Question

An astronomical telescope has an angular magnification of magnitude of $5$ for distant objects. The length of a telescope is $36\text{cm.}$ The focal lengths of its objective and eye piece can be-

• A. $30\text{cm};6\text{cm}$
• B. $6\text{cm};30\text{cm}$
• C. $60\text{cm};12\text{cm}$
• D. $12\text{cm};60\text{cm}$

Answer 1

The correct option is A $30\text{cm};6\text{cm}$

Given,

$\text{Magnification}{M}_{\infty }=5;L=36\text{cm}$

$M_{\infty }=\frac{f_0}{f_e}......\left(1\right)$

$\Rightarrow 5=\frac{f_0}{f_e}$

$f_0=5f_e$

The length of the tube i.e., distance between the objective and eye piece lens is,

$L=f_0+f_e$

where, $f_0=\text{focal length of objective}$

$f_e=\text{focal length of eyepiece}$

$36=5f_e+f_e$

$36=6f_e$

$\therefore f_e=6\text{cm}$

Putting the value of $f_e$ in (1) we get,

$5=\frac{f_0}{6}$

$f_0=30\text{cm}$

<!--td {border: 1px solid #ccc;}br {mso-data-placement:same-cell;}--> Hence, $\left(A\right)$ is the correct answer.