Chronology Current Month Current Thread Current Date
[Year List] [Month List (current year)] [Date Index] [Thread Index] [Thread Prev] [Thread Next] [Date Prev] [Date Next]

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



Hi Philip,
Your intuition is correct - it is not just a coincidence. Energy conservation is built into Snell's laws.
As a simpler (mechanical and one dimensional) example, consider a transverse wave on a string which has a discontinuous change of mass-density at some mid-point. How do we quantify the reflected and transmitted waves which arise at this point of medium change, given the incident wave f(x-vt)? We use the travelling wave functions, f(x +/- vt) for these waves, recognizing different velocity values in the two media. Then we impose the continuity across the boundary of the string displacement and its slope. If you calculate the expressions for energy (kinetic and potential) transport in a "string wave", you will see that the above process of imposing continuity conditions at the boundary automatically guarantees energy conservation at the boundary - ie, incident energy flow = (reflected + transmitted) energy flow.
An analogous, but more complicated, treatment of E/M waves at a boundary leads to Snell's law and includes energy conservation.

Corrections, amplifications and comments are welcome

Bob Sciamanda
Physics, Edinboro Univ of PA (Em)
treborsci@verizon.net
http://mysite.verizon.net/res12merh/

--------------------------------------------------
From: "Philip Keller" <PKeller@holmdelschools.org>
Sent: Thursday, June 10, 2010 12:40 PM
To: "'Forum for Physics Educators'" <phys-l@carnot.physics.buffalo.edu>
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.
_______________________________________________
Forum for Physics Educators
Phys-l@carnot.physics.buffalo.edu
https://carnot.physics.buffalo.edu/mailman/listinfo/phys-l




=======
Email scanned by PC Tools - No viruses or spyware found.
(Email Guard: 7.0.0.18, Virus/Spyware Database: 6.15190)
http://www.pctools.com/
=======





=======
Email scanned by PC Tools - No viruses or spyware found.
(Email Guard: 7.0.0.18, Virus/Spyware Database: 6.15190)
http://www.pctools.com/
=======