Built on Facts

In full early-90s nostalgia mode, you skate down the street in your roller blades. Your thrill at the excitement of the open road distracts you, and one foot goes off the pavement into the soggy soil beside the road. That foot immediately slows down due to the drag and as a result of the difference in speed between the foot on the road and the foot on the dirt steers you right off the road where I hope you don’t hurt yourself.

Refraction is the same thing, but with light.

Pass from one medium to another in which light travels at a different speed, and the light will bend. Students grumble about this sometimes. Isn’t the speed of light a universal constant, after all? Well yes – sort of. When passing through a material however, the interaction with each successive atom takes time and that in effect slows down the average speed. In fact while it’s impossible to exceed the speed of light, it’s perfectly possible to exceed the average speed of light when it’s being slowed down in a material. Cherenkov radiation is one example.

Different material slow down light by different factors. We quantify this with what we call a refractive index. Diamond has a fairly high refractive index of about 2.4, so light travels at a speed of c/2.4 in that material. This is partially responsible for the beautiful optical effects of a well-cut diamond.

What’s more interesting is the fact that the refractive index is generally not a constant. Within the same material it can be different for different wavelengths. Usually – but not quite always – higher frequency light experiences a higher refractive index. It gets bent harder. It’s not obvious at the level of classes I teach why this should be so. Since the details aren’t really the key issue, the main thing to remember whether it’s high frequency or high wavelength that gets bent most strongly. It can be difficult to remember, until I remind the class about this:

And it’s been my experience that in 2009 – a full thirty-six years after its release – everyone recognizes it. And in my sections no one ever misses any question involving refractive index as a function of wavelength.

Comments

#1 Pierce R. Butler
February 12, 2009

Hmm… that which was straight & white encounters a triangle, and emerges bent and in a rainbow formation.

Obviously, what this proves is that Pink Floyd, Isaac Newton, and probably all of physics, are gay.

And you still think American children should be exposed to this science stuff?!? Where’s Homeland Security when we need ‘em?
#2 Uncle Al
February 12, 2009

Diamond with n_D = 2.42, dispersion 0.044, Abbe number 32.3 is kicked in the nuts by rutile with n_D = 2.60, dispersion 0.280, Abbe number 5.71. Te-enriched Ge-As-Se-Te glass (TeGAST) has n_D = 3.5.

A cut diamond’s fire comes from large dispersion (small Abbe number). The higher the n_D the larger the critical angle for total internal reflection. Such a gem loses much less light to transmission at facets, giving high brilliance.

Anomalous refraction has higher frequencies experience lower refractive indices, typically near an intense, sharp optical transition – the secret to slowing light propargation in a medium to a 35 mph crawl.
#3 ObsessiveMathsFreak
February 12, 2009

When passing through a material however, the interaction with each successive atom takes time and that in effect slows down the average speed.

Is that the standard explanation for different refractive indices. I always wondered about this, particularly for gases like air. Is it the case then, that some photons will go faster through rarified mediums than others will?
#4 Emory Kimbrough
February 12, 2009

Which reminds me of the world’s #1 inherited textbook goof, passed down through endless generations of textbooks.

How many times have you seen the diagram of Newton’s experiment showing one prism splitting white light into a spectrum, then a second identical-but-inverted prism recombining the spectrum into white light? In fact, I dare you to find an elementary-school textbook series that does _not_ include the two-prism Newton diagram, like this one:

http://www.goalfinder.com/images/SPLPRO12/i4.jpg

…uh…guys…It takes _four_ such prisms to split then recombine a parallel beam of light (or two prisms plus a converging lens). I wonder how many thousands of primary- and secondary-school teachers have tried to set up the standard textbook diagram as a simple in-class demo, only to become very frustrated and puzzled at their inability to make it work.
#5 Lassi Hippeläinen
February 12, 2009

Just make sure you are looking at the front side of the album cover. The rear side is… a different story.
#6 dWj
February 12, 2009

The first context in which one encounters “c” is as the speed at which light propagates in a vacuum, but I wonder whether giving it a name other than “the speed of light” would be helpful, partly to alleviate confusion about refractive media, and partly to avoid giving the impression that light is somehow special or important to the structure of space-time. We could just call it “c”, but that seems potentially unclear. “The speed of massless propagation”? “1″ works pretty well…

(“The Minkowsky constant”?)
#7 Excited State
February 12, 2009

Not being much of a Pink Floyd fan, I couldn’t use this image to help me remember it for my optics exam. But after the exam, I went to the bookstore to sell my books back, and saw someone wearing the t-shirt, and realized that I had gotten the problem wrong.
#8 Eric Lund
February 12, 2009

@Lassi: ISTR that the back cover of the CD booklet (and presumably also the original vinyl record sleeve) is basically the same image rotated by 180 degrees and shifted to give the illusion that the spectrum is recombining into a beam of white light which is split again in an endless loop. (I’m working from memory here, as I am at the office and my copy of the CD is at home.) In that sense, it’s making the error that Emory referred to (unless you assume a converging lens at the appropriate edge). But if you consider the two sides separately, it’s still valid, since physics is invariant under proper rotations.

Or did they sell a different back cover at the time and place you bought your copy?
#9 Lassi Hippeläinen
February 13, 2009

I have it in vinyl, of course. Actually in white vinyl, which seems proper, considering the last song “Eclipse”. With the black centre label the disc looks like one.

The Quantum Pontiff has an image of borked the back side, too:
http://scienceblogs.com/pontiff/2009/02/over_at_the_fact_builders.php

Artistic Licence is always a good excuse…
#10 stebrach
February 16, 2009

The image on the back cover is not a 180 degree rotation of the image on the front cover.
#11 JM
March 16, 2009

Use the acronym: PFM

Explanation. This is courtesy of a friend of mine from uni many years ago who coincidentally was a huge Pink Floyd fan. But the acronym is the name of an italian prog rock band from the period he was also fond of PFM

It is short for Permiata Forneria Marconi (translation: Marconi’s Premier Bakery)

But in physics it means “Purple Freaks (out) Most”

Never forgotten it.