By Alhazen (lbn al-Haytham), 965-1039 ; A. Mark Smith (editor, translation, commentary)
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Additional info for Alhacen on the principles of reflection. A Critical Edition, with English Translation and Commentary, of Books 4 and 5 of Alhacen’s De aspectibus. Volume One - Introduction and Latin Text ; Volume two - English Translation
11, p. 329). Every plane of reflection passing through that viewpoint will form a great circle on the mirror’s surface, and every point on every great circle within the exposed portion of the mirror can serve as a point of reflection for that viewpoint. 13, p. 330). 14-5,16, pp. 330-331). 22, p. 333). 23, pp. 333-334). 24, p. 334). But if the cut is oblique to the axis, the plane will form an elliptical section (or, as Alhacen calls it, a “cylindric section” [sectio columpnaris]) on the mirror’s surface.
415-427) discussed earlier on pp. xxxvi-xxxviii above, Alhacen addresses the same problem in proposition 25, pp. 427-432, but this time with points A and B lying different distances from the mirror’s center. Thus, as illustrated in figure 17a, p. 534, normals AG and BG are not equal. Unlike the previous case, this one is far from trivial, and Alhacen’s method for solving it is commensurately complex. Take random line D’M’, and divide it at point Q’ so that M’Q’:Q’D’ = BG:AG. Bisect line D’M’ at point N’, and draw perpendicular B’N’T’ through it.
45, p. 341-342). Therefore, since an infinite number of cutting planes can be passed through the viewpoint along the normal dropped from it to the mirror, an infinite number of conic sections can be formed on the mirror’s surface. Within each plane, the particular conic section will have a unique pair of lines extending from its focus to intersect the mirror along the normal. There will thus be an infinite number of such intersection-points on the exposed portion of the mirror’s surface, each serving as a point of reflection for the given viewpoint.
Alhacen on the principles of reflection. A Critical Edition, with English Translation and Commentary, of Books 4 and 5 of Alhacen’s De aspectibus. Volume One - Introduction and Latin Text ; Volume two - English Translation by Alhazen (lbn al-Haytham), 965-1039 ; A. Mark Smith (editor, translation, commentary)