Path of a beam of light through an optical coating

A simple model for the path of a light beam through an optical coating is the path of a ray predicted by Snell's law. By determining the exit point of a beam for various types of coating, one finds that the simple model is a good approximation in the case of antireflection coatings, but not for coatings of other designs. An approximate method for determining the correct path of a beam through the coating is derived and the path is illustrated using a Gaussian incident beam and tracing the position of the peak field of the beam as it traverses the coating.