Question

An astronomical telescope of ten-fold angular magnification in normal adjustment has a length of $44\text{cm}$. The focal length of the objective is -

• A. $440\text{cm}$
• B. $44\text{cm}$
• C. $40\text{cm}$
• D. $4\text{cm}$

Answer 1

The correct option is C $40\text{cm}$

Given:
$m=10$
$L=44\text{cm}$

We know that, in normal adjustment, the final image is formed at infinity.

The angular magnification is given by,

$m=\frac{f_o}{f_e}$

$\Rightarrow 10=\frac{f_o}{f_e}$

$\Rightarrow f_o=10f_e$

Also, tube length,

$L=f_o+f_e$

$\Rightarrow 44=10f_e+f_e$

$\Rightarrow f_e=4\text{cm}$

So, $f_o=10f_e=10\times 4=40\text{cm}$

Hence, option $\left(C\right)$ is the correct answer.