Fermat's principle assures that the angles given by
Snell's law always reflect light's quickest path between P and Q.
Fermat's principle in optics states:
The actual path between two points taken by a beam of light is the one which is traversed in the least time.
This principle was first stated by Pierre de Fermat.
Whilst Huygens' principle is useful for explaining diffraction, it is of little use for calculating the properties of light mathematically. Fermat's Principle (as quoted above in its original form) can be used to describe the properties of light-rays reflected off mirrors, refracted through different media, or undergoing total internal reflection. It can be used to derive Snell's law.
The modern, full version of Fermat's Principle states that the optical path length must be extremal, which means that it can be either minimal or maximal. Maxima occur in gravitational lensing and at points of inflection.