Question

A telescope has an objective of focal length $30\text{cm}$ and an eyepiece of focal length $3.0\text{cm}$. It is focused on an object of distance $2.0$ meter. For seeing with relaxed eye, calculate the separation between the objective and the eyepiece.

• A. $33\text{cm}$
• B. $27\text{cm}$
• C. $38.3\text{cm}$
• D. None of these

Answer 1

The correct option is C $38.3\text{cm}$

For seeing with relaxed eye, the final image should be formed at $\infty$

For objective lens
$\frac{1}{v}-\frac{1}{u_0}=\frac{1}{f_0},$
$\begin{array}{c}{u}_0=-200\text{cm}\\ f_0=+30\text{cm}\end{array}$
$\frac{1}{v_0}-\frac{1}{-200}=\frac{1}{30}$
So, $v_0=\frac{600}{17}=35.3\text{cm}$
Distance between objective and eyepiece is
$L=v_0+f_e=35.3+3=38.3\text{cm}$