# Focal length of telescope

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1. Sep 25, 2014

### djerry

1. The problem statement, all variables and given/known data

An optical telescope with a 12mm eyepiece makes the Moon appear to have an angular
diameter of 30 degrees. What is the focal length of the telescope's objective?

2. Relevant equations

magnification=focal length of objective/focal length of eyepiece

3. The attempt at a solution

I'm not sure what I'm able to do given a diameter and angular diameter in order to get the magnification and focal length of the eyepiece as needed.

2. Sep 25, 2014

### collinsmark

There are a couple of different approaches from this point. But one way or another, you need to find the angular diameter of the Moon as seen with the naked eye.

And there are multiple ways to do that too.
(a) You could look up the answer, or
(b) you could calculate it yourself. If you calculate it yourself, you will still need to look up a couple of things: (i) the diameter of the moon (in units of length such as meters) and (ii) the distance between the Earth and the Moon (also in units of length). The ratio of the two is the fraction of the circle occupied by the moon along its path along the sky. Knowing that the total angular length of a complete circle is 360o, how much of that circle is taken up by the moon's diameter, as measured in degrees? [Edit: what I describe here is technically an approximation, but it is valid if the diameter of the moon is << than the distance between the Earth and moon.]

3. Sep 25, 2014

### Staff: Mentor

Presumably the 12mm figure for the eyepiece is its focal length, no?

What's the naked eye diameter of the Moon in degrees?