Can you use a camera lens on a telescope without an eyepiece?

Question

In astrophotography, common setups are:

- prime focus = no camera lens, no telescope eyepiece
- eyepiece projection = no camera lens, yes telescope eyepiece
- afocal = yes camera lens, yes telescope eyepiece

What about a fourth setup: using a camera lens with a telescope, but without an eyepiece?

Does that make optical sense? If not, why not?

user68557 · Accepted Answer

Let's say you want to make a photo of the moon (viewing angle: +/-0.25°) with a 1000mm telescope.

☑ Objective ☐ Eyepiece ☐ Camera lens

The objective as only lens in this case focuses the light from the moon 1000mm behind, and creates a real image of 2*tan(0.25°)*1000=8.7mm size of the moon. With an APS-C camera, the moon will fill roughly half the height of the image.

Pro: Just a single lens
Con: Low, fixed magnification

☑ Objective ☑ Eyepiece ☐ Camera lens

Place an eyepiece lens of may be 10mm so that the first real image is 10-20mm in front of it, so it creates a second, magnified real image. If the distance is more than 20mm, the second image is smaller, not bigger that the first. And at 10mm and below, the lens does not focus the light to a second image.
At 15mm, the eyepiece creates an image 30mm behind itself with a magnification factor of 2. The moon will have a diameter of 17.4mm, i.e. it's already too large to fit on an APS-C sensor placed here. Shift the eyepiece a little back, and the moon will fit.

Pro: Good magnification, adjustable over large range
Con: Need to adjust lens position to choose magnification, and then adjust sensor position to focus

☑ Objective ☑ Eyepiece ☑ Camera lens

This configuration is the same as looking through the telescope with the eye. The eyepiece is placed 1010mm behind the objective, i.e. the first image is in the focus of the eyepiece. The eyepiece creates parallel rays, which leave at +/-atan(8.7mm/10mm)=+/-23.6°. The viewing angle is about 94 times bigger than the original +/-0.25° for the moon!. The final image is created by the camera lens, which has to be focused to infinity. Assuming a simple 50mm lens (and so the sensor 50mm behind), the moon would have a diameter of 43,7mm on the sensor. That doesn't even fit a full frame sensor!

Pro: High magnification, which can be adjusted by just zooming in. Position of eyepiece is fixed. Position of camera doesn't matter much, since the rays to the camera are parallel. Though, the distance should not be too large, since that would narrow down the image circle.

☑ Objective ☐ Eyepiece ☑ Camera lens

From the lens equations, this is not different from the second option. But: normal camera lenses have a minimum focus distance, i.e. minimum distance from the first image created by the objective. The second image they project on the sensor is smaller than the first image. A macro lens has a shorter minimum distance, but typically do not magnify. The better ones maintain the size, and the most expensive ones might magnify... a little bit.

Long story short: You'd need one of the most expensive macro lenses to get somewhere near option 2, which is quite cheap.

Note:

This answer concentrates on lens equations only. The chosen values allow simple calculations, but might not be ideal in reality due to other reasons. Image circle, distortions etc., were not taken into account.