# Given telescope diameter and focal length only, how can I find the size of a produced image?

I'm new to astronomy and I'm struggling to understand this concept. For example, A 20-cm diameter telescope with a focal length f = 2 meters produces an image of the moon 1.7 cm in diameter. How large is the image of the moon produced by a 5-meter diameter telescope, focal length f = 16.7 meters?

$$\sin(\theta) \approx\ tan(\theta) \approx \theta$$
when $$\theta$$ is in radians. So the size of the Moon will be about $$\theta F$$ where $$F$$ is the focal length.
In other words, ignore the diameter of the aperture, objective lens or mirror. Just use the pinhole camera model for imaging systems. If you have a multi-element telescope (e.g. Cassegrain or refractor with a Barlow lens) make sure to use the effective focal length of the system at the image plane for $$F$$. A Cassegrain might have a 40 cm focal length objective but a 120 cm effective focal length for the whole system. You might have a 100 cm focal length refractor but with a 2x Barlow lens you effective focal length will be 200 cm.