What is the approximate focal length for a 10X telescope with a 20 cm length?

[BuBbLeS01]

Test TOMORROW PLEASE HELP ME! Telescope!

Homework Statement

I need serious help! I have a test tomorrow and I am having trouble with microscope/telescope questions...

A person is designing a 10X telescope is limited to a length of 20 cm, what is the approximate focal length of the objective?

Homework Equations

The Attempt at a Solution

M = 10X
L = 20 cm
Fo = ?

The equation I found for a telescope is M = -Fo/Fe and the rest of the equations involve theta which I don't have. And I don't have Fe?

 

[BuBbLeS01]

I got it nevermind.

 

[Moetasim]

Hello! I am here to help you with your question. Don't worry, I will break it down for you step by step.

First, let's define some terms. The focal length (Fo) is the distance between the lens and the point where the image is formed. The magnification (M) is the ratio of the image size to the object size. In this case, we know that M = 10X, which means the image size will be 10 times larger than the object size.

Next, we have the length of the telescope (L), which is given as 20 cm. This is the total length of the telescope, including both the objective lens (which collects the light) and the eyepiece (which magnifies the image).

Now, let's use the equation you found, M = -Fo/Fe, where Fe is the focal length of the eyepiece. We can rearrange this equation to solve for Fo, which is what we are looking for.

M = -Fo/Fe
10 = -Fo/Fe (since M = 10X)
10Fe = -Fo (multiply both sides by Fe)
-Fo = 10Fe
Fo = -10Fe (multiply both sides by -1)

Now, we can substitute this value for Fo into the equation L = Fo + Fe, where L = 20 cm. This will give us an equation with only one unknown variable, Fe.

L = Fo + Fe
20 = -10Fe + Fe (substitute -10Fe for Fo)
20 = -9Fe
Fe = -20/9 (divide both sides by -9)

So, the focal length of the eyepiece (Fe) is approximately -20/9 cm. But remember, this is the focal length of the eyepiece, not the objective lens. To find the focal length of the objective lens (Fo), we can use the equation we found earlier, Fo = -10Fe.

Fo = -10Fe
Fo = -10(-20/9) (substitute -20/9 for Fe)
Fo = 200/9 cm (multiply -10 by -20/9)

Therefore, the approximate focal length for a 10X telescope with a 20 cm length is 200/9 cm. I hope this helps you understand and solve similar problems in the future. Good luck