Question

Why is it advantageous to use a large-diameter objective lens in a telescope?
A. It diffracts the light more effectively than smaller-diameter objective lenses.
B. It increases its magnification.
C. It enables you to see more objects in the field of view.
D. It reflects unwanted wavelengths.
E. It increases its resolution.

Answer 1

Hint: Using the concept of diffraction of light we can get a brief knowledge about the problem so as to move further in this problem. Now using the formula of minimum angular separation we can get the relation between the wavelength of the incident light, the diameter of the objective lens in the telescope and the minimum angular separation.

Complete step by step answer:
Diffraction of light is a phenomenon that occurs when a light wave passes by a corner or through an opening or slit that is physically the approximate size and even smaller than that of the light’s wavelength. When a light proceeding from a small source falls upon an opaque object or solid object a shadow is cast upon a screen that is placed behind the opaque object then this shadow is found to be the border of alternative brightness and darkness which is caused due to the diffraction of light.

Now when diffraction of light passes through or reflected back from the objective elements of a telescope can cause the images of two sources which are having a small angular separation to overlap and fail to be seen as separate images.
So using the formula of minimum angular separation formula we can write,
${\theta _{\min }} = \dfrac{{1.22\lambda }}{D}$
Where, $\lambda $ is the wavelength of the incident light, $D$ is the diameter of the objective lens in the telescope.

Now we can say that minimum angular separation ${\theta _{\min }}$ is inversely proportional to the diameter of the objective lens $D$. Thus we can say that using a large-diameter objective lens in a telescope increases its resolution.

Therefore the correct option is E.

Note: Telescope is a device that is used to form a magnified image and that object is far away from us. Keep in mind that a telescope is the most important investigative tool in astronomy. Telescope makes distant objects clear, brighter and closer so that we can see distant objects. Note that it has three main functions: light gathering, resolution and magnification.