XI—On the Curves produced by Reflection from a Polished Revolving Straight Wire

Extract

If light, emanating from a fixed source, be reflected to the eye, also fixed, from the surface of a polished cylinder, which cylinder changes its position in some definite manner, the point of reflection moves in some curve or locus whose nature may be made the subject of investigation.

In the present paper I propose to examine that case in which an indefinitely thin cylinder is restricted to pass through a fixed point. The locus of the point of reflection is then a curved surface, For the present I shall still farther restrict the polished line to the plane passing through the vertex, the source of light, and the eye ; the locus being then a plane curve.

Let then a fine polished straight line, extended indefinitely both ways, turn on the vertex O, while light emanating from the source A is reflected to the eye at B; it is required to investigate the locus of the point C at which the reflection takes place.

The reflection is only possible while the polished line passes outside of the angle AOB. When the wire lies along AO, the point of reflection is at A ; when along OB, at B; and when it is equally inclined, outwards, to OA and OB, the reflection occurs at O, wherefore the curve must pass through the three points O, A, and B.