Multiple Choice
A 60-power telescope has an eyepiece with a focal length of 4cm. How long is this telescope?
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Telescopes
Multiple Choice
In order to clearly see the Great Red Spot, a persistent storm visible on the surface of Jupiter, you'd need an angular magnification of no less than 150. If you have a telescope with an objective lens with a focal length of 1800mm, what is the maximum focal length of the eyepiece?
A
0.083 mm
B
270,000 mm
C
12 mm
D
1800 mm
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Verified step by step guidance1
Recall the formula for angular magnification (M) of a telescope in terms of the focal lengths of the objective lens (f_o) and the eyepiece (f_e):
\[M = -\frac{f_o}{f_e}\]
The negative sign indicates image inversion, but for magnitude, we consider the absolute value.
Identify the given values from the problem:
- Angular magnification required: \(|M| \geq 150\)
- Focal length of the objective lens: \(f_o = 1800\) mm
- Focal length of the eyepiece: \(f_e = ?\) (to be found)
Rearrange the magnification formula to solve for the eyepiece focal length \(f_e\):
\[f_e = \frac{f_o}{|M|}\]
Substitute the known values into the rearranged formula:
\[f_e = \frac{1800}{150}\]
This will give the maximum focal length of the eyepiece that still achieves the required angular magnification.
Interpret the result:
The calculated \(f_e\) is the maximum focal length of the eyepiece lens to achieve at least 150 times angular magnification, meaning any eyepiece with a focal length less than or equal to this value will work.
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