Optics - Diameter of moon viewed through telescope

[elizabeth9681]

Homework Statement

I've been stuck on this problem for a while now, and have tried it several different ways, but with no results. I'm sure I'm missing something obvious or simply approaching it from the wrong direction.

The moon subtends an angle of 0.5 degrees at the objective lens of a terrestrial telescope. The focal lengths of the objective and ocular lenses are 20 cm and 5 cm, respectively. Find the diameter of the image of the moon viewed through the telescope at near point of 25 cm.

Homework Equations

M = - fo/fe where fo = focal point of objective and fe = focal point of eyepiece

 

[Nate810]

The Attempt at a Solution I've tried to work this problem multiple times, and so far I have come up with the following equation, but I'm not sure if it's correct: M = (20/5) * (25/20) = 1.25 From here, I'm not sure what to do. Any help would be greatly appreciated.

 

[m2003]

tan(theta) = opposite/adjacent
diameter = 2 * radius


As a scientist, my first suggestion would be to review the basics of optics and the properties of lenses. It is important to understand how the focal length of a lens affects the magnification and image size.

In this problem, we are given the focal lengths of both the objective and ocular lenses, as well as the distance to the near point. We can use the equation M = -fo/fe to calculate the magnification of the telescope, where fo is the focal length of the objective lens and fe is the focal length of the ocular lens. This will give us the ratio of the size of the image to the size of the object.

Next, we can use the equation tan(theta) = opposite/adjacent to find the angle of the image of the moon in the telescope. This angle will be the same as the angle subtended by the moon at the objective lens, which is given as 0.5 degrees.

Using the angle and the distance to the near point, we can then calculate the diameter of the image of the moon using the formula for the diameter of a circle, which is 2 * radius. This will give us the diameter of the moon as viewed through the telescope.

It is also important to note that the distance to the near point may affect the final calculation, as the human eye has a limited ability to focus at close distances. Therefore, the diameter of the moon viewed through the telescope may vary slightly depending on the individual's near point. Overall, understanding the basics of optics and applying the appropriate equations will help to solve this problem.