Page:Optics.djvu/37

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14.It will easily be seen that the effect of a concave mirror is to give convergence to rays, that is, to increase convergence when it exists in the incident rays, to give convergence to parallel rays, and even to divergent within a certain limit, and beyond that to lessen their divergence.

Convex mirrors on the contrary give divergence to parallel rays, increase previous divergence, and make even convergent rays diverge, or at least diminish their convergence.

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CHAP. III.

ABERRATION IN REFLEXION AT SPHERICAL SURFACES.

15.We found in the beginning of the last Chapter, that a cone of rays incident on a spherical surface were not so reflected as to meet in a point, but that the point $q$ which we called the focus of the reflected rays was, in fact, the mathematical limit of the intersections with the axis of rays chosen more and more nearly coincident with it. Let us now examine how much the intersection of the axis with a ray at a small but sensible distance from it, differs from this.

Taking the centre of the surface as the point to measure from, (Fig. 12.)

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radius, $Aq$ is one third of it. There may be some little obscurity attending the application of the particular formula deduced above for convex mirrors, owing to our having put positive symbols for $AE$ and $Aq,$ which, in algebraical strictness, are negative. The student should use only the original formula ${\frac {1}{\Delta }}+{\frac {1}{\Delta '}}-{\frac {2}{r}}=0,$ putting negative values for $\Delta$ or $r$ when necessary. Thus if the radius of a convex mirror be 6 inches, and the distance of the radiant point from it 9, we have ${\frac {1}{9}}+{\frac {1}{\Delta '}}+{\frac {2}{6}}=0,$ whence $\Delta '=-{\frac {9}{4}}$ or $2{\tfrac {1}{4}}$ inches behind the mirror.