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An example of a spherical cap in blue (and another in red) In geometry, a spherical cap or spherical dome is a portion of a sphere or of a ball cut off by a plane.It is also a spherical segment of one base, i.e., bounded by a single plane.
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 θ ∈ [ 0 , π ] {\displaystyle \theta \in [0,\pi ]} : it is the angle between the z -axis and the radial vector connecting the origin to the point in ...
Electronic instruments similar to the spherometer in design are used at inspection plants for casing, tubing, and drill pipe. The equivalent measurements in optics would be for a cylinder, or lens with a cylindrical component having an optical axis, where a plane through the lens would produce an oval circumference.
When the sagitta is small in comparison to the radius, it may be approximated by the formula [2] s ≈ l 2 8 r . {\displaystyle s\approx {\frac {l^{2}}{8r}}.} Alternatively, if the sagitta is small and the sagitta, radius, and chord length are known, they may be used to estimate the arc length by the formula
Diagram showing a section through the centre of a cone (1) subtending a solid angle of 1 steradian in a sphere of radius r, along with the spherical "cap" (2). The external surface area A of the cap equals r2 only if solid angle of the cone is exactly 1 steradian.
[31] [32] As shown above, the Gaussian lens equation for a spherical lens is derived such that the 2nd surface of the lens images the image made by the 1st lens surface. For multi-lens imaging, 3rd lens surface (the front surface of the 2nd lens) can image the image made by the 2nd surface, and 4th surface (the back surface of the 2nd lens) can ...
For a spherical object whose linear diameter equals and where is the distance to the center of the sphere, the angular diameter can be found by the following modified formula [citation needed] δ = 2 arcsin ( d 2 D ) {\displaystyle \delta =2\arcsin \left({\frac {d}{2D}}\right)}
A lens contained between two circular arcs of radius R, and centers at O 1 and O 2. In 2-dimensional geometry, a lens is a convex region bounded by two circular arcs joined to each other at their endpoints. In order for this shape to be convex, both arcs must bow outwards (convex-convex).