A lens of large focal length and large aperture is best suited as an objective of an astronomical telescope since :

The correct option is All of the above.

To understand why a lens with a large aperture is best suited as the objective of an astronomical telescope, let us analyze each of the given points step-by-step:

1. Light Gathering Power:
The primary function of an astronomical telescope is to observe distant, faint celestial bodies. The amount of light collected by the objective lens depends directly on its surface area. Since the area of a circular aperture of diameter $D$ is proportional to the square of the diameter, the light gathering power is also proportional to $D^2$:
$\text{Light Gathering Power}\propto D^2$
Therefore, a larger area of the objective lens ensures better light gathering power, allowing faint objects to appear brighter and clearer.

2. Resolving Power (Resolution):
Resolving power is the ability of an optical instrument to distinguish between two closely spaced point objects. For a telescope, the resolving power is given by the formula:
$\text{Resolving Power}=\frac{D}{1.22\lambda }$
where $D$ is the diameter of the aperture (objective lens) and $\lambda$ is the wavelength of light. From this expression, we can see that a larger aperture $D$ directly increases the resolving power, providing a much better resolution.

3. Quality and Visibility of Images:
Because a larger aperture collects more light (enhancing brightness/visibility) and resolves finer details (improving sharpness), it directly contributes to the overall quality and visibility of the resulting astronomical images.

Since all of the individual statements are correct, the correct choice is All of the above.