Question

A telescope has a objective of focal length $50cm$ and an eye-piece of focal length $5cm$. The least distance of distinct vision is $25cm$. The telescope is focused for distinct vision on a scale of $200cm$ away. The separation between the objective and the eye-piece is

• A. $75cm$
• B. $60cm$
• C. $71cm$
• D. $74cm$

Answer 1

The correct option is C $71cm$

For objective $u_0=-200cm$,

Using Lens formula,
$\frac{1}{v_0}-\frac{1}{-200}=\frac{1}{50}$
$\therefore v_0=\frac{200}{3}cm$

For eye-piece $v_e=-25cm$,
Using Lens formula,
$\frac{1}{-25}-\frac{1}{(-u_e)}=\frac{1}{5}{u}_e=\frac{25}{6}cm$

Therefore, separation between objective and eye-piece,
$L=v_0+u_e=\frac{200}{3}+\frac{25}{6}=\frac{425}{6}=71cm$(approx)