An astronomical telescope has magnifying power 6 for distant objects

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Option 1 : 6 cm and 48 cm

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CONCEPT:

Telescope: The instrument which makes the distant object appear nearer is called a telescope.
The telescope has two convex lenses- one of them is called as an objective lens and another one is known as the eyepiece

The magnification of a telescope is given by:

M = f0/fe

Where f0 is the focal length of the objective and fe is the focal length of the eyepiece.

The distance between the two lenses is given by:

L∝ = f0 + fe

CALCULATION:

Given that \({m_ \propto } = 8\;\;and\;{L_ \propto } = 54\)

By using \(\left| {{m_ \propto }} \right| = \frac{{{f_0}}}{{{f_e}}}\;\;and\;{L_ \propto } = {f_0} + {f_e}\)

⇒ f0/fe = 8

⇒ f0 = 8fe

Also f0 + fe = 54

⇒ 8fe + fe = 54

So fe = 54/9 = 6 cm

We get, fe = 6 cm and f0 = 48 cm.

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