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In the following equations, denotes the sagitta (the depth or height of the arc), equals the radius of the circle, and the length of the chord spanning the base of the arc. As 1 2 l {\displaystyle {\tfrac {1}{2}}l} and r − s {\displaystyle r-s} are two sides of a right triangle with r {\displaystyle r} as the hypotenuse , the Pythagorean ...
A profile gauge probe is used to measure a section across the lens surface. The rotation symmetry of the lenses means that the combination of several of these profiles provides a sufficiently precise knowledge of the shape of the lens. Any damage to the lens surface caused by the probe tip would be removed in subsequent steps. [6]
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 ] Solid angles can also be measured in square degrees (1 sr = ( 180/ π ) 2 square degrees), in square arc-minutes and square arc-seconds , or in fractions of the sphere (1 sr = 1 / 4 π ...
Spherical coordinates (r, θ, φ) as commonly used: (ISO 80000-2:2019): radial distance r (slant distance to origin), polar angle θ (angle with respect to positive polar axis), and azimuthal angle φ (angle of rotation from the initial meridian plane). This is the convention followed in this article.
The focal length of a ball lens is a function of its refractive index and its diameter. The effective focal length (EFL) of a ball lens is much larger than the back focal length (BFL), the distance from the back surface of the lens to the focal point. Ball lenses have the shortest possible focal length for a given lens diameter (for a spherical ...
In optics and especially telescope making, sagitta or sag is a measure of the glass removed to yield an optical curve. It is approximated by the formula It is approximated by the formula S ( r ) ≈ r 2 2 × R {\displaystyle S(r)\approx {\frac {r^{2}}{2\times R}}} ,
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 ...
For a single lens surrounded by a medium of refractive index n = 1, the locations of the principal points H and H ′ with respect to the respective lens vertices are given by the formulas = ′ = (), where f is the focal length of the lens, d is its thickness, and r 1 and r 2 are the radii of curvature of its surfaces. Positive signs indicate ...