Surfaces refracting or reflecting radiation in a prescribed manner

This talk is about the design of mirrors and lenses that transmit radiation in a prescribed way. It is assumed that radiation emanates from a source point or in a beam of parallel rays. As an example, I will explain and solve the problem of designing a blind-spot free passenger mirror in a car. It turns out that this problem leads to a first order differential equation that can be solved by elementary methods. The very same idea can be used to design lenses magnifying the image with a prescribed factor. Time permitting, I will give an idea about the more complicated case when the input and output energies are taken into account. This leads to PDEs of Monge-Ampère type.