Question

An astronomical telescope has objective and eyepiece of focal lengths $40\, cm$ and $4 \,cm$ respectively. To view an object $200\, cm$ away from the objective, the lenses must be separated by a distance :

• A. 46.0 cm
• B. 50.0 cm
• C. 54.0 cm
• D. 37.3 cm

Answer 1

Answer: (C)

54.0 cm

Answer 2

Using lens formula for objective lens
$\frac{1}{v_{0} } -\frac{1}{u_{0}} = \frac{1}{f_{0}} \Rightarrow \frac{1}{v_{0}} = \frac{1}{f_{0}} + \frac{1}{u_{0}}$
$\Rightarrow \frac{1}{v_{0}} = \frac{1}{40} + \frac{1}{-200} = \frac{+5-1}{200}$
$\Rightarrow v_{0} = 50 cm$
Tube length $\ell = \left|\text{v}_{0}\right| + f_{e} = 50 + 4 = 54 \; cm$