The term optical path is used in two different ways. It can mean either the distance traveled in an optical system by light (more properly called the optical path length), or the optical depth measured along the true (slant) optical path ds. The latter definition therefore is a multiple of K (the extinction coefficient) of the former.
In the convention used by atmospheric scientists studying the Earth, is measured upwards from the surface
where K is the extinction coefficient, is the opacity, and is the density, so
However, in the planetary and stellar atmospheres convention, is measured downwards from the top of the atmosphere, so
and
Optical Depth, Optical Path Length, Radiative Transfer
