Light path exiting a telescope eyepiece or finder

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?


--
Thanks,
James

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.

Can you see the whole of your monitor without moving your eyes? Most
people can. Trace the lines from the edges of the monitor to your eye
and you'll see that the human eye can indeed focus a converging light
cone.


Tim

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/
Unofficial C5+ Home Page at http://astro.isi.edu/c5plus/
The PleiadAtlas Home Page at http://astro.isi.edu/pleiadatlas/
My Own Personal FAQ (SAA) at http://astro.isi.edu/reference/faq.html

Tim Auton wrote:
Can you see the whole of your monitor without moving your eyes? Most
people can. Trace the lines from the edges of the monitor to your eye
and you'll see that the human eye can indeed focus a converging light
cone.

Uhh, no. Think about how you see an individual pixel. Light rays
emanate from that pixel and are focused by your eye to a point on your
retina. Light from another pixel diverges from *that* pixel and is
focused to a second point on your retina. And so on. Your eye does
not take light from the entire screen and focus that down to a point;
that would mix the light from the whole screen, which would produce an
indiscriminate blur, if in fact your eyes could do it.

Your eye lenses are convex. They cannot focus light that converges
strongly--certainly not anything that would converge to your retina
without the lens being there. At best, they can focus very weakly
converging light. Fortunately, most objects emit only diverging light;
it takes an optical element, such as a magnifying glass, to produce
converging light. That is why you only see a blur if you look around
the room with a magnifying glass held up to your eye.

--
Brian Tung
The Astronomy Corner at http://astro.isi.edu/
Unofficial C5+ Home Page at http://astro.isi.edu/c5plus/
The PleiadAtlas Home Page at http://astro.isi.edu/pleiadatlas/
My Own Personal FAQ (SAA) at http://astro.isi.edu/reference/faq.html

James Harris wrote:

Can anyone explain how light really passes through a telescope???
snip 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

You are both right. The image of extended objects like the Moon are
not formed only by a single bundle of parallel rays coming down the
telescope tube and out the eyepiece.

Such a cylinder of parallel light rays does exist. You can see it by
focusing a telescope on the Moon and then standing up to two feet
behind the eyepiece. You can still see a dim image of the Moon in the
eyepiece.

But there are two other key parallel beams of light traveling through
telescope that do come to a convergent focus.

Extended objects like the Moon, by definition, have an arcsecond size.
For an extended object like the Moon that size is about 1800
arcseconds. Some of the bundles of parallel beams of light rays come
from center of the object - that is your cylinder of light -

http://members.csolutions.net/fisher...Telescope1.gif

- but some come from one side of the object at a slight angle of
divergence to the optical axis -

http://members.csolutions.net/fisher...Telescope4.gif

At the intersection where these bundles of parallel light meet on the
observer side of the eyepiece -

http://members.csolutions.net/fisher...Telescope5.gif

- is where the virtual image of the extended object forms -

http://members.csolutions.net/fisher...Telescope7.gif

The distance between this virtual image and the eyepiece is the
eyepiece's eye relief distance.

You can see this effect by again focusing a telescope on the Moon. When
you stand back from the eyepiece there is a dim image formed by the
parallel set of rays travelling directly down optical axis of the
telescope. If you move your eye to the eyepiece at the eye relief
distance, more of the light beams with an angular divergence will enter
your eye pupil. The image will be brighter.

I recommend that you take a few minutes to play with a telescope ray
tracing Javascript applet, put on the web by Professor Mark Peterson of
Mount Holyoke College -

http://www.mtholyoke.edu/~mpeterso/c...twolenses.html

Using this ray tracing simulater, you can put three bundles of parallel
light through the telescope and angle two of them with respect optical
axis. Put one on the optical axis, a second parallel to the top of the
lens and a third parallel to the bottom of the lens. Do this by -

1) Selecting the "astronomical telescope" link to put a telescope in
the simulator.

2) Use the "Beam" button, to add two beams.

3) Once selected, there are drag "dots" on the beams that allow you to
position and angle them with respect to the optical axis.

4) After you are practiced at using the simulater add a virtual eye and
retina using the "add an 'eye' at the far right" link below the
simulator window. (I found easier to create the desired simulation by
manually adding another lens at the far right using the "Lens" button
and a field stop using the "Aperature" button.)

When using the Mark Peterson lens and telescope simulator, the
following is a screen shot of the type of telescope and eye you want to
try to create:

http://members.csolutions.net/fisher...Telescope8.jpg

The apparent-field-of-view (AFOV) in the eyepiece is itself an extended
object of sorts.

Peace - Canopus56

Brian Tung wrote:
[snip excellent explanation]

Just to expand on this with a diagram, the light from a single star
would follow the path shown in the diagram at the top of:
http://www.astunit.com/tutorials/telescope.htm

If you now imagine a star below the optical axis, its rays would form a
pattern symmetrical with that shown in the diagram, the line of symmetry
being the optical axis (grey horizontal line). You will see that the
bundles of rays from the two stars cross each other on the eye side of
the eyepiece. The smallest circle through which they all pass is the
position of the exit pupil. (It is in the position of the image of the
objective formed by the eyepiece.)


Best,
Stephen

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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?


--
Thanks,
James

Hi james, check it out yourself, try focussing on the moon then hold a
piece of frosted glass or tracing paper behind the eyepiece. Does the
image diameter increase as you move the screen further from the
eyepiece ?
jc

"John Carruthers" wrote in message
oups.com...

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?


Hi james, check it out yourself, try focussing on the moon then hold a
piece of frosted glass or tracing paper behind the eyepiece. Does the
image diameter increase as you move the screen further from the
eyepiece ?
jc

James
The light from the distant object should be emerging in a parallel sided
cylinder when the telescope is correctly focussed at a distant object.

John
I'm not sure what 'image' you would get using the method described - I
suspect the nearest to an image you could bring to focus would be that of
the Objective behind the eyepiece.

John Carruthers wrote:
Hi james, check it out yourself, try focussing on the moon then hold a
piece of frosted glass or tracing paper behind the eyepiece. Does the
image diameter increase as you move the screen further from the
eyepiece ?

No image is formed on the frosted glass, if the telescope is in focus;
a telescope is an afocal system. What you see instead is a convolution
of pencils of light formed over the entire illuminated surface of the
Moon. There will essentially be no detail visible there.

--
Brian Tung
The Astronomy Corner at http://astro.isi.edu/
Unofficial C5+ Home Page at http://astro.isi.edu/c5plus/
The PleiadAtlas Home Page at http://astro.isi.edu/pleiadatlas/
My Own Personal FAQ (SAA) at http://astro.isi.edu/reference/faq.html

Brian Tung wrote:
[snip excellent explanation]

Just to expand on this with a diagram, the light from a single star
would follow the path shown in the diagram at the top of:
http://www.astunit.com/tutorials/telescope.htm

If you now imagine a star below the optical axis, its rays would form a
pattern symmetrical with that shown in the diagram, the line of
symmetry being the optical axis (grey horizontal line). You will see
that the bundles of rays from the two stars cross each other on the eye
side of the eyepiece. The smallest circle through which they all pass
is the position of the exit pupil. (It is in the position of the image
of the objective formed by the eyepiece.)