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October 8, 2014
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Hi Bob,
It's not so difficult.
Focal length is defined as the point where the rays from an infinitely distant object with parallel rays focuses to a point.
In a normal scope used with an eyepiece and your eye, the objective is accepting parallel rays from the object and output parallel rays to the eye. Your eye also accepts approximately parallel rays and converges them on the retina.
The objective will converge the rays and come to a focus at some point, the focal length. There is a virtual image there. You can hold a piece of paper up and see it if it's a bright enough object like the moon. Don' try it with the sun!
An eyepiece is a fancy magnifying glass. It also has a focal length but is typically used backwards from the way an objective is. Objectives receive parallel light and converge them where as eyepieces receive diverging light and convert them to parallel rays when all is in focus for your eye.
When the telescope and eyepiece are focused for your eye, the eyepiece is focused on the virtual image from the objective just like a magnifying glass would be focused on an object.
The focal point of a lens/mirror or eyepiece is based on something at an infinite distance and parallel rays. It is a special case of what lenses can do. They focus light at all distances and the amount of divergence or convergence changes with distance.
The case of parallel rays either coming into a lens or going out of a lens is particularly useful for telescopes and such but all manner of converging and diverging are used in different optical systems.
As an example of something that doesn't use parallel rays, a Barlow is a negative lens that modifies the convergence of the objective so it is converges slower so the cone is like that of a longer focal length objective. It isn't using parallel rays at all (in normal usage). A Barlow can be adjusted to output parallel rays and then is called a Galilean eyepiece. Same glass, different focuses, different converging/diverging behavior.
A focal reducer also doesn't use parallel rays. It is a positive lens that makes the objective rays converge faster moving the focal length closer to the objective.
In the case of eyepiece projection, it is positioned so the focus of the eyepiece is shifted so it isn't producing parallel rays on the output but converging rays. When focused properly, they focus on the sensor. The eyepiece acts sort of like the equivalent of the lens of the eye and eyepiece all in one.
The focus point of the eyepiece for looking with your eye is different than the one for eyepiece projection.
Ken
October 8, 2014
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Bob, great question and one that I can't answer. I'd suggest you ask this over at the Cloudy Nights Forum as there are a lot more people there with expertise in this area.
Dave W.
Hi, I am just learning about astronomy. I am confused about something based on ray tracing diagrams I have seen. According to one about the basic optical system of a telescope, sets of parallel rays enter the objective. Some sets are parallel to the optical axis and some are off axis. The objective focuses the rays to a point on a plane at the focal point of the objective. Beyond this point. the rays fan out again and enter the eyepiece. The rays emerge from the eyepiece as a narrower beam of parallel rays. On-axis rays continue parallel to the optical axis. Off-axis rays, off by a certain angle, emerge parallel from the eyepiece but at a sharper (greater) angle than they entered the objective with. This increased angle is the cause of magnification. The on and off-axis rays, as narrow, parallel bundles, all intersect at a plane called the "exit pupil." Though not shown in the diagram, I suppose the exit pupil is where the observer's eye goes. The lens in his or her eye acts as a new objective, taking the incoming bundles of parallel rays and focusing each to a point on the retina.
(BTW, this diagram I found in "Telescope Optics: A Comprehensive Manual for Amateur Astronomers" by Rutten and van Venrooij.)
All fine so far. But I've seen ray tracing diagrams of what happens with eyepiece projection and they confuse me. In eyepiece projection, the rays emerge from the eyepiece and go directly to the CCD chip. One diagram I saw showed what looked like parallel rays emerging from the eyepiece and going direct tho the sensor chip. With no equivalent of the observer's eye's lens in the path, I don't see how the rays get focused on the chip to form an image. Another diagram showed the rays exiting NOT as parallel bundles from the eyepiece, but as being focused to a point on the sensor chip. This would form an image on the chip, but the rays NOT coming out parallel from the eyepiece contradicts the first diagram of the telescope's basic optical system.
Other things I've read insist that the eyepiece in eyepiece projection focuses an image on the sensor chip. I suppose this must be the case, but it contradicts the idea of the rays emerging from the eyepiece as parallel bundles, which must yet be focused. Is the first diagram I looked at in "Telescope Optics" wrong?
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