Investigation of the limits of the Lens Maker's formula using an experimentally verified mathematical model to determine the focal point of a convex lens for arbitrary angle of incidence

摘要

While several studies have presented experimental research and simulations in tracking the focal point, a closed form mathematical model to understand the movement of the focal point of a convex lens when light is incident at an arbitrary angle is missing. Such closed form mathematical solutions allow significantly faster computation than numerical simulations. In addition, they provide significant physical insights that cannot be obtained from simulations or experiments. This work presents a closed form mathematical solution based on analytic geometry for calculating the position of the focal point of a convex lens at an arbitrary lens orientation and arbitrary angle of incidence. Results obtained from this method are verified using Lens Maker's formula for thin lenses. The theoretical model presented here also agrees well with the experimental results. The verified method is then used to determine the criteria for the validity of thin lens approximation. As a consequence, the paper presents an explicit requirement on the radius of curvature of the lens in terms of its length, refractive index and four dimensionless constants for thin lens approximation to be applicable.