Question

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

Answer 1

The correct option is A $54.0$ cm

On applying the lens formula for the objective lens:

$\frac{1}{f_0}=\frac{1}{v_0}-\frac{1}{u_0}$

$\frac{1}{v_0}=\frac{1}{f_0}+\frac{1}{u_0}$

$\frac{1}{v_0}=\frac{1}{40}+\frac{1}{-200}$

$v_0=50cm$

Therefore, tube length $=v_0+f_e=50+4=54cm$