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focusing properties of parabolic mirrors
Suppose we take the parabola y = x^2 and rotate it around the
y axis, outside the x-y plane or "page". The result is a paraboloid surface. If the correct side of the surface is reflective, rays of light parallel to the y axis, oriented in the negative-y direction, will reflect off the surface and all pass through a common point, the focus. (source: Greek geometers) What happens with parallel rays that are not parallel to the y axis? Do they pass through a common point after being reflected off the surface? Wikipedia has an entry about "Coma" he http://en.wikipedia.org/wiki/Coma_%28optics%29 I'm inclined to believe that parallel off-axis rays will not pass through a common point after being reflected off the paraboloid surface... David Bernier |
#2
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they don't; probably some sort of caustic surface.
it can just be considered as one end of am ellipse and one of its foci. David Bernier wrote: What happens with parallel rays that are not parallel to the y axis? Do they pass through a common point after being reflected off the surface? --ils ducs d'Enron! http://tarplet.net/bush12.htm |
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"David Bernier" wrote in message .. . Suppose we take the parabola y = x^2 and rotate it around the y axis, outside the x-y plane or "page". The result is a paraboloid surface. If the correct side of the surface is reflective, rays of light parallel to the y axis, oriented in the negative-y direction, will reflect off the surface and all pass through a common point, the focus. (source: Greek geometers) What happens with parallel rays that are not parallel to the y axis? Do they pass through a common point after being reflected off the surface? Wikipedia has an entry about "Coma" he http://en.wikipedia.org/wiki/Coma_%28optics%29 I'm inclined to believe that parallel off-axis rays will not pass through a common point after being reflected off the paraboloid surface... It depends upon the f/d ratio. If fast (4 to 6) then it goes out of focus quickly off axis. If the mirror is slow (10 to 14) then it does not. there is a crossover at the larger f/d ratios (over 10) where the mirror can be spherical and not parabolic. Therefore the rays as you ask above would be in focus, the same focus. (f,d =focal length, diameter) |
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David Bernier wrote:
description of parabolic surfaces (source: Greek geometers) What happens with parallel rays that are not parallel to the y axis? Do they pass through a common point after being reflected off the surface? Wikipedia has an entry about "Coma" he http://en.wikipedia.org/wiki/Coma_%28optics%29 I'm inclined to believe that parallel off-axis rays will not pass through a common point after being reflected off the paraboloid surface... David Bernier Hi David, one click from the wikipedia website is http://www.opticalmechanics.com/about_coma.htm which decribes the effect of coma for newtonian telescopes, which IMHO is what you're looking for. Best Regards, Joerg -- Joerg Glissmann - Guending - Germany remove PANTS to reply ;-) |
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wht is the diameter of a parabola?
NG, Sing wrote: It depends upon the f/d ratio. If fast (4 to 6) then it goes out of focus quickly off axis. If the mirror is slow (10 to 14) then it does not. there is a crossover at the larger f/d ratios (over 10) where the mirror can be spherical and not parabolic. Therefore the rays as you ask above would be in focus, the same focus. (f,d =focal length, diameter) --ils ducs d'Enron, Strep Throat, the Bay o'Pigs & Iran-contra! http://tarpley.net/bush7.htm http://tarpley.net/bush12.htm http://tarpley.net/bush18.htm |
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In article ,
David Bernier writes: ...a paraboloid surface. If the correct side of the surface is reflective, rays of light parallel to the y axis, oriented in the negative-y direction, will reflect off the surface and all pass through a common point, the focus. What happens with parallel rays that are not parallel to the y axis? Do they pass through a common point after being reflected off the surface? No, but rays nearly parallel to the axis pass near a common point. The result is that a simple paraboloid produces acceptable images over a finite angular field of view, the size being determined by the focal ratio of the paraboloid and by how bad an image can be tolerated. As you indicate, coma is usually the biggest aberration, but astigmatism and spherical aberration (and higher order aberrations) are present too. Just for fun, I tried ray-tracing a 100 mm diameter f/10 paraboloid. As expected, rays parallel to the axis focus (ignoring diffraction) to a perfect point at a distance of 500 mm from the mirror vertex. Rays coming in 1 degree off-axis produce an image with an rms radius of 28 microns. You may want to try web searches for "optical ray tracing" or for "third-order aberrations" or similar. -- Steve Willner Phone 617-495-7123 Cambridge, MA 02138 USA (Please email your reply if you want to be sure I see it; include a valid Reply-To address to receive an acknowledgement. Commercial email may be sent to your ISP.) |
#7
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