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
Distance from a point to a plane the point on a plane formula_33 closest to an arbitrary point formula_34 is formula_2 given by where and the distance from the point to the plane is Distance from a point to a plane In Euclidean space, the point on a plane formula_1 that is closest to the origin has the Cartesian coordinates formula_2, where The distance between the origin and point formula_2 is formula_5. If what is desired is the distance from a point not at the origin to the nearest point on a plane, this can be found by a change of variables that moves the origin to