Generic 1-parameter families of caustics by reflexion in the plane

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Abstract
Let M (the mirror) be a plane oval (a smooth curve without inflexions), and let sεℝ2\M be the light source. Rays of light emanating from s are reflected by M, and the caustic by reflexion of M relative to s is the envelope of these reflected rays. In this article we suppose that M is generic (the precise assumption is stated later) and that s moves along a smooth curve in the plane; we are then able to describe how the local structure of the caustic changes. In order to state the result we recall a few facts from [3].

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