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

Limit of Angular Resolution:
The limit of angular resolution refers to the smallest angular separation between two objects that a telescope can distinguish as separate entities. It is determined by the wave nature of light, which causes diffraction. When light passes through the aperture of the telescope, it forms a diffraction pattern instead of a single point. If the diffraction patterns of two objects overlap significantly, they appear as a single object.
The angular resolution is mathematically given by:
θ=1.22λD,\theta = 1.22 \frac{\lambda}{D},
where:
• θ\theta is the angular resolution in radians,
• λ\lambda is the wavelength of light,
• DD is the diameter of the aperture of the telescope.
A smaller θ\theta indicates better resolution, allowing the telescope to distinguish finer details.
Resolving Power of a Telescope:
The resolving power of a telescope is its ability to distinguish between two closely spaced objects, such as stars or planets. It is inversely related to the angular resolution:
Resolving Power∝1θ.\text{Resolving Power} \propto \frac{1}{\theta}.
A telescope with high resolving power can resolve objects that are very close to each other in the sky. The resolving power depends on the wavelength of light and the diameter of the telescope's aperture. Larger apertures and shorter wavelengths improve the resolving power.
Relationship and Significance:
• The limit of angular resolution defines the theoretical boundary for the telescope's resolving power.
• The resolving power determines the practical ability to distinguish between objects, accounting for factors like atmospheric disturbances and imperfections in the optical system.
In summary, the resolving power ensures that telescopes can reveal fine details of celestial objects, making it crucial for astronomical observations and studies.