A lens of large focal length and large aperture is best suited as an objective of an astronomical telescope since :
a large aperture contributes to the quality and visibility of the images.
a large area of the objective ensures better light gathering power.
a large aperture provides a better resolution.
all of the above.
all of the above.
The correct answer is: all of the above.
In an astronomical telescope the objective lens should have both a large focal length and a large aperture because each of the following reasons is true:
1. Large aperture contributes to the quality and visibility of the images.
A larger aperture lets more photons from faint celestial objects reach the eye or detector, making faint details brighter and easier to see. This directly improves image quality and visibility.
2. Large area of the objective ensures better light‑gathering power.
The light‑gathering power of a lens is proportional to the area of its aperture (A = π r²). Doubling the radius quadruples the collected light, so a bigger objective collects significantly more light.
3. Large aperture provides a better resolution.
The diffraction‑limited angular resolution of a circular aperture is given by the Rayleigh criterion θ ≈ 1.22 λ ⁄ D, where D is the aperture diameter. Increasing D reduces θ, allowing the telescope to resolve finer details.
Because all three statements are valid, the most appropriate choice is “all of the above.”