Optics: Finding the Diameter of the Image of the Moon through a Telescope

[zoetrope]

I've been stuck on this problem for a while now, and have tried it several different ways, but with no results. This leads me to believe that 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.

Any help would be appreciated! Thanks!

zoetrope

 

[member 553083]

equation: Magnification = (Focal length of the objective lens) / (Focal length of the ocular lens) Given: Objective lens focal length = 20 cmOcular lens focal length = 5 cm Magnification = (20 cm) / (5 cm) Magnification = 4 Image diameter = 0.5° x 4 Image diameter = 2°

 

[wais]

:

Hi there,

It sounds like you have been working on this problem for a while and are feeling frustrated. Don't worry, it's common to get stuck on problems in optics. First, let's break down the problem and see if we can approach it in a different way.

The question is asking for the diameter of the image of the moon viewed through the telescope. To find this, we need to use the formula for magnification, which is M = -di/do, where di is the image distance and do is the object distance. We also know that the angle subtended by the moon is 0.5 degrees, which means it covers 0.5/360 = 1/720 of the field of view.

Now, let's consider the image distance (di). We can use the thin lens formula: 1/di + 1/do = 1/f, where f is the focal length of the objective lens. We know that f = 20 cm, and since the telescope is being used at the near point of 25 cm, we can plug these values into the formula to solve for di. This should give you a value for di.

Next, we can use the magnification formula to find the diameter of the image. Remember, the magnification is -di/do, and we know the value of di from the previous step. We just need to find the value of do, which is the object distance. Since the telescope is being used at the near point of 25 cm, do = 25 cm.

Once you have the values for di and do, you can use the magnification formula to find the diameter of the image. I hope this helps and good luck! Don't get discouraged, sometimes it just takes a different approach to solve a problem. Keep trying and you'll get it.

 

[thepatientmental]

commented: It seems like you have all the necessary information to solve this problem. Have you tried using the thin lens equation and the magnification formula to find the diameter of the image? Also, make sure you convert all lengths to the same unit before solving. If you're still having trouble, perhaps try drawing a ray diagram to visualize the setup and see if that helps. Good luck!

Thank you for your response! I did try using the thin lens equation and magnification formula, but I may have made a mistake in my calculations. I will double check my conversions and try drawing a ray diagram as you suggested. I appreciate your help!