On the validity of an approximation for the deviation of a light beam. by a prism

Abstract.

According to many textbooks on optics, the deviation angle of a prism with the apex angle (or prism angle), γ, and the refractive index, n, with respect to the surrounding medium can be approximated by δ_appr=(n-1)γ, if γ≪π/2 and the angle of incidence α₁≪π/2. The validity of this approximation is investigated considering the relative error of the deviation. It is shown that this approximation can be extended to angles of incidence α₁=nγ with very fair accuracy and even to larger prism angles γ<π/4 in the range of angles of incidence near the minimum of deviation depending on the acceptable relative error.