[UPSC CSE 2026] Diffraction (Q226, 15M)

Using Fraunhofer diffraction theory, derive the expression for the intensity distribution due to a circular aperture and obtain the condition for the first minimum. Using this result, derive the expression for the resolving power of an optical instrument. Finally, calculate the minimum angular separation that can be resolved by a telescope of aperture diameter D = 10\text{ cm} for light of wavelength 500\text{ nm}.