Answer to the Exposure Riddle
To understand why the exposure doesn't change as you move the camera farther from the wall, you first need to understand the inverse square law. The inverse square law states that the amount of light that falls on an area of fixed dimensions diminishes with the square of the distance from the source. Examine the diagram below, which shows that the amount of light falling on square A at distance D is four times greater than the amount of light falling on the same-size square at distance 2D (twice as far from the source).
The inverse square law is easiest to understand if you think about a point light source like a star. However, we can apply the inverse square law to nearby objects as well. Think of the wall as being composed of a very large number of very small points. Light scatters from each of these points in all directions. As you move the camera back, the lens captures fewer and fewer of the rays coming from each point, but there are more points in the field of view. Double the distance from the source and the intensity of light from each point drops by a factor of four. That is compensated for by the increase in the number of points (the area of the wall) within the field of view, again by a factor of 4. The two factors balance out, and the exposure is the same.
So if each point on the wall is only one-fourth as bright when you move the camera backwards to double the original distance from the wall, why don't our eyes see the wall as darker? Probably for the same reason the camera sees the wall as having the same brightness. Less light from each point enters our pupils, but we see many more points in our field of view as we glance at the wall, so the brightness appears to be the same.
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