Optical path length

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In optics, optical path length (OPL) or optical distance in a homogeneous medium is the product of the geometric length of the optical path followed by light and the refractive index of the medium through which a light ray propagates; for inhomogeneous media, the product above is generalized as an integral. In many textbooks, it is symbolically written as Λ. A difference in OPL between two paths is often called the optical path difference (OPD). OPL and OPD are important because they determine the phase of the light and governs interference and diffraction of light as it propagates.

Formulation[]

In a medium of constant refractive index, n, the OPL for a path of geometrical length s is just

If the refractive index varies along the path, the OPL is given by a line integral

where n is the local refractive index as a function of distance along the path C.

An electromagnetic wave propagating along a path C has the phase shift over C as if it was propagating a path in a vacuum, length of which, is equal to the optical path length of C. Thus, if a wave is traveling through several different media, then the optical path length of each medium can be added to find the total optical path length. The optical path difference between the paths taken by two identical waves can then be used to find the phase change. Finally, using the phase change, the interference between the two waves can be calculated.

Fermat's principle states that the path light takes between two points is the path that has the minimum optical path length.

Optical path difference[]

The OPD corresponds to the phase shift undergone by the light emitted from two previously coherent sources when passed through mediums of different refractive indices. For example, a wave passed through air will appear to travel a shorter distance than an identical wave in glass. This is because the source in the glass will have experienced a smaller number of wavelengths due to the higher refractive index of the glass.

The OPD can be calculated from the following equation:

where d1 and d2 are the distances of the ray passing through medium 1 or 2, n1 is the greater refractive index (e.g., glass) and n2 is the smaller refractive index (e.g., air).

See also[]

References[]

  • Public Domain This article incorporates public domain material from the General Services Administration document: "Federal Standard 1037C". (in support of MIL-STD-188)
  • Jenkins, F.; White, H. (1976). Fundamentals of Optics (4th ed.). McGraw-Hill. ISBN 0-07-032330-5.
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