James Harris wrote:
Can anyone explain how light really passes through a telescope???
Opinions I've heard seem contradictory so I'd appreciate some
clarification. In particular (and this is the practical reason for
asking the question) when light exits an eyepiece does it emerge as a
cylinder or as a cone? If a cone is it narrowing - i.e. focussed on a
point after the eyepiece - or is it diverging - i.e. already past the
point of focus?

My local telescope supplier tells me the light is converging but I
doubt the human eye could focus on that. My view is that the light
should emerge as a cylinder (i.e. appearing at infinity) of diameter up
to the size of the pupil of the eye and that the lens of the eye
focusses this on to the retina just as it would when viewing a distant
object. The counterexample he gave is of eye relief where the distance
from the eyepiece matters. I guess there is something in that so am
puzzled. Can anyone shed some light (sic, sorry) on this?

I hope so. I'm going to explain everything in terms of a refractor,
with lenses for both objective and eyepiece, but a similar explanation
holds for any design.

Suppose you point a telescope at a star. In the ray conception of
light, rays diverge from the star, but the star is so far away that by
the time the light reaches your telescope, the rays that enter your
telescope are as good as parallel. Since your objective is generally
circular, a cylinder of light from the star is what goes in.

The objective then refracts this cylinder into a cone, which converges
to a point at the focal plane. Since there's nothing there to stop the
light, it diverges again in a second, smaller cone, which terminates at
the eyepiece.

The eyepiece refracts this light a second time into a cylinder again,
and it is this cylinder that your eye lens (and cornea) refract a third
time into a third cone, whose point lies, hopefully, on your retina, at
which point your brain processes the signal into a mental picture of the
star.

Now, for a star at the center of the field of view, all the cones and
cylinders have an axis of symmetry that is identical with the axis of
the telescope itself. This is what you typically see in telescope
cutaway diagrams. The situation is somewhat different for stars at the
edge of the field. Suppose that you point your telescope slightly above
the star. In that case, the cylinder of light is a bit askew; when it
reaches the objective, it does so "from below," relative to the scope's
axis, and the light is moving slightly upward.

The objective refracts it into a cone of light, but the cone of light
is also pointed slightly upward, so that it converges to a point on the
focal plane that is slightly higher than before. The diverging cone is
also still headed upward, and it reaches the eyepiece well above center.

The periphery of an eyepiece refracts light more than its center, since
the angles are steeper there. The eyepiece refracts the diverging cone
into a cylinder, as before, but now the cylinder starts from the top of
the eyepiece and is heading *downward*. That is why images in a
refractor (without a star diagonal) are inverted; light entering the
objective from below exits the eyepiece from above.

This means that if you have stars all over the field of view, each one
generates a final cylinder of light emanating from the eyepiece. Each
cylinder starts from a different circular base on the eyepiece--else,
the stars would appear to coincide--but since the ones near the top are
headed downward, and the ones near the bottom are headed upward, they
all converge to a disc. This disc is separated from the eyepiece by a
distance called the *eye relief*. It is at this distance that it is
easiest to fit all the light cylinders into your eye's pupil, so that
one can see *all* the stars (or more generally, the entire field of
view).

This explains why eye position is so critical when using low power. If
you use high power, the exit pupil is small because the cylinders are
so small. The eye relief is the same, but since the cylinders are thin,
you can be too far forward, backward, or off to the side, and the
cylinders still all get into your eye, allowing you to see the entire
image. It is at low power where the cylinders are so wide that any
individual one barely gets into your eye in the first place. Any kind
of misalignment, and many of them simply won't get in, and you see a
black splotch over part of the field of view.

Hope that helped. Let me know if you have any further questions.

--
Brian Tung
The Astronomy Corner at http://astro.isi.edu/
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