Re: [math-fun] Reflection from a moving mirror
Gene wrote: << 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?
Aside: --------------------------------------------------------------- [[[[[Above all, this reminded me that I have never understood why mirror reflection occurs. It's tempting to think it's just like a ball bouncing off a hard surface, but since a photon is much smaller than an atom (and certainly than an atom of, say, silver), I'd expect that even the smoothest mirror humans can make would have a rather irregular surface when measured on the scale of one photon.]]]]] --------------------------------------------------------------- Amiddle: But let's ignore all this stuff and assume mirror reflection from a stationary mirror is just like an ideal projectile's bouncing off a hard surface (but relativistically). In this case I'd start by using the frame of reference of the mirror, with the light source doing the moving. Since the speed of light does not depend on the motion of the light source, all three laws of reflection should hold *in the frame of reference of the mirror*. To get the final answer -- what an observer in the reference frame of the light source would see -- we'd then just need to express what we know about the mirror's frame of reference in terms of the light source's. We could simplify things by assuming the motion of the mirror is slow enough compared to c that we can ignore relativity. Assuming the mirror is moving at constant speed, this should put the kibosh to 1) and 3) above, but 2) should still be true. --Dan _____________________________________________________________________ "It don't mean a thing if it ain't got that certain je ne sais quoi." --Peter Schickele
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Dan Asimov