Rayleigh distance Rayleigh distance Rayleigh distance in optics is the axial distance from a radiating aperture to a point at which the path difference between the axial ray and an edge ray is λ / 4. An approximation of the Rayleigh Distance is formula_1, in which Z is the Rayleigh distance, D is the aperture of radiation, λ the wavelength. This approximation can be derived as follows. Consider a right angled triangle with sides adjacent formula_2, opposite formula_3and hypotenuse formula_4. According to Pythagorean theorem, formula_5. Rearranging, and simplifying formula_6 The constant termformula_7 can be neglected. In antenna applications, the Rayleigh distance is
Sound pressure Since formula_18, the amplitude of the specific acoustic impedance is given by Consequently, the amplitude of the particle displacement is related to that of the acoustic velocity and the sound pressure by When measuring the sound pressure created by a sound source, it is important to measure the distance from the object as well, since the sound pressure of a "spherical" sound wave decreases as 1/"r" from the centre of the sphere (and not as 1/"r", like the sound intensity): This relationship is an "inverse-proportional law". If the sound pressure "p" is measured at a distance "r" from the centre