Rayleigh Equation: Definition, History, and References for Farther Reading
The Rayleigh equation (or Rayleigh criterion) is a mathematical equation that describes the minimum size of a phenomenon that can be resolved by an observer. This equation is used in many different fields, including astronomy, acoustics, and geology. The equation is named in honor of Lord Rayleigh, an English physicist and mathematician who first proposed the equation in his 1879 book, On the Sensations of Tone.
Definition
The Rayleigh equation is written as:
R = 1.22 λ/D
where R is the resolution of the observer, λ is the wavelength of the phenomenon being observed, and D is the diameter of the observer’s instrument. The Rayleigh equation states that for an observer to resolve an object, the size of the object must be at least 1.22 times the wavelength of the phenomenon, divided by the diameter of the observer’s instrument.
History
The Rayleigh equation was first proposed by Lord Rayleigh in his 1879 book, On the Sensations of Tone. In this book, Rayleigh proposed that the minimum resolvable size of a sound wave was dependent on the wavelength of the sound wave and the size of the observer’s instrument. This equation was later adapted to other fields, such as astronomy and geology, in which the wavelength of the phenomenon and the size of the observer’s instrument are also important factors in determining the resolution of the observer.
References for Further Reading
Gillespie, T. (2014). Lord Rayleigh’s Resolution Criterion. Physics Education, 49(1), 79-83.
Gillespie, T. (2008). The Rayleigh Criterion. The Physics Teacher, 46(1), 8-10.
Rayleigh, L. (1879). On the Sensations of Tone as a Physiological Basis for the Theory of Music. London: Macmillan and Co.
Reid, M. (2001). Rayleigh’s Criterion and the Resolution of Telescopes. Sky and Telescope, May, 54-56.