Understanding Telecentricity in Newtonian Telescopes

[Wminus]

Homework Statement

See the image I uploaded.

Homework Equations

Paraxial approximations

The Attempt at a Solution

I think the image is formed after the ocular, and I understand the system is afocal. The magnification is also less than 1, but the angular magnification is >1.

What I am stuck on, is the telecentricity. How am I to ray-trace the aperture so I get an entrance and exit pupil? What is F2?

I tried ray-tracing the plane mirror in the middle, but I ended up with its image being formed somewhere besides the ocular. Help!

 

[Wminus]

Can somebody assist me?

 

[Drakkith]

What is F2?

Do you know what is F1 is?

 

[Wminus]

F1 is the focus of the curved mirror, f2 is the mirrored f1. I was a bit confused because it didn't seem like f2 was a focus when i drew rays, but i see i was weong now.

Also, the telescope can't be telecentric because then it would perform an orthographic projection, which means the size of objects seen thru it (eg stars) wouldn't decrease in size as they get farther away. This is impossible

 

[Andy Resnick]

How about this- if you 'unfold' the light path and think of the obscuration as a 'dummy' surface, where is the aperture stop located? Where is the exit pupil located?

 

[Wminus]

How about this- if you 'unfold' the light path and think of the obscuration as a 'dummy' surface, where is the aperture stop located? Where is the exit pupil located?

What do you mean with unfold? The plane mirror is the aperture stop, I know that.

Hmm, so you are saying that since the plane mirror is ahead of the focus of the curved mirror, it must mean that it will produce a virtual image from the curved mirror. OK, but what happens when the ocular focuses the light image of the aperture stop? Where will the exit pupil end up?

 

[BvU]

The plane mirror is the aperture stop, I know that

What makes you think you know that ? What limits the amount of light that takes part in the image formation ?

Then: in the figure 1 the ray trajectories from the mirror up to F2 have been unfolded by drawing the dashed lines to F1. You can draw the eye lens and the observer to the left of F1 to simplify the picture. Of course now the observer is in the light path, but to understand the working, imagine the concave mirror is big enough (or that the eye is a camera).

A second unfolding step can be made by replacing the concave mirror by a convex lens (same diameter and focal distance). So you flip the eye lens and the observer to the right. The image is at the righthand side at same distance as F1. And you have a Keplerian telescope. Study some keplerian telescope ray diagrams, e.g. here .

 

[andrevdh]

http://www.skyandtelescope.com/astronomy-equipment/an-eyepiece-primer/
F₂ is where the telescope's parabolic mirror forms the image that is viewed with the eyepiece.
Note that the eyepiece is positioned so that it forms an image of this at infinity, that is the eyepiece lens'
focal point is also located at F₂. This is evident form the parallel rays exiting the eyepiece.

 

[Wminus]

thanks guys

What makes you think you know that ? What limits the amount of light that takes part in the image formation ?

Then: in the figure 1 the ray trajectories from the mirror up to F2 have been unfolded by drawing the dashed lines to F1. You can draw the eye lens and the observer to the left of F1 to simplify the picture. Of course now the observer is in the light path, but to understand the working, imagine the concave mirror is big enough (or that the eye is a camera).

A second unfolding step can be made by replacing the concave mirror by a convex lens (same diameter and focal distance). So you flip the eye lens and the observer to the right. The image is at the righthand side at same distance as F1. And you have a Keplerian telescope. Study some keplerian telescope ray diagrams, e.g. here .

Ahh, so it's the ocular that is the aperture stop? OK, if I image the ocular towards the left, it seems like its object-side image never focuses => the entrance pupil is infinitely away => the telescope is image-side telecentric.

However, the EXIT pupil is just the ocular, and hence it's not object side telecentric.

OK; but what about the plane mirror? It doesn't act like an aperture stop? After all, it significantly limits the amount of light coming into the system.

And by the way, in a real reflector telescope, can you see an image of the plane mirror when you look inside the ocular?

 

[Drakkith]

And by the way, in a real reflector telescope, can you see an image of the plane mirror when you look inside the ocular?

Only if your mirror is bad or dirty or you have a giant hole in the side of the tube. The telescope tube is usually sealed everywhere but the aperture and where you stick the eyepiece in so that no light can get inside unless it comes through the aperture and is focused by the primary mirror. If I punched a hole in the side of the tube and shined a flashlight in you can be certain that you'd lose most of the contrast in your image thanks to all the extra light being scattered and reflected about. Since there are no light sources inside the tube all of the light normally entering the eyepiece comes from the sky. In order to see the secondary mirror you'd need the mirror to be very dirty, so that you could see the dirt, or be in terrible shape, with the reflective coating missing in large patches or the surface to be very rough and uneven. If it's clean, smooth, and shiny then it's just going to reflect the image of the sky like it's supposed to.

 

[andrevdh]

Look at the stops and pupils sections
http://www.handprint.com/ASTRO/ae2.html
Exit pupil
http://www.handprint.com/ASTRO/ae3.html#centobs

 

[andrevdh]

I would like to see your (failed) ray diagram.