Spherical Mirrors

The question is about selecting the best objective lens for an astronomical telescope. Let's analyze each of the given options to understand why a lens with a large focal length and large aperture is preferable:

1. A large aperture contributes to the quality and visibility of the images. A larger aperture allows more light to enter the telescope, improving the brightness of the image and enhancing the visibility of faint astronomical objects.
2. A large area of the objective ensures better light gathering power. This is directly related to the lens's ability to gather light. When the aperture is larger, the lens can capture more photons from distant stars or galaxies, which is crucial for astronomical observations, especially under low-light conditions.
3. A large aperture provides a better resolution. According to the Rayleigh criterion, the resolution (or ability to distinguish between two close objects) improves with an increase in aperture size. This is because the resolving power of a lens is proportional to its diameter.

Based on the analysis, all the options provided are correct because each explains a beneficial characteristic of a large aperture and focal length in an astronomical telescope. Therefore, the correct answer is all of the above.