Page:Elementary Text-book of Physics (Anthony, 1897).djvu/435

§ 343] a meridian section of an element of a spherical surface of which $$Fn$$ is an axis.

Sections of wave surfaces reflected from the ellipsoid have their centre at $$F',$$ and are also sections of wave surfaces reflected from the elementary spherical surface. Evidently the same would be true for any other meridian section passing through $$FA$$ of the sphere of which the elementary surface forms a part, and the form of the wave surfaces may be conceived by supposing the whole figure to revolve about $$FA$$ as an axis. The arc $$ac$$ describes a zone of the sphere, $$s, s, r, r,$$ describe wave surfaces, and $$F'$$ describes a circumference having its centre on $$FA.$$ The wave surfaces are portions of the surfaces of curved tubes of which the axis is the arc described by the point $$F'.$$ The line described by $$F'$$ is a focal line, and all the light from the zone described by $$ac$$ passes through it, or does so very approximately. If $$ac$$ be taken nearer to $$A$$ on the sphere, $$F'$$ approaches the axis along the curve $$F'F$$ and finally coincides with $$F,$$ the focus conjugate to $$F.$$ $$F'F$$ is a caustic curve, which, when the figure revolves about the axis $$AF,$$ describes a caustic surface''. It will be noted that all the light from the zone described by $$ac$$ passes through the axis $$AF$$ between the points $$x$$ and $$y.$$ The light coming from $$F$$ and reflected from a small portion of the spherical surface around $$b,$$ the middle point of $$ac,$$ is then concentrated first in a line through $$F'$$ at right angles to the paper, and again into the line $$xy$$ in the plane of the paper. Nowhere is it concentrated into a point. A line drawn through $$b$$ and the middle of the focal line through $$F'$$ is the axis of the