Question

Find the length of the astronomical telescope if it is adjusted such that the final image is formed at the least distance of distinct vision. Focal length of objective lens and eyepiece are $80\text{cm}$ and $5\text{cm}$ respectively.

• A. $81\text{cm}$
• B. $84\text{cm}$
• C. $82\text{cm}$
• D. $85\text{cm}$

Answer 1

The correct option is B $84\text{cm}$

Given:
$f_o=80\text{cm}$
$f_e=5\text{cm}$

Also, the final image is formed at the least distance of distinct vision.

So, $v_e=-D=-25\text{cm}$

On using lens formula for eyepiece,

$\frac{1}{v_e}-\frac{1}{u_e}=\frac{1}{f_e}$

$\Rightarrow \frac{1}{(-25)}-\frac{1}{u_e}=\frac{1}{5}$

$\Rightarrow u_e=-4.2\text{cm}$

We know that, for this adjustment, the length of the telescope is given by,

$L=f_o+|u_e|$

$\Rightarrow L=80+4.2\approx 84\text{cm}$

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