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:
Prism pair (taken from laseroptix.com)
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.
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Hmmm… I can’t convince myself that you’re right. The lens should probably be rotated to be more aligned with the “optical axis” of the dispersed light, but in my head reversibility trumps your argument. I feel a nearly irresistible urge to go in to the lab and reproduce this… Nearly.
No matter how you rotate the lens, the rays will take a path that give them an entrance angle that’s changed from my bottom picture (which is the angle they need to be at to come out parallel). It would be cool to get them to come out both parallel and on top of each other, but a single lens can’t do that.
There is a diagram from Newton’s Opica where he does just what XKCD shows to answer Decarte’s idea that colors are made from the prism rather than present in the white light. Gotta think that worked.
What Newton shows is the first part: that colors can be separated by the prism. That’s certainly true. It’s the second part that won’t work. The easiest way to see it is to take the part before the lens and flip it to be like the part after the lens. At first it seems like that’s what’s displayed. However, the roles of the colors reverse.
cool! very confusing indeed.
Adding a second lens would turn this into a 4-f pulse-shaper, which should take care for this matter:
http://www1.chem.leeds.ac.uk/PICNIC/picnic%20pictures/leeds6a.jpg
http://en.wikipedia.org/wiki/File:Pulseshaper_neutral.svg
right, Ori, exactly!