The Question is: An objective lens of a telescope has a 1.90 m focal length. When viewed through this telescope, the moon appears 5.25 times larger than normal. How far apart are the objective lens and the eyepiece when this instrument is focused on the moon?
I know that the magnification equation is: normal near point distance(25) / focal length of the magnifying glass. However, I am confused on how I can use this to solve the problem. I would really appreciate your help! Thank You!
Oh wait, I just tried a different equation and want to confirm that this is correct: M = Fobj/Fep =>
Fep = Fobj/M ==> Fep = 19cm/5.25 = 3.62 + 19cm = 22.62 cm
To solve this problem, let's break it down step by step:
1. The given information includes:
- Focal length of the objective lens (f) = 1.90 m
- Magnification (M) = 5.25
2. The magnification equation relates the magnification (M) to the focal length of the objective lens (f) and the focal length of the eyepiece (f') as follows:
M = -f / f'
Since we are given M, we can rearrange the formula to solve for f':
f' = -f / M
3. Plug in the given values:
f' = -1.90 m / 5.25
f' ≈ -0.362 m
Note: The negative sign indicates that the eyepiece should be placed on the opposite side of the lens from where the image is formed.
4. Now, we need to determine the distance between the objective lens and the eyepiece, which we can call D.
The total length of the telescope (L) is the sum of the distances between the objective lens and the eyepiece, as well as the focal length of the objective lens:
L = D + f
5. To find D, we need to rearrange the equation:
D = L - f
6. Since we know that the magnification is equal to the ratio of the image distance (di) to the object distance (do):
M = di / do
In this case, the object distance (do) is essentially the focal length of the objective lens (f), and the image distance (di) is the total length of the telescope (L). Thus:
M = L / f
7. Rearrange the equation to find L:
L = M * f
8. Plug in the given values:
L = 5.25 * 1.90 m
L ≈ 9.975 m
9. Now we can calculate D:
D = 9.975 m - 1.90 m
D ≈ 8.075 m
Therefore, the objective lens and the eyepiece should be approximately 8.075 meters apart when the telescope is focused on the moon.