How does magnifying power change for an objective lens if the focal length of the objective lens is increased?

The correct option is: "The microscope will decrease but for the telescope, it will increase".

To understand why this is correct, let us analyze the formulas for the magnifying power of both a compound microscope and an astronomical telescope, and see how they depend on the focal length of the objective lens ($f_o$).

1. Magnifying Power of a Microscope:
The magnifying power ($m$) of a compound microscope is given by the relation:
$m\approx -\frac{L}{f_o}·\frac{D}{f_e}$
where:
- $L$ is the length of the microscope tube,
- $D$ is the least distance of distinct vision,
- $f_o$ is the focal length of the objective lens,
- $f_e$ is the focal length of the eyepiece lens.

From this equation, we can see that the magnifying power of a microscope is inversely proportional to the focal length of the objective lens:
$m\propto \frac{1}{f_o}$
Therefore, if the focal length of the objective lens ($f_o$) is increased, the magnifying power of the microscope will decrease.

2. Magnifying Power of a Telescope:
The magnifying power ($M$) of an astronomical telescope in normal adjustment is given by the relation:
$M=-\frac{f_o}{f_e}$
where:
- $f_o$ is the focal length of the objective lens,
- $f_e$ is the focal length of the eyepiece lens.

From this equation, we can see that the magnifying power of a telescope is directly proportional to the focal length of the objective lens:
$M\propto f_o$
Therefore, if the focal length of the objective lens ($f_o$) is increased, the magnifying power of the telescope will increase.

Conclusion:
When the focal length of the objective lens is increased, the magnifying power of the microscope decreases, while the magnifying power of the telescope increases.