Question

The magnification produced by an astronomical telescope when the final image is formed at infinity is $10$ and the length of the telescope is $1.1\text{m}$. The magnification when the final image is formed at least distance of distinct vision is -

• A. $10$
• B. $12$
• C. $14$
• D. $16$

Answer 1

The correct option is C $14$

When the final image is formed at infinity :

The length of the tube is given by,

$L=f_o+f_e$

$\Rightarrow 110=f_o+f_e$

​​​​​​​$\Rightarrow f_o=110-f_e$

Also, magnifying power,

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

$\Rightarrow 10=\frac{110-f_e}{f_e}$

$\Rightarrow f_e=10\text{cm}$

When the final image is formed at the least distance of distinct vision :

Magnifying power is given by,

$m^{\prime }=\frac{f_o}{f_e}(1+\frac{f_e}{D})$

$\Rightarrow m^{\prime }=10(1+\frac{10}{25})=14$

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