The resolving power of a telescope is its ability to show two close objects (for example two stars) as separate images. Light passing through the circular aperture of the objective is diffracted, so each point source forms a small diffraction pattern, not a perfect point.
The Rayleigh criterion states that two point sources are just resolved when the central maximum of the diffraction pattern of one image falls on the first minimum of the other.The minimum angular separation that can be resolved is:θ ≈ λ / D where θ is in radians, λ is the wavelength and D is the diameter of the objective lens or mirror. A smaller θ means a better resolving power, so large apertures and short wavelengths give finer detail.Worked example: the Hubble Space Telescope has a mirror of diameter 2.4 m. For light of wavelength 550 nm:
θ ≈ 550 × 10-9 / 2.4 = 2.3 × 10-7 rad.The diameter also sets the collecting power, the amount of energy collected per second. This is proportional to the area of the objective, so:collecting power ∝ D2 Doubling the diameter increases the collecting power by a factor of 4, so fainter objects can be seen.
The Rayleigh criterion states that two point sources are just resolved when the central maximum of the diffraction pattern of one image falls on the first minimum of the other.The minimum angular separation that can be resolved is:θ ≈ 550 × 10-9 / 2.4 = 2.3 × 10-7 rad.The diameter also sets the collecting power, the amount of energy collected per second. This is proportional to the area of the objective, so: