“Compare red nail polish to red ink: both are red, but the nail polish will be visible on black paper because it reflects light. The ink won’t be, because it absorbs light.”
doesn't seem right to me, but I'm not an expert. The ink doesn't reflect light? If you put a drop of red ink on a sheet of glass, it won't look red? Isn't the difference because the ink will soak in to the paper while the polish will sit on top of it?
Ink is transparent; It lets through or absorbs light that hits it. Red ink lets though red light and absorbs the rest. Shine white light through it, and it will look red.
Shining white light on a black piece of paper with red ink on it will look black. What light is not absorbed by the ink is absorbed instead by the paper.
Of course red ink reflects light, as you say, but that is just because of reality. It is not essential to its function. If it were possible to make a 100% non-reflective ink, it would work perfectly well.
I hope this clears it up :)
Ink is semi-transparent. So think of white paper as a light source, and the red ink absorbs all colors but red coming off the paper before it reaches your eye.
Nail polish isn't transparent, but it still looks red because it simply reflects red light. That light never reaches the paper -- it bounces off the nail polish and comes back to your eye.