Thanks to all who responded to my question. I believe I have it sorted
out now. They key was first establishing a rigorous definition of "an
apparent size of 1 arcsecond" (which is reiterated by Paul below). The
flip side of my question (Does this mean that rays of light from the
object are diverging at an angle of 1 arcsecond?) is now seen as false.
Here's what I mean ...
When I see ray diagrams of light entering a telescope or eye, light from
astronomical sources is always drawn a parallel rays. It makes the
diagrams and calculations much simpler, and is for all practical
purposes true. But there's always this usually unspoken disclaimer that
the rays are only "nearly" parallel since no object is really "at
infinity". So there has to be some divergence, and I was wondering if
that divergence would equal the angular size. It would not.
Say you have an 8" aperture scope. The light rays from, say Sirius,
emanate in all directions. Only those coming from a small area of that
star (projected out to the scope) will enter the scope. Since those rays
start geometrically from the center of Sirius, the actual amount of
divergence in those "parallel" rays would depend on the distance of the
star. Of course, for any astronomical object the rays would be SO CLOSE
to parallel as to not affect the scope's optical behavior.
If we do the trig for this scenario, using Sirius and an 8" scope, the
angle of the rays projected out from the center of Sirius to an 8"
aperture would be about 1.4 x 10^-16 degrees. You can check my calcs if
you want, but I think I got that right. Just a long skinny triangle and
an inverse tangent. What's more important to me than the actual number
is understanding just how good the parallel ray assumption is ... and
where it comes from. Thanks again all for your feedback. -Dan Heim
On 8/28/2018 5:13 PM, Paul Lind wrote:
I like Padraig's answer. An optical description is: "THE OBJECT SUBTENDS AND--
ANGLE OF 1 ARCSECOND AS SEEN BY THE OBSERVER." That is to say that if two
lines are drawn from obersvers eye (considered very small) to opposite edges
of the object, the angle is 1 arcsecond. Of course the object itself may
radiate in all directions, as was already said.