Page:Harold Dennis Taylor - A System of Applied Optics.djvu/26

 SECTION I

A RECAPITULATION

will first of all recapitulate those well-known formulæ of the first approximation relating to ultimate axial rays constituting direct or axial pencils, or, in other words, extremely narrow pencils whose central or principal ray coincides with the axis or straight line joining the origin or apex of the pencil to the centre of curvature of the spherical surface. Spherical aberration is in such cases a vanishing quantity and is therefore not regarded. Throughout this work it is assumed that all reflecting and refracting surfaces are either plane or spherical.

Case of a Plane or Curved Reflector

Throughout the diagrams in this book light is supposed to be travelling from left to right.

Plane reflector.— Here if Q (Plate I.) be the origin and Q..A, the principal ray, be perpendicular to the reflecting surface R..R, then after reflection the rays will proceed backwards as if originating from a virtual point q situated on Q..A projected and at a distance A..q

from the surface equal to A..Q. On the contrary, if the incident pencil is of rays converging to the apex q, then they will be reflected back to a real point Q such that A..Q = A..q and Q..q is normal to R..R.

If the reflecting surface be curved spherically as r.r, Figs. 2a, 2b, 2c, and 2d, c being the centre of curvature and Q the origin or apex of the incident pencil, then the formula

universally applies and interprets itself in all cases if the following conventions are strictly adhered to, viz.—