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A 5-inch, f/10 telescope has a 2-inch eyepiece focal. Its magnifying power is _____.

10X

25X

50X

100X

Verified Answer :

Answer:

Magnifying power = 25

Explanation:

Magnification power (M) of a telescope is a measure of the extent to which it enlarges the object under view. It given in terms of the ratio of the focal length of the telescope objective to that of the eyepiece

\(M = \frac{objective\ focal\ length}{eyepiece\ focal\ length}-----(1)\)

The f/ratio measures the light gathering power of a lens. It is expressed in terms of the focal length of the lens divided by its diameter.

\(f/ratio = \frac{focal\ length}{diameter} ------(2)\)

It is given that:

eyepiece focal length = 2-inch

f/ratio = 10

Diameter of the objective = 5-inch

Based on eq(2), the focal length of the objective would be:

\(focal\ length = f/ratio * diameter = 10*5 = 50\ inches\)

Based on eq(1), the magnifying power would be:

\(M = \frac{50}{2} = 25\)

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