Internal Reflection from a Water surface

As in the case of rare-to-dense, or external, reflection (see previous article), a ray of light that propagates through water and is incident on an air/water interface will also be partially refracted and partially reflected. In this case (a dense-to-rare effect) it is termed internal reflection.

The intensity of the reflected beam relative to that of the incident beam (the "reflectance"), again depends on the angle of incidence and the direction of polarization of the light, as shown below.

At normal incidence the reflectance is identical (about 2%) to the case of external reflection , for both the parallel and perpendicular polarization components. But while the reflectance of the perpendicular component increases monatonically with the angle of incidence, the reflectance for the parallel component first decreases to zero before increasing. This vanishing of the reflectance occurs at the polarizing angle given by

tan(i) = n(a)/n(w)

which in this case is 37 degrees. Note that both curves approach 100% as the angle of incidence approaches the critical angle of 48.8 degrees (when r=90 degrees) and that for angles greater than this there is no refracted beam. This is known as total internal reflection (see the article).


J. D. Jackson, "Classical Electrodynamics" (John Wiley and Sons 1962), Vol. 1, Chapter 7.

F. A. Jenkins and H. E. White, "Fundamentals of Optics" (McGraw-Hill 1957), Chapter 25.