An Elementary Text book of Physics volume 3

Cover An Elementary Text book of Physics volume 3
An Elementary Text book of Physics volume 3
R Wallace Robert Wallace Stewart
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If the aperture of the mirror is small the arc AL may be taken as a straight line, and as the triangles FAL and FP'Q are similar, we have AL _ AF^ P'Q' := P'F' But AL is evidently equal to PQ, and therefore AP AF AP' ~ = PF' Now let a, b, and c denote respectively the numbers measuring the lengths of AP, the distance of the object from the mirror, Fig. 66.
AP', the distance of the image from the mirror, and AF, the focal length of the mirror. That is, a, b, and c are merely numbers measuring th
...ese distances in any convenient unit ivith- out consideration of direction. Then we have AP = a, AP' r= b, AF = c, P'F = b - c, a c b = 6~-T' and or, ab ac = be.
That is, ac + be = ab, and dividing throughout by abc, we get I + ~ = - b a c This is a numerical relation between a, b, and c, for this parti- cular case of reflection at the surface of a concave mirror. This REFLECTION AT SPHERICAL SURFACES. 105 relation evidently applies also to the conjugate case in which the object is placed between F and C, and a real image is formed beyond C, at a distance from the mirror greater than its radius of curvature.


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