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This article uses the standard notation ISO 80000-2, which supersedes ISO 31-11, for spherical coordinates (other sources may reverse the definitions of θ and φ): . The polar angle is denoted by [,]: it is the angle between the z-axis and the radial vector connecting the origin to the point in question.
Once the radius is fixed, the three coordinates (r, θ, φ), known as a 3-tuple, provide a coordinate system on a sphere, typically called the spherical polar coordinates. The plane passing through the origin and perpendicular to the polar axis (where the polar angle is a right angle ) is called the reference plane (sometimes fundamental plane ).
A diagram showing how to find the optical center O of a spherical lens. N and N' are the lens's nodal points. The optical center of a spherical lens is a point such that if a ray passes through it, the ray's path after leaving the lens will be parallel to its path before it entered.
Let P be the point on the lower unit hemisphere whose spherical coordinates are (140°, 60°) and whose Cartesian coordinates are (0.321, 0.557, −0.766). This point lies on a line oriented 60° counterclockwise from the positive x -axis (or 30° clockwise from the positive y -axis) and 50° below the horizontal plane z = 0 .
A gradient-index lens with a parabolic variation of refractive index (n) with radial distance (x).The lens focuses light in the same way as a conventional lens. Gradient-index (GRIN) optics is the branch of optics covering optical effects produced by a gradient of the refractive index of a material.
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.
This term is generally used in physics regarding the study of lenses and mirrors (see radius of curvature (optics)). It can also be defined as the spherical distance between the point at which all the rays falling on a lens or mirror either seems to converge to (in the case of convex lenses and concave mirrors) or diverge from (in the case of ...
Prolate spheroidal coordinates μ and ν for a = 1.The lines of equal values of μ and ν are shown on the xz-plane, i.e. for φ = 0.The surfaces of constant μ and ν are obtained by rotation about the z-axis, so that the diagram is valid for any plane containing the z-axis: i.e. for any φ.