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Old Dec 2nd 2008, 09:41 PM   #1
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image of the moon

You wish to form an image of the moon, diameter 3500 km, a distance of 380 000 km away, with a reflecting telescope. If the image needs to be 4.5 cm in diameter, find the required focal length of the mirror in the telescope.
Formulas are
$\displaystyle \frac{1}{f}=\frac{1}{di}+\frac{1}{do}$
$\displaystyle \frac{hi}{ho}=\frac{-di}{do}$
F stands for focal point, di is distance to the image, do is distance to the object, hi is height of the image and ho is height of the object.

$\displaystyle \frac{4.5*10^-5}{3500}=\frac{-di}{380000}$
$\displaystyle f=-4.88*10^-3$
$\displaystyle \frac{1}{f}=\frac{1}{380000}+\frac{1}{-4.88*10^-3}$
$\displaystyle f= -4.88*10^-3 km $
is this correct???
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Old Dec 3rd 2008, 08:27 AM   #2
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It looks OK.
You can simplify a little bit if you neglect 1/do in the first equations (it's practically at infinite). You keep it in the second one, of course.
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