Re: [math-fun] newton rotating liquid mirror
I've no clue why the mailing list software didn't like this. Bill Ackerman's note is at the bottom. Good luck untangling the quoted stuff in the middle. --Rich ---- Date: Thu, 05 Mar 2015 13:24:37 -0500 Subject: Re: [math-fun] newton rotating liquid mirror From: Bill Ackerman <wbackerman@gmail.com> On 05-Mar-15 12:50, Eugene Salamin via math-fun wrote: [Hide Quoted Text] A lake at the South Pole would have the shape of the geoid, the equipotential surface due to gravity and centrifugal force. Would you expect the lake to somehow have a concave surface? Think about cost and maintainability. Which is easier, a liquid mirror on Earth with an extremely elaborate servo controller, or one on an asteroid? -- Gene From: Henry Baker <hbaker1@pipeline.com> To: math-fun <math-fun@mailman.xmission.com> Sent: Thursday, March 5, 2015 9:37 AM Subject: Re: [math-fun] newton rotating liquid mirror Couldn't we build such a mirror at the South Pole using just the Earth's rotation? It would want to be pretty big, but there's lots of open space down there. Even if you didn't care about visible light wavelengths, you could still provide a bunch of liquid-filled tubes to distribute the correct height to each location where you could put a small radio antenna. Alternatively, you go through the asteroid belt to find a decent size spinning asteroid and install your mirror there. Yes, you don't have much control over where it points, but there are some types of investigations where that might not matter. At 08:56 AM 3/5/2015, Warren D Smith wrote: Adam P.G's blog seems amazinger and amazinger. I don't understand his life census, but it too seems amazing. I noticed some post by him about the spinning liquid parabolic mirror being invented by Isaac Newton. I actually made one of those mirrors once using a phonograph turntable and plastic resin. The mirror was quite decent, although I daresay it was not good enough for a quality telescope. A lot of people may be willing to donate an old phonograph turntable no longer useful to them for music. _______________________________________________ math-fun mailing list math-fun@mailman.xmission.com https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun _______________________________________________ math-fun mailing list math-fun@mailman.xmission.com https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun Ignoring Gene Salamin's objection that the shape of the mirror has to follow a geoid (or, equivalently, that, if the mirror is large, one has to compensate for the fact that gravity doesn't pull "straight up" when far from the center), the focal length of the mirror would be about 1/4 of an astronomical unit (distance from Earth to Sun). There are better ways of utilizing the required technology to make good telescopes. The idea of faithfully recreating very old historical techniques and artifacts with modern equipment comes up every once in a while. Presumably for nostalgic or entertainment reasons. Perhaps the most famous of these was the reconstruction of Charles Babbage's mechanical "difference engine" at the British museum in 1991. (The bicentennial of Babbage's birth.) The machine works, following Babbage's plans almost exactly. Imagine--getting the design for a computer exactly right, the first time. Take that, Intel!
Suppose instead we have a solid, *flat* mirror that we rotate in its own plane about the center of the mirror. Does this affect how it will reflect light, maybe in a very subtle way? --Dan
Only at wavelengths comparable to the inter-atomic distance, where refraction effects start to occur. On Thu, Mar 5, 2015 at 12:36 PM, Dan Asimov <asimov@msri.org> wrote:
Suppose instead we have a solid, *flat* mirror that we rotate in its own plane about the center of the mirror.
Does this affect how it will reflect light, maybe in a very subtle way?
--Dan _______________________________________________ math-fun mailing list math-fun@mailman.xmission.com https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
-- Mike Stay - metaweta@gmail.com http://www.cs.auckland.ac.nz/~mike http://reperiendi.wordpress.com
Are those visible wavelengths? (If not, then using false color images:) what would that look like?
On Mar 5, 2015, at 1:00 PM, Mike Stay <metaweta@gmail.com> wrote:
Only at wavelengths comparable to the inter-atomic distance, where refraction effects start to occur.
On Thu, Mar 5, 2015 at 12:36 PM, Dan Asimov <asimov@msri.org> wrote:
Suppose instead we have a solid, *flat* mirror that we rotate in its own plane about the center of the mirror.
Does this affect how it will reflect light, maybe in a very subtle way?
--Dan _______________________________________________ math-fun mailing list math-fun@mailman.xmission.com https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
-- Mike Stay - metaweta@gmail.com http://www.cs.auckland.ac.nz/~mike http://reperiendi.wordpress.com
_______________________________________________ math-fun mailing list math-fun@mailman.xmission.com https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
Sorry, I meant diffraction, not refraction (though x-rays pass through lithium metal, so they make x-ray optics out of it). For diffraction at inter-atomic distances, the light would be x-rays. The atoms would spread ever so slightly, and at a given diffraction angle, the light would be "redder". On Thu, Mar 5, 2015 at 1:02 PM, Dan Asimov <asimov@msri.org> wrote:
Are those visible wavelengths? (If not, then using false color images:) what would that look like?
On Mar 5, 2015, at 1:00 PM, Mike Stay <metaweta@gmail.com> wrote:
Only at wavelengths comparable to the inter-atomic distance, where refraction effects start to occur.
On Thu, Mar 5, 2015 at 12:36 PM, Dan Asimov <asimov@msri.org> wrote:
Suppose instead we have a solid, *flat* mirror that we rotate in its own plane about the center of the mirror.
Does this affect how it will reflect light, maybe in a very subtle way?
--Dan _______________________________________________ math-fun mailing list math-fun@mailman.xmission.com https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
-- Mike Stay - metaweta@gmail.com http://www.cs.auckland.ac.nz/~mike http://reperiendi.wordpress.com
_______________________________________________ math-fun mailing list math-fun@mailman.xmission.com https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
_______________________________________________ math-fun mailing list math-fun@mailman.xmission.com https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
-- Mike Stay - metaweta@gmail.com http://www.cs.auckland.ac.nz/~mike http://reperiendi.wordpress.com
If it spins fast enough there will be shifts due the angle of incidence differing from the angle of reflection http://physics.weber.edu/galli/RelativisticReflection.pdf This would distort any image in the mirror. Brent On 3/5/2015 12:36 PM, Dan Asimov wrote:
Suppose instead we have a solid, *flat* mirror that we rotate in its own plane about the center of the mirror.
Does this affect how it will reflect light, maybe in a very subtle way?
--Dan _______________________________________________ math-fun mailing list math-fun@mailman.xmission.com https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
For a mirror moving parallel to its surface: (1) the incident ray, the reflected ray, and the surface normal remain coplanar, (2) the angle of reflection equals the angle of incidence, and (3) the frequency of the reflected light equals the frequency of the incident light. This follows from a Lorentz transformation from the rest frame of the mirror to the lab frame. However, if the frequency of the light in the rest frame differs significantly from that in the lab frame, the reflection may not behave as it would if the mirror were not moving, e.g. X-ray diffraction might appear. -- Gene From: meekerdb <meekerdb@verizon.net> To: math-fun <math-fun@mailman.xmission.com> Sent: Thursday, March 5, 2015 1:30 PM Subject: Re: [math-fun] newton rotating liquid mirror If it spins fast enough there will be shifts due the angle of incidence differing from the angle of reflection http://physics.weber.edu/galli/RelativisticReflection.pdf This would distort any image in the mirror. Brent On 3/5/2015 12:36 PM, Dan Asimov wrote:
Suppose instead we have a solid, *flat* mirror that we rotate in its own plane about the center of the mirror.
Does this affect how it will reflect light, maybe in a very subtle way?
--Dan _______________________________________________
participants (5)
-
Dan Asimov -
Eugene Salamin -
meekerdb -
Mike Stay -
rcs@xmission.com