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Opl Opt

Optical Path Length

The optical path length is proportional to the time light needs to travel between two points

    \[ OPL = \int_{a}^{b} n(s) ds \]

OPL

In a homogenous medium with refractuion index n and physical point distance d this formula simplifies to

    \[ OPL = n d \]

In glass with the index of refraction of 1.5 for some wavelength for a physical point distance of d=10mm the optical path length

    \[ OPL = 1.5 \cdot 10mm = 15mm \]

As glass has a different index of refraction for different wavelengths, the OPL is different for each wavelength
Some OPLs for glass type BK7 and a physical point distance of d=10mm
[table caption=”sample OPLs for BK7″ width=”400″ colwidth=”100|100|100|100″ colalign=”left|left|left”]
wavelength,index of refraction,phys. distance, OPL
400nm,1.5308,10mm,15.308mm,
500nm,1.5214,10mm,15.214mm,
600nm,1.5163,10mm,15.163mm,
850nm,1.5098,10mm,15.098mm,
940nm,1.5084,10mm,15.084mm
[/table]
In paraxial imaging system all of the light rays connecting a source point a to it’s image point have equal OLPs