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A lens with a different shape forms the answer to Mrs. Miniver's problem, on finding a lens with half the area of the union of the two circles. Lenses are used to define beta skeletons, geometric graphs defined on a set of points by connecting pairs of points by an edge whenever a lens determined by the two points is empty.
Cylindrical lenses. A cylindrical lens is a lens which focuses light into a line instead of a point as a spherical lens would. The curved face or faces of a cylindrical lens are sections of a cylinder, and focus the image passing through it into a line parallel to intersection of the surface of the lens and a plane tangent to it along the cylinder's axis.
The lens is moved until a sharp image is formed on the screen. In this case 1 / u is negligible, and the focal length is then given by . Determining the focal length of a concave lens is somewhat more difficult. The focal length of such a lens is defined as the point at which the spreading beams of light meet when they are extended ...
In the concave case, the line through one of the diagonals bisects the other.) One diagonal is a line of symmetry. It divides the quadrilateral into two congruent triangles that are mirror images of each other. [7] One diagonal bisects both of the angles at its two ends. [7]
The cardinal points were all included in a single diagram as early as 1864 (Donders), with the object in air and the image in a different medium. Cardinal point diagram for an optical system with different media on each side. F for Focal point, P for Principal point, NP for Nodal Point, and efl for effective focal length. The chief ray is shown ...
A drawing of a butterfly with bilateral symmetry, with left and right sides as mirror images of each other.. In geometry, an object has symmetry if there is an operation or transformation (such as translation, scaling, rotation or reflection) that maps the figure/object onto itself (i.e., the object has an invariance under the transform). [1]
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In plane geometry, a lune (from Latin luna 'moon') is the concave-convex region bounded by two circular arcs. [1] It has one boundary portion for which the connecting segment of any two nearby points moves outside the region and another boundary portion for which the connecting segment of any two nearby points lies entirely inside the region.