Fresnel Formulae Applied to the Phenomena of Nonreflecting Films

The Fresnel formulae are applied to the calculations of the amplitudes of rays reflected and transmitted by nonreflecting films of transparent isotropic substances. Two cases are considered. In the first, the film of refractive index $n_0$ is bounded on both sides by a medium of refractive index $n_0$. In the second, the film is bounded by media of refractive indexes $n_0$ and $n_2$. It is shown how in the first case these formula lead to zero reflection when the thickness $t$ of the film is given by $n_{1}t cos r_1=\frac{\mathrm{}(2n+2)\mathrm{}\lambda }{4}$. In the second case for zero reflection the thickness must be given by $n_{1}t cos r_1=\frac{\mathrm{}(2n+1)\mathrm{}\lambda }{4}$.