The absorptivity of a specularly reflecting cone for oblique angles of view

The absorptivity of a specularly-reflecting conical cavity is a function only of the number of reflections, n, undergone by an incident ray before it is reflected out again. A simple general expression for n is derived which applies to oblique incident rays as well as paraxial rays. It is shown that as the point at which the incident ray first strikes the conical surface moves from the rim towards the apex. a point is reached beyond which n increases by one.