MadSci Network: Physics

Re: Why is reflection independent of the wavelength ?

Date: Wed Jul 6 16:07:26 2005
Posted By: Ben Tordoff, Grad student, Lasers in nuclear physics, University of Jyvaskyla
Area of science: Physics
ID: 1118827131.Ph

Unfortunately I don't have the Hecht book to hand so I am unable to read 
that author's line of reasoning so I shall explain in terms of my own. 
When discussing the wavelength dependence of reflection one assumes 
conservation of energy and momentum. 

E=hc/lambda (Planck constant x speed of light/wavelength) = pc (momentum 
x speed of light).

Equating the relativistic and classical energy expressions for energy of 
a photon, we arrive at the De Broglie wavelength (without actually doing 
the full derivation)

lambda = h/p

So the wavelength of the light is inversely proportional to the momentum 
of the photon. Assuming conservation of momentum (as is done for perfect 
reflection), the wavelength does not change. To prove that photons have 
momentum and can transfer it to matter, I refer you to atom traps. A 
special type of these traps uses lasers to stop individual atoms and hold 
them in place by transferring photon momentum to the atom so that the 
overall momentum of the atom is zero and it does not move. The url below 
is a link to a leading group in the US who developed this technique and 
has shown it to have many applications:

From another point of view, in the field of laser physics, when 
performing resonator calculations (you do these to see if a system will 
lase amongst other things) a flat mirror takes the mathematical form of 
the identity matrix, ie the matrix which describes the propagating wave 
is unchanged when operated on by the mirror operator. If you are not 
talking about a perfectly reflecting flat mirror then you use a different 
operator matrix,



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