Question

A Galilean telescope has an objective of focal length $100$ cm and magnifying power $50$. The distance between the two lenses in normal adjustment will be:

• A. 98 cm
• B. 100 cm
• C. 150 cm
• D. 200 cm

Answer 1

Answer: (A)

In Galilean telescope a convergent lens is used as the objective and a divergent lens as the eye piece. Magnifying power and length of telescope are written as:
$ M=\frac{{{f}_{o}}}{{{u}_{e}}} $
and $ L={{f}_{o}}-{{u}_{e}} $
In normal adjustment, i.e., in relaxed eye state
$ {{u}_{e}}={{f}_{e}} $
So, $ {{M}_{\infty }}=\frac{{{f}_{o}}}{{{f}_{e}}}=50 $
or $ {{f}_{e}}=\frac{{{f}_{o}}}{50}=\frac{100}{50}=2\,cm $
and $ {{L}_{\infty }}={{f}_{o}}-{{f}_{e}} $
$ \therefore $ $ {{L}_{\infty }}=100-2=98\,cm $