Optics/Half space and retina/Formula and continuous/Exercise

Suppose that in the origin ${}0\in \mathbb {R} ^{3}$, there is the pupil of an eye (or just a small hole), and in the plane determined by ${}x=-1$, we have a retina ${}N\cong \mathbb {R} ^{2}$ (or a photographic plate). Determine the mapping

$\mathbb {R} _{+}\times \mathbb {R} \times \mathbb {R} \longrightarrow \mathbb {R} ^{2}$

that describes the natural vision (or taking a photo) (that is, a point of the half space is mapped through the pupil to a point of the retina). Is this mapping continuous? It is linear?

Create a solution