Transmission of p- and s-polarized light through a prism and the condition of minimum deviation

The condition of minimum deviation (MD) by a transparent optically isotropic prism is re-derived, and expressions for the intensity transmittances T(p)(theta) and T(s)(theta) of an uncoated prism of refractive index n and prism angle alpha for incident p- and s-polarized light and their derivatives with respect to the internal angle of refraction theta are obtained. When the MD condition (theta=alpha/2) is satisfied, T(s) is maximum and T(p) is maximum or minimum. The transmission ellipsometric parameters psi(t),Delta(t) of a symmetrically coated prism are also shown to be locally stationary with respect to theta at theta=alpha/2. The constraint on (n,alpha) for maximally flat transmittance (MFT) of p-polarized light at and near the MD condition is determined. The transmittance T(p) of prisms represented by points that lie below the locus (n,alpha) of MFT exhibits oscillation as a function of theta. No similar behavior is found for the s polarization. Magnitudes and angular positions of the maxima and minima of the oscillatory T(p)-versus-theta curves are also calculated as functions of alpha for a ZnS prism of refractive index n=2.35 in the visible.