Question

An astronomical telescope has objective and eyepiece of focal lengths $40cm$ and $4cm$ respectively. To view an object $200cm$ 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)

Using lens formula for objective lens
$\frac{1}{v_0}-\frac{1}{u_0}=\frac{1}{f_0}\Rightarrow \frac{1}{v_0}=\frac{1}{f_0}+\frac{1}{u_0}$
$\Rightarrow \frac{1}{v_0}=\frac{1}{40}+\frac{1}{-200}=\frac{+5-1}{200}$
$\Rightarrow v_0=50cm$
Tube length $\ell =\left|{\text{v}}_0\right|+f_e=50+4=54cm$