Question

The resolving power of a telescope depends on
A) Focal length of eye lens
B) Focal length of objective lens
C) Length of the telescope
D) Diameter of the objective lens

Answer 1

Hint: This problem can be solved by using the direct formula for the resolving power of a telescope. The resolving power of a telescope is a measure of the telescope’s ability to distinguish two objects that are very close together and their angular separation is very less.

Formula used:
$RP\propto \dfrac{a}{1.22\lambda }$

Complete step-by-step answer:
The resolving power of a telescope is one of its most important features and parameters. It is the measure of the telescope’s ability to clearly distinguish two objects whose angular separation is smaller than the least angular separation that the observer’s eye can distinguish.
The resolving power of a telescope can be written to be proportional to the diameter of the objective lens and inversely proportional to the wavelength of the light.
Therefore, the relation between resolving power $RP$ of a telescope, the diameter$a$ of the objective lens and the wavelength $\lambda $ of the light is
$RP\propto \dfrac{a}{1.22\lambda }$ --(1)
From (1), we can see that the resolving power of a telescope depends upon the diameter of the objective lens.
Therefore, the correct option is D) Diameter of the objective lens.

Note: The resolving power of the telescope is the reason why an astronomical telescope can clearly distinguish between two stars whose angular separation is very small. Since stars and other celestial bodies are very far off, their angular separations are usually very small. Hence, astronomical telescopes require a high resolving power. This is the reason why astronomical observatories have astronomical telescopes that are so huge and have an objective lens with a very big diameter.