Another though experiment is to imagine a ballon, with a light source in the middle. All the energy from the light is illuminating the surface of the balloon. If you inflate the ballon the surface are increases, so the light is shared more thinly. In fact for each doubling or the radius, the surface area goes up by 4. If you marked a set of points on the balloon representing light rays, and an area on the ballon the number of points in the area represent the amount of light hitting it. Then inflate the balloon to twice its diameter, the area would now be four times the size, but has exactly the same rays hitting it, so the illumination (candles per square meter, or candles per square foot) has divided by four.
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