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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.
In the first chapter, entitled Patterns with Classical Symmetry, the author introduces the concepts of motif, symmetry operations, lattice and unit cell, and uses these to analyze the symmetry of 13 of Escher's tiling designs. In the second chapter, Patterns with Black-white Symmetry, the antisymmetry operation (indicated by a prime ') is ...
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 ...
An optical axis is an imaginary line that passes through the geometrical center of an optical system such as a camera lens, microscope or telescopic sight. [1] Lens elements often have rotational symmetry about the axis. The optical axis defines the path along which light propagates through the system, up to first approximation.
Removing mirrors at the order-3 point creates [6,3 +], 3*3 symmetry, index 2. Removing all mirrors creates [6,3] + (632) subgroup, index 2. The communtator subgroup is [1 +,6,3 +], (333) symmetry, index 4. An index 6 subgroup constructed as [6,3*], also becomes (*333), shown in blue mirror lines, and which has its own (333) rotational symmetry ...
For concave lenses, the focal point is on the back side of the lens, or the output side of the focal plane, and is negative in power. A lens with no optical power is called an optical window, having flat, parallel faces. The optical power directly relates to how large positive images will be magnified, and how small negative images will be ...
A variation on the Luneburg lens antenna is the hemispherical Luneburg lens antenna or Luneburg reflector antenna. This uses just one hemisphere of a Luneburg lens, with the cut surface of the sphere resting on a reflecting metal ground plane. The arrangement halves the weight of the lens, and the ground plane provides a convenient means of ...
English: Thick lens diagram. d=thickness of lens at center; e=thickness of lens at edge; r1=radius of curvature of the first surface; r2=radius of curvature of the second surface; H=primary principal plane; H′=secondary principal plane; F=front focal point; F′=back focal point; S1=vertex of the first optical surface; S2=vertex of the second ...