I still don't get it, Gene. We're talking about _reflection_, not refraction, so the motion of the reflector can only affect something if it can be sensed. Short of the wavelength of the light being able to "feel" the bumps, I don't see how that can happen. If the flat mirror moves in such a way that the perpendicular distance between it and the sender or receiver changes, then the light can sense the motion; otherwise not. The "re-radiating" idea is only necessary if the light can feel the bumps. Otherwise, the light doesn't "see" anything. I would imagine that this situation is tested inside some of the accelerators around the world all the time because there are all kinds of light waves bouncing around inside a tube with a vacuum. What's the answer? At 08:04 AM 9/4/2008, Eugene Salamin wrote:
----- Original Message ---- From: Henry Baker <hbaker1@pipeline.com> To: Eugene Salamin <gene_salamin@yahoo.com> Cc: math-fun <math-fun@mailman.xmission.com> Sent: Wednesday, September 3, 2008 6:04:02 PM Subject: Re: [math-fun] Reflection from a moving mirror
If this experiment occurred in a vacuum, and the wavelength of the light far exceeded the surface roughness of the mirror, how would the light even know that the mirror was moving? -------------------- Consider the propagation of light in a medium of refractive index n. When the medium is at rest, the velocity is c/n. If the medium moves with velocity v in the same direction as the light, the velocity of the light follows from the relativistic velocity addition formula:
v' = (c/n + v)/(1 + (v/c)/n) = c/n + (1 - n^-2) v,
approximately for v << c. This was measured interferometrically in flowing water by Fizeau in 1851, and the (1 - n^-2) "aether drag" coefficient was confirmed. Modern electronics permits the experiment to be done by timing pulses of light. In this case, the group index replaces the refractive index in the above equations.
How does the light even know that the water is moving?
Remark about the velocity addition formula. Parametrize the velocity by v/c = tanh s. Then v1 "+" v2 = v3 becomes s1 + s2 = s3. This s is the natural group parameter for Lorentz boosts, just as angle is for rotations.
Gene
At 05:47 PM 9/3/2008, Eugene Salamin wrote:
Test your physical intuition. We know that when light reflects from a stationary mirror
(1) The frequency of the reflected light equals the frequency of the incident light,
(2) The direction of the incident ray, the direction of the reflected ray, and the mirror normal are coplanar, and
(3) The angle of reflection equals the angle of incidence.
Suppose however, that the mirror is moving parallel to its surface. Do these three principles of reflection continue to hold?
Gene