Question

What is meant by the limit of angular resolution and the resolving power of a telescope?

Answer 1

Hint: The angular resolution tells us the ability of an optical instrument to distinguish two close objects. It is a measure of the number of details of an object, which the instrument can collect in the form of an image.

Complete step by step solution:
The angular resolution of an optical instrument is a measure of its ability to distinguish two close objects distinctly. It is equal to the angle subtended by the two close objects at the optical instrument, provided that the two objects are distinguishable by the optical instrument. The examples of the optical instruments, whose angular resolution is measured, include microscope, telescope, eyes, camera etc.
Now, the limit of the angular resolution refers to the smallest value of this angle, up to which the two objects can be distinguishable by the optical instrument. The value of the angular resolution is limited due to the wave nature of light. The phenomenon of diffraction of light, which is a consequence of the wave nature of light, is responsible for this limit. The light passing through an aperture spreads and gets blurred due to diffraction, limiting the resolution.
The limit of the angular resolution is also called the resolving power.
Now, the resolving power of a telescope, according to its definition, is calculated by measuring the angle subtended by two distant objects at the objective lens of the telescope, when those two objects are just observed as separate objects.
The value of this angle subtended is found to be directly proportional to the wavelength of the light used. Also, it is found to be inversely proportional to the aperture, or the diameter of the objective lens of the telescope.
So this angle is given by
$\Delta {{\theta }} = \dfrac{{1.22\lambda }}{D}$, where $1.22$ is equal to the constant of proportionality.
Now, according to the definition, this angle is nothing but the resolving power of the telescope.

Note: The value of the constant of proportionality, equal to $1.22$, is valid for the circular apertures, like the human eye, cameras, telescopes etc. An application of the resolving power is found in the cameras fitted in the Smartphone. We generally ask for the megapixel count of the camera while purchasing a Smartphone. This megapixel count is nothing but the resolving power of the camera.