A printer moves from a small print to one twice as large on each side and finds that the old exposure time now gives a print that is far too light. Why does enlarging the picture cost so much light?

D. Light spreads over an area scaled by magnification squared plus one, dropping intensity.

Because illuminance is light per unit area, and the area grows as the square of the magnification plus one. Doubling each side of the print spreads the same lamp output over four times the paper, so roughly two stops of exposure vanish. The paper sensitivity and the lens aperture have not changed, only the density of light arriving at the baseboard.