge.

The essential difference is that the television or painting is generating the light you see. The light from any given point of the painting radiates out in all directions, always showing the same object.

The mirror doesn't generate its light - it reflects it. So if two observers are in different places and look at the same spot on a mirror, they see different objects there, not the same.

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