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A TREATISE ON OPTICS.　　　　　　　PART I.

Fig. 10.

will also be farther from the perpendicular C M than the same ray in fig. 7.; and as the same is true of the reflected ray N F, it follows that the point F must be farther from C in fig. 10. than in fig. 7.; that is, in the reflexion of converging rays, the conjugate focal distance D F of the mirror is less than its distance for parallel rays.

If we suppose the point of convergence A', fig. 10., to ap- proach to D, or the rays A M, A N to become more conver- gent, then the incident rays A M, A N will recede from the perpendiculars C M, CN; and as the reflected rays M F, NF will also recede from C M, CN, the focus F will like- wise approach to D; and when A' reaches D, F will also reach D.

If the rays A M, A N become less convergent, that is, if their point of convergence A' recedes farther from D to the left, the focus F will recede from D to the right; and when A' is infinitely distant, or when A M, AN are parallel, as in fig. 7., F will be half-way between D and C.

In these cases the place of the focus F will be found by the following rule.

RULE. Multiply the distance of the point of convergence from the mirror by the radius of the mirror, and divide this product by the sum of twice the distance of the radiant point and the radius C D, and the quotient will be the distance of the focus, or FD, the focus F being always in front of the mirror.

Reflexion of Rays from Convex Mirrors.

(21.) Reflexion of parallel rays. Let M N, fig. 11., be a convex mirror whose centre is C, and let A M, AD, AN be parallel rays falling upon it. Continue the lines CM and CN to E, and M E, NE will be perpendicular to the surface of

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