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The solid angle of a sphere measured from any point in its interior is 4 π sr. The solid angle subtended at the center of a cube by one of its faces is one-sixth of that, or 2 π /3 sr. The solid angle subtended at the corner of a cube (an octant) or spanned by a spherical octant is π /2 sr, one-eight of the solid angle of a sphere. [1]
The sagitta also has uses in physics where it is used, along with chord length, to calculate the radius of curvature of an accelerated particle. This is used especially in bubble chamber experiments where it is used to determine the momenta of decay particles. Likewise historically the sagitta is also utilised as a parameter in the calculation ...
A spherical lens has an aplanatic point (i.e., no spherical aberration) only at a lateral distance from the optical axis that equals the radius of the spherical surface divided by the index of refraction of the lens material. Spherical aberration makes the focus of telescopes and other instruments less than ideal. This is an important effect ...
the azimuthal angle φ, which is the angle of rotation of the radial line around the polar axis. [b] (See graphic regarding the "physics convention".) 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.
A light ray enters a component crossing its input plane at a distance x 1 from the optical axis, traveling in a direction that makes an angle θ 1 with the optical axis. After propagation to the output plane that ray is found at a distance x 2 from the optical axis and at an angle θ 2 with respect to it.
Another method for producing aspheric lenses is by depositing optical resin onto a spherical lens to form a composite lens of aspherical shape. Plasma ablation has also been proposed. Lapping tool on a spindle below the lens, and mounting tool on a second spindle (swung out) uses pitch to hold the lens shown with its concave side down
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.
Angular diameter: the angle subtended by an object. The angular diameter, angular size, apparent diameter, or apparent size is an angular separation (in units of angle) describing how large a sphere or circle appears from a given point of view. In the vision sciences, it is called the visual angle, and in optics, it is the angular aperture (of ...