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These radiations are commonly produced by accelerating (or decelerating) charged particles. 3. Ultraviolet (UV) rays: The frequencies in UV rays range between 7×1014 to 3 × 1016 Hz (whose energy falls between 3 and 120 eV). 5 to 30 PHz; the wavelengths are λ = 10-200 nm. 5 PHz and wavelengths are λ = 200-400 nm. Unlike X-rays, ultraviolet radiation has a low power of penetration. 4. Optical band: The frequencies of optical band (visible band) fall between 4 × 1014 and 7 × 1014 Hz (λ 400-700 nm).

17) the position vector of a point, (x, y, z), in space. 16) is a linear second-order differential equation of a hyperbolic signature. In general, the differential equation is nonlinear, but in this case with the initial apptroximation it is assumed to be linear. The general solution of this equation in free space, in the form of V = V (r·ˆs, t), represents a plane wave in the direction given by the unit vector, ˆs(= sx , sy , sz ), since at each instant of time, V is constant over each of the planes, ˆs·r = constant, which are perpendicular to ˆs.

This information is encoded in the complex exponential representation. 61) This complex representation is preferred for linear time invariant systems, because the eigenfunctions of such systems are of the form e−i¯ωt , in which ω ¯ = 2π¯ ν is the angular frequency. 62) is the solution to the wave equation and represents spherical wave propagating outward from the origin. The irradiance of the spherical wave is proportional to the square of the amplitude a(r, ν)/r at a distance r. 63) in which stands for a Fourier transform.

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Algebre des ensembles by Sierpinski W.

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