Phase Condition for Light Incident Normally on a Semireflecting Film

Abstract

It is shown that for a semireflecting film whose reflection and transmission factors are reiρ and teiτ, the conservation of energy requires that the angle ρ−τ must lie between cos−1(A/2rt) and cos−1(−A/2rt) where A=1−r2−t2. The corresponding condition for an asymmetrical film is derived. The effect of this phase condition on multiple beam reflection fringes and filters is studied theoretically. It is possible to set an upper limit to the error incurred in the calculation of reflected intensities on the usual assumption that ρ−τ=π/2. Expressions are found for the maximum and minimum intensities with ρ−τ at its limit. It is extablished that a necessary condition for the reflected intensity distribution to become transmission-like is that r+t⩽1.