Fermat’s Principle

If light travels from one point to another, it takes paths of a length that in first approximation is equal to the length of optical paths length closely adjascent to the actual path.

from one point to another light always chooses a path which’s OPL does not change if the path slightly varies.
Light always takes the shortest path in terms of speed but in general not the path of shortest distance.

The actual path taken has either a maximum or a minimum OPL compared to adjascent optical paths or is equal to the OPL of adjascent paths.

Optical Path Length

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

    \[ OPL = \int_{a}^{b} n(s) ds \]


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
In paraxial imaging system all of the light rays connecting a source point a to it’s image point have equal OLPs