The Rayleigh criterion defines the minimum angular separation at which two point light sources can be resolved as distinct. It is determined by the diffraction limit of an optical system.
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The Rayleigh criterion is used to determine the resolving power of optical instruments like telescopes and microscopes.
According to the Rayleigh criterion, two sources are considered resolvable when the central maximum of one diffraction pattern coincides with the first minimum of the other.
Mathematically, it is given by $\theta = 1.22 \frac{\lambda}{D}$, where $\theta$ is the angular resolution, $\lambda$ is the wavelength of light, and $D$ is the diameter of the aperture.
The factor 1.22 in the formula arises from calculations involving a circular aperture and Airy disk patterns.
Smaller wavelengths and larger apertures improve resolving power according to this criterion.
Review Questions
What does the Rayleigh criterion define in terms of optical resolution?
How is the angular resolution calculated using the Rayleigh criterion?
Why does increasing aperture size improve resolving power under the Rayleigh criterion?
A pattern produced by light passing through a circular aperture, consisting of a central bright spot surrounded by rings; it plays a role in determining resolution limits.