|MadSci Network: Physics|
Hi, 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: http://www-mep.phy.anl.gov/atta/ 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, Regards Ben
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