By Alhazen (lbn al-Haytham), 965-1039 ; A. Mark Smith (editor, translation, commentary)
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Extra 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
In concave cylindrical mirrors, when the viewpoint lies inside the mirror, its entire surface is exposed to view. 51, p. 343). , along a line of longitude, along a circle, or along an elliptical section. 55, pp. 343-344). 56, p. 344). The same reasoning therefore applies to this mirror as to its convex counterpart. An infinite number of planes can be passed through the viewpoint along the normal dropped from it to the mirror so as to form elliptical sections on the exposed portion of the mirror.
Furthermore, both the number and determination of these points depend on how the object-point and the center of sight are disposed with respect to the reflecting surface itself. Faced with an extraordinarily complex phenomenon, then, Alhacen felt compelled—and understandably so—to address it on a case-by-case basis. Moreover, he was concerned not only with convex and concave spherical mirrors, but with convex and concave cylindrical and conical mirrors as well. ” In this section, we will examine Alhacen’s approach to this problem in its full scope, dealing in order with convex spherical, convex cylindrical, convex conical, concave spherical, concave cylindrical, and concave conical mirrors.
The first has to do with the location of images seen along the normal. , propositions 2 and 8, pp. 399-401 and 404-405). Ac- INTRODUCTION xlv cording to the cathetus-rule, such images should lie where the cathetus dropped from that spot on the cornea intersects the line of reflection. But in this case the two lines coincide, so there is no point of intersection. How, then, do we judge the location of images along that line? Alhacen’s response is that we do so within the context of proximate points, whose images are defined by appropriate intersections.
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)