Rayleigh Criterion

The Rayleigh criteria establishes the smallest distance between two light sources that can be resolved into separate objects.

When a point source, such as a star, is examined using a circular aperture telescope, the image is a disc encircled by a number of very faint rings, rather than a point source. Fraunhofer diffraction of light by the circular aperture produces these rings. The Rayleigh criteria was designed with an incoherent optical system in mind. Because fluorescence is an incoherent process in which two luminous point objects fluoresce independently, it can be used in fluorescence microscopy.

Resolving power  

The ability of microscopes, telescopes, or any optical device to resolve two nearly situated objects as independent objects is referred to as resolving power. Due to overlapping diffraction patterns formed by two nearly situated objects, any optical instrument’s resolving power has a theoretical upper limit. The resolving power of any instrument is influenced by a number of things. Modifications can be made to improve resolution or resolving power. There is no unit for resolving power; it is a dimensionless quantity.

Limit of resolution

The angular or linear distance between two objects that have just been resolved is the limit of resolution. It’s similar to the concept of resolving power. In fact, the resolving power is equal to the inverse of the resolution limit. As a result, a lower limit of resolution indicates a stronger objective lens resolving ability.

Diffraction limit

When a point item is viewed through an aperture (a circular opening), a diffraction pattern instead of a point image is created. The diffraction pattern is more visible when the item size is comparable to the wavelength of the light. As we go away from the centre, the diffraction pattern appears as concentric rings that fade out. Airy discs or Airy patterns are what they’re called. Diffraction, comparable to that produced by a single slit, is responsible for this pattern. Different sections of the circular aperture interfere with each other, both constructively and destructively. The effect is most evident when the aperture is tiny, although it can also be seen when the aperture is big.

As we progress, the concentric rings fade away to the point when two Airy discs or patterns are no longer discernible from one another. The diffraction limit is what it’s termed.

Rayleigh’s criterion

The Rayleigh criteria illustrates that diffraction limits the minimum angular spread that an image forming system can resolve to the ratio of the wavelength of the waves to the aperture width. As a result, big apertures are used in high-resolution imaging systems such as astronomical telescopes, long-distance telephoto camera lenses, and radio telescopes.

The distance between two recently resolved objects is determined by Rayleigh’s criterion. It claims that two images are just resolved when one image’s diffraction pattern is greater than the second image’s first minimum diffraction.

The formula for the smallest angular distance between two just resolvable objects is given by Rayleigh’s criterion. The formula will be:  θ=1.22λ/D

Here D = circular aperture

And = wavelength

Resolving power of Telescope

A telescope is a device that is used to see distant objects. It usually consists of lenses, curved mirrors, or a combination of the two to assist us in viewing faraway objects as if we were looking at them from a closer distance. It is most commonly used to observe various planetary objects.

When two distant stars are too close to each other, the angular gap between them is quite small. The telescope’s resolving capacity decides whether the stars seem to us as separate stars.

The resolving power of telescope will be given as: resolving power=1=d/1.22λ

Here is the angular separation between the two objects

d = diameter of lens

= wavelength of light 

Resolving power of microscope

A microscope is a device that allows you to look at microscopic objects that are too small to see with your naked eye. It is made up of two lenses: an objective lens and an eyepiece (also known as an ocular lens). The angle subtended by the diameter of the objective lens at the microscope’s focus and the refractive index of the medium between the lens and microscopic specimen determine the resolving power of a microscope.

The resolving power of microscope will be given as:

 Resolving power=1d=2a/λ

Here a is numerical aperture

is wavelength

Resolving power of human eye

Like any other optical instrument, the resolving power of the eyes is determined by the diameters of the lens, in this case the pupil, and the wavelength, which is equivalent to the wavelength of visible light.

Conclusion

The Rayleigh criteria establishes the smallest distance between two light sources that can be resolved into separate objects. The Rayleigh criteria was designed with an incoherent optical system in mind. The ability of microscopes, telescopes, or any optical device to resolve two nearly situated objects as independent objects is referred to as resolving power. The angular or linear distance between two objects that have just been resolved is the limit of resolution. A telescope is a device that is used to see distant objects. A microscope is a device that allows you to look at microscopic objects that are too small to see with your naked eye.