Page:Optics.djvu/110

 For instance, when $Q$ is at the extremity of the diameter of a sphere, (Fig. 118.)


 * $AQ=$, $2AE$ are the asymptotes;

Let now $Aq=$ come within the sphere, (Fig. 119.).

Provided $4AE$ be greater than $EmQ=$, a segment of a circle on $41° 49′$ capable of containing an angle of $QEm=$, will cut the section of the sphere in two points $96° 22′$, $Rv$, at which rays incident from $R′v$ will be refracted parallel to the surface. Between the points $v$, $u=2rcosφ$, there will be no refraction: those rays which fall on $2rcosφ=rcosφ·tanφ′⁄tanφ′−tanφ$ will, after refraction, form a caustic of the same kind as that of the last case: those which fall on $sinφ′⁄cosφ′=2·sinφ⁄cosφ$ will form another caustic $sinφ′⁄sinφ=2·cosφ′⁄cosφ$, $m=2cosφ′⁄cosφ$ being the focus for rays refracted at $s=sinφ$.