Posted by Dave Bacon on February 12, 2009 Over at the fact builders blog, the fact master discusses The Physics of….Pink Floyd. Being two areas I greatly enjoy, I was reminded by the fact builders picture of the cover of “The Dark Side of the Moon” of a little known piece of Pink Floyd strangeness. Anyone notice something peculiar about the back and cover of DSOTM:
Update: Ian provides a picture of the inside of the DSOTM, where, we find, all hell breaks loose:
Is it that the order of the colours is reversed (wrt the prism) on the back cover?
Years ago, at a conference, someone put up a similar looking picture from the cover of Nature, which had the light bending the wrong way. Then they put up the front cover of this album and said something along the lines of “at least the rock stars can get it right”.
Not only the order of the colors is strange. The colors are converging as they get farther from the prism, instead of diverging as they should.
Refraction, not diffraction. It’s a prism, not a slit.
</optics nerd>
Supposedly the prism used is still here (physics department at Imperial College).
…and now I think about it, maybe John Pendry’s work on metamaterials http://en.wikipedia.org/wiki/Metamaterial was all just about correcting the back cover!
I believe the only problem is the converging, rather than diverging rays.
There is no particular reason to assume, without otherwise being told, that it is the same prism on the front and back covers. Materials exist with both normal (dn/d(lambda) < 0) and anomalous (dn/d(lambda) > 0) dispersion, so there is no particular reason to assume any order of the colors. The two prisms just have different dispersion relations.
Now, convergence is more difficult, but still not impossible. On crossing from a negative to positive index material, converging rays could diverge, and vice versa. However, the diffraction angles are not consistent with negative refraction, so we must rule this out and assume there is a mistake.
the album is a cycle, the white light goes in one prism and is split. the theory at that point of the album artist is that if you fed it into another prism it would converge into the single white beam.
if you keep flipping the album around you can follow the light as it goes in and out of the prism.
this is why the rainbow is diverging from one prism and converging on the other.
have not tried the experiment to see if it would really work like that, don’t have a prism about me at the moment.
The answer to your question is: Yes, everyone’s noticed it. Especially anyone who’s owned it on vinyl.
Incidentally, the pattern is also continued on the inside of the album sleeve, where the rainbow pattern becomes an ECG. I don’t think the inside sleeve was reproduced on the CD, though.
What pter said.
Artistic licence and all that.
Reciprocity – if you want to recombine the rays you got from the prism on the front cover into a white beam again, you have to create a situation which is the time reverse of that on the front cover. (If you imagined that there were arrows pointing in the direction the rays are going, reverse them).
So, the image on the back cover isn’t possible if both the prisms are the same kind (glass, with positive RIs). You need to have a converging set of rays.
Newton did experiments where he split light with one prism and recombined it with another. He used a lens in between them.
One other funny thing occurs in the right-hand image above. The blue light bends a lot when it enters on the left side and only a little when it leaves on the right, while the red light bends only a little on the left side and a lot on the right. But whatever the order of colors is, it seems like the same color, either red or blue, should be the one that bends the most on both sides.
Tez, there is also the possibility that the prism is in Sir Peter’s basement… 
I never liked the fact that the light inside the prism in the cover seems to be grayish and not in color but I am not sure if that is really unphysical. I mean, can you actually see the light inside a prism? I am not so much worried about the order of colors you see. You could see the whole thing in a mirror (or could you?)
As Andrew said, the flipping of the colors is due to opposite dispersion relations. The convergence is due to the left half of the left prism having been doped to have a gradient index so that it acts as a lens (as Matt mentioned above).
The only peculiar thing here is that there are 6 discrete colors. If the light was broadband, you should have a continuous range of colors. If the light was made of 6 discrete colors, they should appear as 6 separated narrow lines (rather than adjacent bands).
Incidentally, the pattern is also continued on the inside of the album sleeve, where the rainbow pattern becomes an ECG. I don’t think the inside sleeve was reproduced on the CD, though.
Indeed. And the vinyl came with additional poster inserts as well, though not all continued the theme.
I think everyone above has hit on the varying oddities in this. But we shouldn’t be surprised by multiple oddities. Storm Thorgerson’s album covers were often as nuanced and perplexing as the Floyd boys themselves.
With all due respect to Newton, both industrially and fashion-aware, there is no spectral band “indigo.” Nor Pink, for that matter (although Philip K. Dick claimed otherwise).
The Mathematics of Rainbows
If you look carefully on the inside of the principal violet arc you will frequently see several pale violet arcs, interspersed with some paler greenish bands. Where do they come from?…
Introduction
The theory of the rainbow that everyone learns in high school physics classes is pretty much the one that René Descartes came up with almost 400 years ago. But if you look carefully at the rainbow in this picture, just underneath its arch, you will see bands that this familiar theory does not explain.
This remarkable photograph is Double-alaskan-rainbow.jpg from the Wikipedia Commons.
It and all images derived from it in this article are distributed under the Creative Commons Share-Alike license.
The correct explanation of these bands depends on the wave theory of light developed in the early nineteenth century, primarily by Auguste Fresnel. The correct application of Fresnel’s theory to rainbows is due to the English mathematician George Biddell Airy, writing about 1840. This theory was superseded in turn by the electromagnetic theory of Maxwell. The description of the rainbow that Maxwell’s theory produces is in some extreme cases quite different from the one produced by the wave theory. But for practical purposes Airy’s theory is sufficient.
Airy’s theory requires numerical evaluation of an improper integral named after him. How to carry out this evaluation also has an interesting history. [truncated]
Bill Casselman
University of British Columbia, Vancouver, Canada
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