The Nephoid is the curve formed by the envelope of rays reflected on a circular surface from a set of initial parallel rays. In other words, the curve which owns all the rays as tangents.

The geomtery of each ray path is relatively straight forward, involving properties of parallel lines and isocelels triangles.

It is interesting to note that the ray path will only form a closed path for angles of which divide $360^{o}$.

For a hemisphere, we would have,

For a set of parallel rays enclosed in a circle we get:

The envelope of the lines becomes clearer as the number of parallel rays are increased.