How Do You Calculate the Focal Length of a Telescope's Objective?

In summary, to find the focal length of the telescope's objective, you need to first calculate the angular diameter of the Moon as seen with the naked eye. This can be done by either looking up the answer or calculating it using the diameter of the Moon and the distance between the Earth and the Moon. Once you have the angular diameter, you can use the equation for magnification to find the focal length of the telescope's objective by dividing it by the focal length of the eyepiece (12mm). The naked eye diameter of the Moon in degrees can be found by calculating the fraction of the circle it occupies along its path in the sky, which can be approximated by dividing the diameter of the Moon by the distance between the Earth and
  • #1
djerry
5
0

Homework Statement



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?

Homework Equations



magnification=focal length of objective/focal length of eyepiece

The Attempt at a Solution


[/B]
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.
 
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  • #2
djerry said:

Homework Statement



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?

Homework Equations



magnification=focal length of objective/focal length of eyepiece

The Attempt at a Solution


[/B]
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.

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

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

1. What is focal length and why is it important in a telescope?

Focal length is the distance between the lens or mirror of a telescope and the point where the light rays converge to form an image. It is an important factor because it determines the magnification and field of view of the telescope.

2. How does the focal length affect the magnification of a telescope?

The longer the focal length, the greater the magnification of the telescope. This is because a longer focal length means the light rays have to travel a longer distance to reach the focal point, resulting in a larger image.

3. Can a telescope with a shorter focal length provide better image quality?

No, the focal length does not affect the image quality of a telescope. The quality of the image depends on the optical design, size, and quality of the lens or mirror, as well as external factors such as atmospheric conditions.

4. How does the focal length impact the field of view of a telescope?

A shorter focal length will result in a wider field of view, allowing you to see a larger portion of the sky. On the other hand, a longer focal length will provide a narrower field of view, allowing you to see more detail in a smaller area.

5. Can the focal length of a telescope be changed?

Yes, the focal length of a telescope can be changed by using different eyepieces. Eyepieces with shorter focal lengths will provide higher magnification, while eyepieces with longer focal lengths will provide a wider field of view.

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