A Space & astronomy forum. SpaceBanter.com

Go Back   Home » SpaceBanter.com forum » Astronomy and Astrophysics » Astronomy Misc
Site Map Home Authors List Search Today's Posts Mark Forums Read Web Partners

focusing properties of parabolic mirrors



 
 
Thread Tools Display Modes
  #1  
Old June 10th 05, 12:51 AM
David Bernier
external usenet poster
 
Posts: n/a
Default 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  
Old June 10th 05, 01:56 AM
Minus XVII
external usenet poster
 
Posts: n/a
Default

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

  #3  
Old June 10th 05, 03:03 AM
NG, Sing
external usenet poster
 
Posts: n/a
Default


"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)


  #4  
Old June 10th 05, 10:01 AM
Joerg Glissmann
external usenet poster
 
Posts: n/a
Default

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 ;-)

  #5  
Old June 21st 05, 12:10 AM
Minus XVII
external usenet poster
 
Posts: n/a
Default

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

  #6  
Old June 21st 05, 12:18 AM
Steve Willner
external usenet poster
 
Posts: n/a
Default

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.)
 




Thread Tools
Display Modes

Posting Rules
You may not post new threads
You may not post replies
You may not post attachments
You may not edit your posts

vB code is On
Smilies are On
[IMG] code is On
HTML code is Off
Forum Jump

Similar Threads
Thread Thread Starter Forum Replies Last Post
spherical mirrors matching the curve of parabolic jtaylor Amateur Astronomy 16 April 29th 05 02:38 AM
Looking for 4" Parabolic Mirrors Supplier matt Amateur Astronomy 15 November 29th 04 03:21 PM
Temperature/cooling etc Dr. Boggis Amateur Astronomy 26 December 8th 03 03:59 PM
olympus om-1, focusing screens and flip mirrors shawn o'deal Amateur Astronomy 7 October 27th 03 11:59 PM
olympus om-1 and focusing screens/flip mirrors shawn o'deal Misc 2 October 26th 03 02:31 PM


All times are GMT +1. The time now is 02:48 PM.


Powered by vBulletin® Version 3.6.4
Copyright ©2000 - 2024, Jelsoft Enterprises Ltd.
Copyright ©2004-2024 SpaceBanter.com.
The comments are property of their posters.