Yes, that diagram helped alot! I think the light bulb just came on. :)Â
I was earlier playing around with some ray diagrams and had realized
that, for a distant object seen through a scope, light rays that form
the image of any extended object actually have to be _converging_
slightly to enter the telescope. Your diagram confirmed that. That's
obviously the case when the object's actual diameter exceeds the scope
aperture, which is always the case in astronomy. Your earlier comment
relating angular size to the off-axis angle now makes total sense.
For some reason (when I asked my original question) I was assuming the
_divergence_ of rays from a source (which obviously happens) had
something to do with the formation of an image in a scope. So my
question was poorly formulated. Appreciate the optical insights, thanks.
It's a little harder to see in the case of an object _smaller_ than the
scope aperture (like a bird), but if I understand correctly now, in this
non-astronomical case the optical system would indeed have to deal with
_diverging_ rays in order to form an image. Do I have that correct?Â
-Dan Heim
On 8/29/2018 8:32 PM, Scott Rick wrote:
Letâs assume that you have the object exactly in the center of the FOV
and that the object is so far away that the light from each point on
the object is coming into the telescope as parallel rays. The rays
from the center of the object will focus on the optical (central) axis
of the scope. The light from points away from the center of the object
are coming in at a small angle off of the optical axis and focus to
the side of the axis thus making an image that represents the angular
size of the object. The graphic shown by clicking on the following
link shows three sets of incoming parallel light rays. The green rays
are from the center of the object and focus on the axis. The red and
blue traces are for points on the object that are away from its center.
http://naturalimagesgallery.com/telescope_off_axis_ray_trace.gif
Let the blue rays represent the limb or edge of the object. The
distance off the optical axis where it comes to focus shows the size
of the image created by the telescope. This is not the divergence of
light from the object but how the object looks from the point of view
of the telescope. In the case of a star, the light from it radiates in
all directions away from it. We only see the light rays emitted in our
direction. Each point on the object radiates light in all directions
so even those point on the limb radiates some light in our direction.
Does this explanation help?
Rick
On Aug 29, 2018, at 1:57 PM, Dan Heim <dan@xxxxxxxxxxxxx
<mailto:dan@xxxxxxxxxxxxx>> wrote:
The star's limb will define the maximum off-axis angle and that is
half of the apparent diameter of the star. If the apparent diameter
is 1 arc-sec, then the maximum angle of the off-axis rays are 0.5
arc-sec.<<
So are you saying the divergence (from parallel) of the light rays
from any object would be half that object's apparent diameter? That's
not immediately obvious to me. Could you elaborate please? Thanks.
 -Dan Heim
On 8/29/2018 1:40 PM, Scott Rick wrote:
When it comes to ray tracing, you look at the rays coming in along
the optical axis and those that define the field of view (FOV). In
this case, the apparent size of Sirius is much smaller than the FOV
but it does have rays that come from its entire surface. The star's
limb will define the maximum off-axis angle and that is half of the
apparent diameter of the star. If the apparent diameter is 1 arc-sec,
then the maximum angle of the off-axis rays are 0.5 arc-sec. You need
to take into account the diffraction effects of having a finite
aperture. This will cause point objects to focus to a finite disc
called the Airy disc (named after George Bidell Airy). The size of
the Airy disc is only dependent on the f-ratio of the telescope.
Hereâs a link to a Wikipedia article that has information and
equations for the Airy disc.
https://en.wikipedia.org/wiki/Airy_disk ;
<https://en.wikipedia.org/wiki/Airy_disk>
Rick Scott
