Rayleigh criterion

Examples of Rayleigh criterion in the following topics:

• The Rayleigh Criterion

  • The Rayleigh criterion determines the separation angle between two light sources which are distinguishable from each other.
  • In the 19th century, Lord Rayleigh invented a criteria for determining when two light sources were distinguishable from each other, or resolved.
  • Shown here is the Rayleigh criterion for being just resolvable.

• The Heisenberg Uncertainty Principle

  • If a large aperture is used for the microscope, the electron's location can be well resolved (see Rayleigh criterion); but by the principle of conservation of momentum, the transverse momentum of the incoming photon and hence the new momentum of the electron resolves poorly.

• Scattering of Light by the Atmosphere

  • Rayleigh scattering describes the air's gas molecules scattering light as it enters the atmosphere; it also describes why the sky is blue.
  • Rayleigh scattering is the elastic scattering of waves by particles that are much smaller than the wavelengths of those waves.
  • Rayleigh scattering is due to the polarizability of an individual molecule.
  • This increases the Rayleigh scattering effect and removes all blue light from the direct path of the observer.
  • Describe wave-particle relationship that leads to Rayleigh scattering and apply it to explain common phenomena

• An objective measure for finding the best line

  • Perhaps our criterion could minimize the sum of the residual magnitudes:
  • The line that minimizes this least squares criterion is represented as the solid line in Figure 7.12.
  • The following are three possible reasons to choose Criterion (second equation) over Criterion (first equation):
  • Computing the line based on Criterion (second equation) is much easier by hand and in most statistical software.
  • The first two reasons are largely for tradition and convenience; the last reason explains why Criterion (7.10) is typically most helpful.

• Polarization By Scattering and Reflecting

  • Just as unpolarized light can be partially polarized by reflecting, it can also be polarized by scattering (also known as Rayleigh scattering; illustrated in ).
  • Also known as Rayleigh scattering.

• Blackbody Radiation

  • This expression is most useful in the regime where the intensity of the blackbody is proportional to the temperature i.e. the Rayleigh-Jeans limit.

• Thermodynamics

  • This expression is most useful in the regime where the intensity of the blackbody is proportional to the temperature i.e. the Rayleigh-Jeans limit.Here we have,

• Blackbody Temperatures

  • This expression is most useful in the regime where the intensity of the blackbody is proportional to the temperature i.e. the Rayleigh-Jeans limit.

• Grading Students

  • Within each criterion, the teacher would then list degrees of fulfillment and pair those degrees with a letter or number grade.
  • An essay, for example, which was characterized by very clear prose might receive an "A" for that criterion.
  • If that same essay, however, was deeply unoriginal, it might receive a "C" for that criterion.
  • And if it lacked documentation all together, it might receive a "D" or an "F" for that criterion.
  • (She might weigh each criterion equally, or might assign the most important relatively more weight).

• Concavity and the Second Derivative Test

  • The second derivative test is a criterion for determining whether a given critical point is a local maximum or a local minimum.
  • In calculus, the second derivative test is a criterion for determining whether a given critical point of a real function of one variable is a local maximum or a local minimum using the value of the second derivative at the point.