3.A.1 Lens Considered as a Prism Having a Variable Angle

Let C ₁, C ₁ S ₂ = R ₁, C ₂, and C ₂ S ₁ = R ₂, respectively, be the centers and the radii of curvature of the two interfaces. B and B ? are two conjugate points. We use the following notations: I ₁ J ₁ = I ₂ J ₂ = r, OB = p, and OB ? = p ?, as well as the geometric indications given in Figure 3.A.1. The lens can be considered as a prism with an angle , which would vary proportionally to the distance r to the axis. A ray is all the more deviated so that it hits the input interface at a point located farther from the axis. The angles being small, we use the law of Kepler to evaluate the deviation of the ray B ₁ I ₁ ? = ( n ? 1) , we obtain

Figure 3.A.1: For the light ray B ₁ I ₁ I ₂ B ₂ the lens is equivalent to a refracting prism of the same index and having an angle A equal to the angle of the two planes that are tangent to the interfaces at points I ₁ and I ₂. As the lens is considered to be thin, the points S ₁, J ₁, J