Friday’s XKCD comic was about Pink Floyd’s Dark Side of the Moon album cover:
I just want to pick on the optics part. Mind you, I think the humor is great!
So what’s wrong? It looks like the lens would gather the light back together again, then allowing the prism to put the colors together. Unfortunately, that trick won’t work. The easiest way to see it is to notice that the role of red and blue reverse (red closest to the left prism tip while blue is closest to the right prism tip).
If you were to put a lens, with a focal length 1/4 of the distance between the prisms, right in between the prisms, you’d definitely bring the light back to nearly a point at the first surface of the second prism. However, the angles of each color will not be what they need to be so that they’ll all come out parallel to each other out the second face.
How do I know this? Because I know what it takes to get all the colors to come out parallel (though not on top of each other). To do that, you don’t use the lens at all. That way, each color hits the second prism with exactly the angle it needs to come out at the original input angle of the first prism. The problem is, they’re not on top of each other; rather, they’re spread out spatially.
Here’s an image of how ultrashort laser people use prism pairs to compress their chirped pulses:
Note how after the first pair the colors are all parallel but that the second pair is needed to bring them back on top of each other. Note how the initial pulse has red towards the front. Apparently, this apparatus takes more time to go through for red than blue. Why? At first, it seems like red travels less far, and that’s true. However, red travels through more glass, and thus it slows down more. Very cool optical engineering.
I haven’t taken the time to do it, but I’m really curious what the light would do if you did what’s in the XKCD image. It seems to me that the light would come out with the rainbow spreading out with blue on top.