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In optics, optical path length (OPL, denoted Λ in equations), also known as optical length or optical distance, is the length that light needs to travel through a vacuum to create the same phase difference as it would have when traveling through a given medium.
Optical path (OP) is the trajectory that a light ray follows as it propagates through an optical medium. The geometrical optical-path length or simply geometrical path length ( GPD ) is the length of a segment in a given OP, i.e., the Euclidean distance integrated along a ray between any two points. [ 1 ]
Subscripts 1 and 2 refer to initial and final optical media respectively. These ratios are sometimes also used, following simply from other definitions of refractive index, wave phase velocity, and the luminal speed equation:
De Witte's treatment is more original than that description might suggest, although limited to two dimensions; it uses calculus of variations to show that Huygens' construction and Fermat's principle lead to the same differential equation for the ray path, and that in the case of Fermat's principle, the converse holds. De Witte also noted that ...
The optical path length from the light source is used to compute the phase. The derivative of the position of the ray in the focal region on the source position is used to obtain the width of the ray, and from that the amplitude of the plane wave. The result is the point spread function, whose Fourier transform is the optical transfer function.
When the two waves are in phase, i.e. the path difference is equal to an integral number of wavelengths, the summed amplitude, and therefore the summed intensity is maximum, and when they are in anti-phase, i.e. the path difference is equal to half a wavelength, one and a half wavelengths, etc., then the two waves cancel and the summed ...
This path difference is (+) (′). The two separate waves will arrive at a point (infinitely far from these lattice planes) with the same phase , and hence undergo constructive interference , if and only if this path difference is equal to any integer value of the wavelength , i.e. n λ = ( A B + B C ) − ( A C ′ ) {\displaystyle n\lambda ...
A blazed diffraction grating reflecting only the green portion of the spectrum from a room's fluorescent lighting. For a diffraction grating, the relationship between the grating spacing (i.e., the distance between adjacent grating grooves or slits), the angle of the wave (light) incidence to the grating, and the diffracted wave from the grating is known as the grating equation.