As the waves propagate along, the values of x and t will change, but as the two waves are identical. The equation is expected to predict the intensity for multiple scattering at earlier times and shorter distances than the diffusion equation can. The phase difference between the two waves can be written in terms of the difference in position, time, and the phase constant, using Equation 1.2.9: 2 (x1 x2) 2 T (t1 t2) + 1 2 2 x 2 T t +. One formula for light intensity is I nfh At, I n f h A t, where: n n is the number of photons h h is Planck's constant f f is the frequency A A is the incident area t t is time. Begin with the equation that states the definition of intensity. Using the Fourier transform, an approximation based on expanding at small wave vectors k leads to an equation similar to the diffusion equation. 27.9 Extended Topic Microscopy Enhanced by the Wave Characteristics of Light. The equation can be decomposed into two terms: a propagator term obtained from the determinant of the coupled equations describing the individual components of the intensity, and a mixing matrix that describes the cross coupling between different orders of the expansion. This equation applies to the radiant intensity rather than the energy density. In this work a higher-order spherical-harmonic expansion of the radiative transfer equation is developed. Example 1: Calculating intensity and power: How much energy is in a ray of Sunlight Begin with the equation that states the definition of intensity: I I PA. This approximation applies to multiple scattering and results in a solution for the energy density, the gradient of which is proportional to the light intensity. where x is the 2D gradient operator over x, denotes the dyadic product between two vectors, and the notation v x (x, z) x (x, z)/k has been adopted for notational simplicity. The first two terms in the spherical-harmonic expansion (the P(1) approximation) of the radiative transfer equation yield the diffusion equation.

Equation for intensity of light