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Gregg Baldwin - (3/24/2019 9:17:49 AM)
RE:Geometrical Optics
It is self-evident that parallel lines divide a circle into equal arcs. From this it can be shown that equal arcs subtend equal angles anywhere on a circle; and that certain triangles within a circle can therefore have the same shape, with their sides forming ratio equalities. Quadrilaterals with corners along the same circle can then describe equalities with multiple ratios. In 1667, Isaac Barrow used this to find triangles using other triangles, describing tangential refraction along a line and at a circle. After a presentation of this material, axial ratio equalities representing various components of total axial magnification are illustrated on an optic axis described as a circle of infinite radius, encouraging a spatial understanding devoid of jargon and sign convention. Off-axis prism and crossed-cylinder problems are then approximated using parabolic surfaces.
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