Question

An astronomical telescope has an angular magnification of magnitude $5$ for an object. The separation between the objective and the eye-piece is $36 \, cm$ . The final image is formed at infinity. The focal length $f_{0}$ of the objective and $f_{e}$ of the eye-piece are

• A. $45cm$ and $-9cm$
• B. $50cm$ and $10cm$
• C. $72cm$ and $2cm$
• D. $30cm$ and $6cm$

Answer 1

Answer: (D)

Magnification, $m=-5=\frac{- f_{0}}{f_{e}}\Rightarrow f_{0}=5f_{e}$
$\Rightarrow L=f_{0}+f_{e}=36$
$\Rightarrow 6f_{e}=36\therefore f_{e}=6 \, cm$
$\Rightarrow f_{0}=5f_{e}=30 \, cm$