How does the Rayleigh criterion relate to the diffraction pattern?

The Rayleigh criterion relates to the diffraction pattern by defining the limit of resolution for an optical system.

The Rayleigh criterion is a standard used in the field of optics to determine the resolving power of an optical instrument, such as a microscope, telescope, or camera. It is named after the British physicist Lord Rayleigh, who first proposed it. The criterion is directly related to the diffraction pattern that light produces when it passes through an aperture, such as the opening of a lens.

When light passes through an aperture, it does not travel in a straight line but spreads out in a pattern known as diffraction. The central point of this pattern, where the light is most intense, is surrounded by a series of darker and lighter rings. This is known as the Airy pattern, named after the British astronomer Sir George Biddell Airy.

The Rayleigh criterion states that two point sources of light can be considered resolved when the centre of the diffraction pattern of one is directly over the first minimum of the diffraction pattern of the other. In simpler terms, this means that two objects are just resolved when the principal maximum of one image coincides with the first minimum of the other image. If the two points are closer together, they will appear as a single, blurred point of light.

The criterion is based on the wavelength of light and the size of the aperture. The smaller the aperture, the larger the diffraction pattern and the lower the resolution. Conversely, the larger the aperture, the smaller the diffraction pattern and the higher the resolution. Similarly, shorter wavelengths of light (such as blue light) will produce a smaller diffraction pattern and higher resolution than longer wavelengths (such as red light).

In summary, the Rayleigh criterion is a fundamental concept in optics that defines the limit of resolution for an optical system. It is directly related to the diffraction pattern that light produces when it passes through an aperture, and it is dependent on the wavelength of light and the size of the aperture. Understanding this criterion is crucial for anyone studying or working in the field of optics.