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Angular deviations and lateral displacements are optical effects widelyinvestigated in literature. In this paper, by using the Taylor expansion of theFresnel coefficients, we obtain an analytic expression for the beam reflectedby and (upper) transmitted through a dielectric prism. These analyticalapproximations lead to a cubic equation which allows to determine the angulardeviations of the optical beams. Near the Brewster angles, under specificconditions, we obtain a universal formulation for the cubic equation. Itsexplicit solution determines the peak position of the reflected and (upper)transmitted beams. The universal solution could be of great utility in futureexperimental implementations. The analytic results show an excellent agreementwith the numerical calculation and the analytic expressions given for thereflected and (upper) transmitted beams should play an important role in theweak measurements analysis.

Angular deviations: From a cubic equation to a universal closed formula to determine the peak position of reflected and (upper) transmitted beams