Question

The focal length of the objective and eyepiece of an astronomical telescope are $20\text{cm}$ and $20\text{cm}.$ If the final image is at the minimum distance of clear vision. Then the length of the tube will be-

• A. $27.1\text{cm}$
• B. $25\text{cm}$
• C. $30\text{cm}$
• D. None of these

Answer 1

The correct option is A $27.1\text{cm}$

Given,

$\text{Focal length of objective},f_o=20\text{cm}\text{Focal length of eyepiece},f_e=10\text{cm}\text{Least distance of distinct vision}=25\text{cm}$

The length of the tube of an astronomical telescope is given by,

$L=f_o+\frac{D{f}_e}{D+f_e}$

$L=20+\frac{25\times 10}{25+10}$

$L=20+\frac{250}{35}$

$L=27.1\text{cm}$

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