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When looking at a diagram of the optical path through a newtonian reflector, the lines always cross before the eyepiece. I understand that the eyepiece is used to focus this diverging light cone so that your eye can observe an image.

If you use a camera in "prime focus" i.e. Without an eyepiece to rectify this diverging light cone, it can discern an image anyway? Would this mean that the focus adjustment (distance from the focal point) merely determines the size of the image on the sensor? Or is there still a point where the image is in focus?

How do we ensure that this occurs while the light cone is still smaller than the sensor? Or is the whole image always varied in focus across the cone, just that the depth of field allows all of it to be in focus enough for a good image?

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The main mirror of a telescope forms an image at the prime focus.

You see the lines being brought to a single point, but that doesn't mean all the light entering the telescope is focused to a single point. It means that all the light from a single point in space is focussed at a single point. Light from different sources is focussed at different points, these points form a plane in the body of the telescope, the "focal plane".

This image can be seen. You can project an image using a single lens, or if you hold up a lens at arm's length and look through it, you will see a small inverted image. The purpose of the eyepiece is to act as a magnifying glass and make this small inverted image appear bigger.

The image is in focus only at the focal plane. If a sensor (without any further lens) is placed at any other point, no image will be seen, or at best a blurry image. We can see the image when we look through the eyepiece only because we have another lens (the cornea of our eye) bringing the light to a second focus on our retina.

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    $\begingroup$ I usually tell people the eyepiece is like a little microscope, and you use it to examine the image formed in the focal plane by the telescope. That image is tiny (disadvantage) but very close (advantage), so the telescope takes a huge image that's far away, and brings it closer to you where you can examine it with a "magnifying glass" - the eyepiece. It turns out it's pretty easy to make lenses to examine and magnify images that are close by, so that's why telescopes work pretty well in the end. $\endgroup$ – Florin Andrei Jul 16 at 19:21

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