Height of the image of Jupiter created by the objective lens

[Nathan B]

Homework Statement

I have the following variables:
f = .93 m
f(e) (eyepiece) = .0082 m
distance toJupiter pj = 588 E^9
diameter of Jupiter dj = 139822 E^3

Find the height of the image of Jupiter created by the objective lens of a telescope.

Homework Equations

M = -q/p
q = f
Where M is the magnification, q is the image location, and p is the object location.

The Attempt at a Solution

This seems like a straight forward problem: find the magnification, multiply by the original diameter, and done:

M = -f / pj
dj2 = dj * f / pj = 139822 E^3 * .93 / 588 E^9 = 2.21 E^-4

According to my homework, this is incorrect and the correct answer is 2.07 E^-4
My answer is so close I figure I must be approximating something I shouldn't, but I can't figure out where I'm going wrong here.

 

[lekh2003]

M = -f / pj
dj2 = dj * f / pj = 139822 E^3 * .93 / 588 E^9 = 2.21 E^-4

According to my homework, this is incorrect and the correct answer is 2.07 E^-4
My answer is so close I figure I must be approximating something I shouldn't, but I can't figure out where I'm going wrong here.

I don't think you are taking into account the focal length of the eyepiece itself. The focal length of the eyepiece has a small effect which is why you are so close to the answer. Just do the same calculations again taking into account the eyepiece.

 

[Nathan B]

lekh2003, how do you propose that I do that? I know I can get angular magnification from the eye piece, but I need lateral magnification and the problem specifically states that it wants the image made by the objective lens.

 

[lekh2003]

lekh2003, how do you propose that I do that? I know I can get angular magnification from the eye piece, but I need lateral magnification and the problem specifically states that it wants the image made by the objective lens.

I'm sorry, I don't know how telescopes work, but I'm going to take a guess here on what you need to do.

When the image of Jupiter passed through the original lens, you found the new height of Jupiter. I think you should just do the same thing again.

You know the height of Jupiter when the image hits the eyepiece and you know the magnification of the eyepiece, so you should have your equation ready to solve for the final height.

I hope this helps.