Optical path length

The optical path length is an important parameter in the study of optics. It is not the same as the physical length the light travels — it is instead the length weighted by the refractive index.

• In a homogeneous medium, we have a straight ray. Then, $\text{OPL}=nL$, where $L$ is length.
• In an inhomogeneous medium, the light is unlikely to be straight, so we’d need to do a line integral. Then, $\text{OPL}={\int }_A^{B}n(s)ds$.

As light traverses an OPL, it accumulates a phase difference, given by:

$${\phi }_{\text{OPL}}=\frac{2\pi }{\lambda }\Delta \text{OPL}$$

For a Fabry-Perot étalon or thin-film device:

$$\Delta \text{OPL}=2nd\cos ({\theta }_t)$$