# Translations:Fermat’s principle - book/20/en

In conclusion, if the curvature of the actual refracting surface is greater than that of the equal-time refraction surface where they are tangent, then the true raypath is a maximum time path. Likewise, it also can be shown that if the curvature of the actual refracting surface is less than that of the tangent equal-time surface, the raypath is a minimum. A refracting surface that is a plane is always of this latter type and therefore always produces a refracted path of minimum traveltime. These conclusions are identical to those derived above for reflecting surfaces. Furthermore, all results stated above that relate maximum, minimum, and stationary reflection paths to various types of reflecting surfaces are also valid for refracting surfaces.