How is optical path length different from actual path length
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Answer:
a medium of constant refractive index, n, the OPL for a path of geometrical length s is just
a medium of constant refractive index, n, the OPL for a path of geometrical length s is just{\displaystyle \mathrm {OPL} =ns.\,}{\displaystyle \mathrm {OPL} =ns.\,}
a medium of constant refractive index, n, the OPL for a path of geometrical length s is just{\displaystyle \mathrm {OPL} =ns.\,}{\displaystyle \mathrm {OPL} =ns.\,}If the refractive index varies along the path, the OPL is given by a line integral
a medium of constant refractive index, n, the OPL for a path of geometrical length s is just{\displaystyle \mathrm {OPL} =ns.\,}{\displaystyle \mathrm {OPL} =ns.\,}If the refractive index varies along the path, the OPL is given by a line integral{\displaystyle \mathrm {OPL} =\int _{C}n\mathrm {d} s,\quad }{\displaystyle \mathrm {OPL} =\int _{C}n\mathrm {d} s,\quad }
a medium of constant refractive index, n, the OPL for a path of geometrical length s is just{\displaystyle \mathrm {OPL} =ns.\,}{\displaystyle \mathrm {OPL} =ns.\,}If the refractive index varies along the path, the OPL is given by a line integral{\displaystyle \mathrm {OPL} =\int _{C}n\mathrm {d} s,\quad }{\displaystyle \mathrm {OPL} =\int _{C}n\mathrm {d} s,\quad }where n is the local refractive index as a function of distance along the path C.
a medium of constant refractive index, n, the OPL for a path of geometrical length s is just{\displaystyle \mathrm {OPL} =ns.\,}{\displaystyle \mathrm {OPL} =ns.\,}If the refractive index varies along the path, the OPL is given by a line integral{\displaystyle \mathrm {OPL} =\int _{C}n\mathrm {d} s,\quad }{\displaystyle \mathrm {OPL} =\int _{C}n\mathrm {d} s,\quad }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.
a medium of constant refractive index, n, the OPL for a path of geometrical length s is just{\displaystyle \mathrm {OPL} =ns.\,}{\displaystyle \mathrm {OPL} =ns.\,}If the refractive index varies along the path, the OPL is given by a line integral{\displaystyle \mathrm {OPL} =\int _{C}n\mathrm {d} s,\quad }{\displaystyle \mathrm {OPL} =\int _{C}n\mathrm {d} s,\quad }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. Fermat's principle states that the path light takes between two points is the path that has the minimum optical path length.
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