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Re: [Phys-l] question about total internal reflection



Actually, sensors can very easily detect such evanescent waves (my dissertation dealt with evanescent acoustical waves), and they can be scattered. The problem is that the presence of a detector alters the conditions of the system, and evanescent waves may be transformed into propagating waves. In fact, the conditions that one needs to do the detection (moderately-pressure release, for example, in the case of acoustical waves) are exactly the conditions needed to do the evanescent->propagating conversion. One gets into the situation of having a good model for the sound of the falling trees in a forest only when one isn't in the forest.

Newton, in his "Opticks", gave some remarkably *right* explanations of how light will behave in such circumstances, including an essentially correct explanation of the Goos-Hanchen effect (called the Schoch shift in acoustics). However, I think that George Green (perhaps 1838?) gave the first mathematical derivation, and that it was the first example of taking complex numbers seriously and getting a real effect out of extending angles (wavenumbers, etc.) into the complex domain. If anyone knows of an earlier example, I'd love to hear of it!

Philip, unfortunately, I cannot give a simple explanation of all of this. If one actually calculates the Poynting vector for these situations, one can track the energy and momentum flows in these cases. But I can indeed confirm that the results do agree with experiment!

(See, e.g., "Evanescent Acoustic Waves From Subcritical Beam Illumination: Laboratory Measurements Near a
Liquid–Liquid Interface", one of my papers)






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As a species, we are forever sticking our fingers into the electric socket of the Universe to see what'll happen next. It's a trait that'll either save us or kill us, but by god it's what makes us human beings. I'd rather be in the company of people who look at Mars than people who contemplate humanity's navel -- other worlds are better than fluff. ~~Sir Terence David John Pratchett
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________________________________
From: Philip Keller <PKeller@holmdelschools.org>
To: Forum for Physics Educators <phys-l@carnot.physics.buffalo.edu>
Sent: Thu, June 10, 2010 10:40:54 AM
Subject: [Phys-l] question about total internal reflection

1. One implication of Snell's law is that for light incident on a boundary with a less dense medium, there must be a maximum angle where transmission can occur. This angle can be calculated by assuming that the refracted light makes a 90 degree angle with the normal in the second medium. But in fact, there is no refracted light -- if you place a sensor along the surface, you fail to detect light. The light has been internally reflected, as a well placed sensor would reveal.

2. This is not a sudden transition -- in fact, a fraction of the light is reflected at any angle of incidence. The reflected portion increases with angle of incidence and the transmitted portion decreases to zero..at that same critical angle? But why is that? It can't just be coincidence that the law that determines the fraction of light transmitted at a given angle from one medium to another happens to predict zero transmission at precisely the angle that Snell's law says it should.

Can anyone point me toward an explanation?

Thanks.
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