From: Michael Lindner 
To: John Sherman , atm{at}shore.net
Reply-To: Michael Lindner 


On Wednesday 16 July 2003 10:02 pm, John Sherman wrote:
> ...Okay, so the angular resolution of the
> telescope is dependent on the aperture. But how can that have anything to
> do with the size of the Airy disc, if the size of the Airy disc is
> dependent on the F/#?

The angular size of the airy disk in radians is

        2.44 lambda/D

where D is the diameter or clear aperture of the scope. Something smaller
than this in the sky won't be resolved completely regardless of the focal
ratio of the scope.

The linear size at the focal plane of something of angular size A is

        F tan(A)

where F is the focal length of the scope. So the physical size of the airy
disk at the focal plane is

        F tan(2.44 lambda/D)

and using the approximation for small angles that tan(X) = X, we get

        2.44 lambda F/D

and F/D is the f-ratio, giving the equation you know and love.

For prime focus photography, you don't care about angular size per se, you
are more concerned about the size of the airy disk at the focal plane. For
visual observing, you don't care how big it actually is at the focal plane,
you care about how large it's going to appear to your eye, which is
magnification x angular size.

Hope your head feels better.
--
Michael Lindner
http://www.starastronomy.org
http://home.att.net/~mikel http://www.atmsite.org
http://home.attbi.com/~dcass/atmfaq/atm-faq.htm

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