Question

An astronomical telescope has an angular magnification of magnitude $5$ for distant objects.The separation between the objective and the eyepiece is $36cm$. The final image is formed at infinity. The focal lengths of the objective and the eyepiece are respectively:

• A. 20 cm, 2 cm
• B. 30 cm, 3 cm
• C. 40 cm, 4 cm
• D. 30 cm, 6 cm

Answer 1

The correct option is D 30 cm, 6 cm

$f_o=?$

$f_e=?$

$M=5=\frac{f_o}{u_o}$,

As $u_e=f_e$

$L=f_o+u_e=36$

$M_{\infty }=\frac{f_o}{f_e}$

$L_{\infty }=f_o+f_e$

$36=f_o+f_e$

$5=\frac{f_o}{f_e}$

$f_o=5f_e$

$\Rightarrow 6f_e=36$

$f_e=6cm$

$f_o=30cm$