Question

An astronomical telescope has a larger aperture to
(A) Reduce spherical aberration
(B) Have high resolution
(C) Increase span of observation
(D) Have low dispersion

Answer 1

Hint: To answer this question, we have to look out for the ways of the effects given in the options. Then with the help of these we can eliminate all the incorrect options and get the correct answer.

Formula used: The formula which has been used to solve this question is given by
 $ RP = \dfrac{{1.22D}}{\lambda } $, here $ RP $ is the resolving power of an astronomical telescope having the aperture of the objective lens as $ D $ and $ \lambda $ as the wavelength of the light.

Complete step by step answer
The spherical aberration occurs, when the collection of light rays incident on a lens are not focused on a single point. To reduce the spherical aberration, we use the lens which does not have a constant curvature. Usually, parabolic lenses are used for this purpose.
So we see that the reduction of the spherical aberration has nothing to do with the aperture of the telescope.
So the option A is incorrect.
The dispersion is the phenomenon of splitting of the white light into its components, when it passes through a refracting surface. It occurs for each ray of light incident on the lens, and hence has nothing to do with the aperture of the telescope.
So the option D is also incorrect.
Now, the resolution of an optical instrument is defined as its ability to observe two different objects distinctly. It is measured by the resolution power of the instrument. The resolving power of the astronomical telescope is given by
 $\Rightarrow RP = \dfrac{{1.22D}}{\lambda } $
So from the above expression we observe that the resolving power is directly proportional to the aperture of the objective lens. So, on increasing the aperture, we will have higher resolution power. So the aperture of an astronomical telescope is kept large.

Hence, the correct answer is option B.

Note
This question could also be attempted without using the exact formula for the resolution power for the astronomical telescope. When the aperture of the objective of the telescope will be large, then it will collect more number of rays. More number of rays will help in forming a much clearer image of the distant object, and hence its resolution will increase.