Page:Optics.djvu/47



So far all is general; in the particular example proposed,

From this it appears that $sin2φ=2y′⁄1+y′^{2}$, or the curve crosses the axis, where $cos2φ=1−y′^{2}⁄1+y′^{2}$, which answers to the point in the parabola for which $X=$,

When $x+vsin2φ=x−y′⁄y″$ this is infinite, so that the caustic like the reflecting curve is perpendicular to the axis at its origin: when

The angle at which the caustic afterwards cuts the axis is therefore that having for its natural tangent $Y=$, which shows it to be one of $y+1−y′^{2}⁄2y″$.

The curve extends without limit in the same directions with its generating parabola.