What is the geometric definition of a ray?

Answer 1

Strictly speaking, a "ray" is in the family of lines and line segments. A line is defined as a one-dimensional object of infinite length with no well-defined endpoints (since "infinity" isn't a well-defined value). It's the 1-D analogue to a plane or a space. A line segment is the finite equivalent of a line. A ray is a bit stranger: it's infinite in length, but has one well-defined end-point, where the ray originates. They show up a lot in classical optics because if nothing interrupts it, a light ray is created at some point and then continues forever.