Telescope Problem Homework: Angle & Diameter of Moon Image

[rayhan619]

Homework Statement

Your telescope has a 700 mm focal-length objective and a 28 mm focal-length eyepiece.
a) What angle (in degrees) does the image of the moon subtend, when you look at it through your telescope?
b) Suppose you decide to take a photograph of the moon using your telescope. You position film so that it captures the image produced by the objective lens. What is the diameter of that image?

Homework Equations

The Attempt at a Solution

i got the first part right. my ans is 13 degree. but how i do b)?

 

[anathema]

For part b), we can use the formula for angular magnification:

M = -fo/fe

Where M is the angular magnification, fo is the focal length of the objective lens, and fe is the focal length of the eyepiece.

Since we are taking a photograph, we want the image to be as large as possible, so we want the angular magnification to be as large as possible. This can be achieved by making the focal length of the eyepiece as small as possible.

So, let's say we use a very small eyepiece with a focal length of 1 mm. Then, the angular magnification would be:

M = -700/1 = -700

This means that the image of the moon will appear 700 times larger than it would be with the naked eye.

Now, to find the diameter of the image, we can use the formula:

d = D/M

Where d is the diameter of the image, D is the diameter of the objective lens, and M is the angular magnification.

In this case, D = 700 mm and M = 700, so:

d = 700/700 = 1 mm

So, the diameter of the image of the moon captured by the objective lens would be 1 mm.

Note: In reality, it would be difficult to use an eyepiece with a focal length of 1 mm, so a more practical approach would be to use a camera with a zoom lens and adjust the focal length to get the desired angular magnification.

 

[nlightner]

For part b), you will need to use the formula for angular magnification, which is given by M = f_obj / f_ep. In this case, f_obj = 700 mm and f_ep = 28 mm. So, M = 700/28 = 25. This means that the image of the moon will appear 25 times larger through the telescope than it would with the naked eye.

To calculate the diameter of the image, you will need to know the actual diameter of the moon. This can be found by doing some research or using a moon diameter calculator. Let's say the diameter of the moon is 3,474 km.

Using the formula for angular magnification again, we can calculate the diameter of the moon's image as follows:

M = D_img / D_obj

Where D_img is the diameter of the moon's image and D_obj is the actual diameter of the moon.

Rearranging the equation, we get:

D_img = M * D_obj

Plugging in the values, we get:

D_img = 25 * 3,474 km = 86,850 km

Therefore, the diameter of the moon's image through your telescope will be approximately 86,850 km.