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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