Question

The magnifying power of an astronomical telescope can be increased if we

• A. Increase the focal length of the objective.
• B. Increase the focal length of the eye piece.
• C. Decrease the focal length of the objective.
• D. Decrease the focal length of the objective and at the same time increase the focal length of the eyepiece.

Answer 1

The correct option is A

Increase the focal length of the objective.

The magnification power of an astronomical telescope

1. Astronomical telescopes are used to see celestial objects in space.
2. The magnification power of an astronomical telescope is given by the form, $m=-\frac{f_o}{f_e}\left(1+\frac{f_e}{D}\right)$, where, $f_o$ is the focal length of the objective, $f_e$ is the focal length of the eyepiece, and $D$ is the least distance of clear vision.

Explanation for the correct option

Option (A): increase the focal length of the objective.

1. As we know, the magnification power of an astronomical telescope is $m=-\frac{f_o}{f_e}\left(1+\frac{f_e}{D}\right)..................\left(1\right)$.
2. Magnification of astronomical telescope when the image is formed at infinity is $m=\frac{-f_o}{f_e}$.
3. It is clear that if we increase the focal length of the objective $\left(f_o\right)$ , then the magnification of the telescope will be increased.

Diagram

The explanation for the incorrect options

Option (B): increase the focal length of the eyepiece.

1. From equation (1) it is clear that $m\propto \frac{1}{f_e}$.
2. if we increase the focal length of the eyepiece then the magnification power will decrease.

Option (C): decrease the focal length of the objective.

1. As we know, magnification power, $m\propto f_o$.
2. So, if we decrease the focal length of the objective then the magnification power will decrease.

Option (D): decrease the focal length of the objective and at the same time increase the focal length of the eyepiece.

1. Magnification power, $m\propto \frac{f_o}{f_e}$
2. So, if we increase the focal length of the eyepiece and decrease the focal length of the objective then the magnification power will decrease at a high rate.

So, option (A) is correct.