Angular deviations and lateral displacements are optical effects widely investigated in the literature. In this paper, by using the Taylor expansion of the Fresnel coefficients, we obtain an analytic expression for the beam reflected by and (upper) transmitted through a dielectric prism. These analytical approximations lead to a cubic equation which allows to determine the angular deviations of the optical beams. Near the Brewster angles, under specific conditions, we obtain a universal formulation for the cubic equation. Its explicit solution determines the peak position of the reflected and (upper) transmitted beams. The universal solution could be of great utility in future experimental implementations. The analytic results show an excellent agreement with the numerical calculation, and the analytic expressions given for the reflected and (upper) transmitted beams should play an important role in the weak measurements analysis.

角偏差和横向位移是文献中广泛研究的光学效应。在本文中，通过使用菲涅耳系数的泰勒展开，我们获得了由介电棱镜反射和（透过）透射的光束的解析表达式。这些解析近似导致三次方程式，该三次方程式可确定光束的角度偏差。在特定条件下，在布鲁斯特角附近，我们获得了三次方程的通用公式。其明确的解决方案确定了反射光束和（上方）透射光束的峰值位置。通用解决方案在将来的实验实现中可能会很有用。解析结果表明与数值计算有很好的一致性，