math intensity equation of light at surface

#Math intensity equation of light at surface series

(2) A graphical example of the grating equation: Figure 2 In terms of f the grating equation becomes

Often gratings are described by the frequency of grating lines instead of the period, where f (in lines/mm) is equal to 10 6/Λ (for Λ in nm). For a given angle of incidence, θ, it gives the angle of diffraction θ m for each “order” m for which a solution to (1) exists. Since AB = Λsinθ m and A’B’ = Λsinθ, where Λ is the grating period and θ m and θ are the angles of diffraction and incidence, respectively, relative to the surface normal, the condition for constructive interference is Mathematically, the difference between paths AB and A’B’ is a multiple of the wavelength when AB – A’B’ = mλ, where m is an integer and λ is the wavelength of light (typically stated in nm). If the difference between adjacent green-blue ray paths diffracted off of identical locations on adjacent periods is equal to a multiple of the wavelength of light, the two blue rays interfere constructively. The light is diffracted in many directions, only one of which is indicated by the blue rays. Referring to Figure 1, imagine a beam of light represented by the two green rays incident on the binary (rectangular profile) grating shown. Constructive interference leads to the grating equation: Figure 1

#Math intensity equation of light at surface series

If the surface irregularity is periodic, such as a series of grooves etched into a surface, light diffracted from many periods in certain special directions constructively interferes, yielding replicas of the incident beam propagating in those directions. When light is incident on a surface with a profile that is irregular at length scales comparable to the wavelength of the light, it is reflected and refracted at a microscopic level in many different directions as described by the laws of diffraction. Gratings are based on diffraction and interference:ĭiffraction gratings can be understood using the optical principles of diffraction and interference.