Believe it or not, there is a lot of math that went into the design of the rock band’s 1973 classic.
Pink Floyd’s Dark Side of The Moon album is instantly recognizable, in large part thanks to its iconic cover art.
Whether you’ve seen it in its original vinyl form or on a t-shirt, it’s hard to think of a more recognizable image in the music industry.
And – surprisingly – there’s a lot of math behind the album cover art, with its simple geometric design and rainbow pattern.
As reported by Chalkdust Magazine, the album cover shows a beam of white light hitting a triangular prism dividing into “building blocks” (which is the rainbow).
This is an example of an “optical phenomenon” known as refraction and dispersion, which might sound a bit complicated, but it’s more understandable once you break it down.
Refraction and scattering explains why the rainbow and the incoming beam are not parallel, and how white light splits as it passes directly through the prism.
Sean Jamshidi, a doctoral student at University College London, analyzed the important mathematical points of the album cover and found three parts to focus on.
The refraction displayed on the album cover is entirely related to the speed at which a beam of light travels (depending on the medium) which can be glass, air or water.
Given the medium, mathematics can calculate the refractive index:
N = c / v
In short, c is the speed of light in a vacuum and v is the speed of light through the medium.
n is close to 1, while for glass it is around 1.5 – therefore light travels more slowly through glass than through air.
Light usually takes the fastest path from A to B, and the difference in speed between air and glass means that the shortest path in terms of distance may not be the fastest.
Moving on to angles, θ1 and θ2 are measured from the normal to the material interface.
Since glass has a higher refractive index than air (n2> n1n2> n1), a light beam passing from air into the glass will bend towards normal (θ1> θ2θ1> θ2).
When the beam leaves the other side of the prism, the reverse happens and the angle increases again.
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In terms of the change of angle on the prism, it can be calculated by a quadrilateral (consisting of the prism and the beam of light.)
This is an example of “Snell’s Law” which, in the mathematical world, is described as “a formula used to describe the relationship between angles of incidence and refraction”.
Sean continued, “Given an entry angle θ1, Snell’s law allows us to calculate θ2. We can then add the angles in the red quadrilateral, which gives θ3.
“In terms of 1 and the refractive indices n1 and n2, we apply Snell’s Law again to the point where light comes out to give us θ4.”
The multi-color beam is pretty much the only glimpse of color we’ve got in this album cover art, and while it’s minimal, it stands in stark contrast to the black background.
In technical terms, Sean explained, “Where is the wavelength of light, A and b are constants that depend on the material.
“In air, the value of b is very small (about 10−18) and therefore the refractive index can be set to a constant, which means that our light beam arrives at the prism with all the colors striking at the same place and at the same time. “
Clearly album art designer Hipgnosis knew a thing or two about math, by combining the ideas of refraction and scattering we can calculate the exact path the light beam takes.
So the next time you listen to Pink Floyd, take a look at the album art and prepare to be blown away by the math in front of you.