In xkcd # 964 "Dorm Poster", the cover art from dark side of the moon is "completed" with another poster that performs the inverse action:
A lens is used to turn the diverging color rays from the first prism into converging ones. Now this is just a comic and I'm not sure if correctness of the optics was a major goal, but I still wonder if this would actually work.
The problem I see is that the angles don't work out.
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On the left, (original cover art) the angle between the white ray and the purple ray is the most acute angle
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On the right, ("inverse" operation) it's exactly the opposite: here, red and white have the most acute angle
Could the rays that hit the right prism in that way really come out as one white ray?
I'm embarrassed to admit that I do not own the album myself in a form that includes the entire cover. After a bit of googling I found the original cover art with both sides here:
On this one, the angles of the individual colored rays are still diverging, because there's no additional lens involved changing that. On both prisms, red and white have the least acute angle.
However, the rays are diverging towards the prism on the left and are also diverging from the prism on the right. There's a rule in optics that rays have no direction and could be considered coming from either direction. According to this rule, there's a problem in the image, because on one prism, the rays are diverging towards it, while on the other, they are converging towards it. Given that the result (white ray) should be the same, this contradicts with the rule, doesn't it?
Can color rays that are diverging towards a prism really be recombined to a white ray in the prism on the left?
tl, dr
Which of the two prism optics pictured above is correct? Or are they both correct? Or neither one?
Best Answer
Re the album artwork, I reckon the prism on the right is almost correct, but the one on the left is incorrect.
Left prism: Noting that it'll look the same whether (a) the coherent white light beam enters the prism from the left, or (b) the many beams enter from the right. Also noting that separate colours are not shown inside the prism. (And whether there's a wavelength corresponding to that purple light.)
(a) A single beam of white light entering the left-hand prism from the left will be split into many individual colours, with higher frequency (bluer) colours being bent further towards the normal as they enter the prism, and further away from the normal as they exit the prism.
(b) Conversely, it's possible to arrange seven beams, each of a different wavelength, that enter the left-hand prism from the right such that each will be diffracted the right amount to create a coherent beam of white light exiting from the left. The blue light will be diffracted towards the normal more than red light on entering, and away from the normal more than the red light on exiting.
I think the only fault here is that the blue side of the spectrum should be a sharper angle (as it's being diffracted more than the red).
But Pink Floyd's left-hand prism is wrong and I've run out of oomph to look at the cartoon...