Question

The magnifying power of a telescope is $9$. When it is adjusted for parallel rays the distance between the objective and eyepiece is $20$ cm. The focal length of lenses are :

• A. $18$cm, $2$cm
• B. $11$cm, $9$cm
• C. $10$cm, $10$cm
• D. $15$cm, $5$cm

Answer 1

The correct option is A $18$cm, $2$cm

Given: The magnifying power of a telescope is 9. When it is adjusted for parallel rays the distance between the objective and eyepiece is 20 cm.

To find the focal length of lenses

Solution:

According to the given criteria,

Magnification, $m=9$

Let focal length of the objective lens be $f_o$, and focal length of the eyepiece be $f_e$.

Then, $f_o+f_e=\mathrm{20....}\left(i\right)$

And, $m=\frac{f_o}{f_e}⟹9f_e=f_o....\left(ii\right)$

From (i) and (ii),

$9f_e+f_e=20⟹f_e=2cm$

Hence $f_o=9f_e=9\times 2=18cm$

are the focal length of the lenses.