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He invented the eyeglass lens designs that became the Zeiss Punktal lenses. The world's first commercial, mass-produced aspheric lens element was manufactured by Elgeet for use in the Golden Navitar 12 mm f /1.2 normal lens for use on 16 mm movie cameras in 1956. [12] This lens received a great deal of industry acclaim during its day.
[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 ...
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.
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.
The first lenses were likely spherical or cylindrical glass containers filled with water, which people noticed had the ability to focus light. Simple convex lenses have surfaces that are small sections of a sphere. A ball lens is just a simple lens where the surfaces' radii of curvature are equal to the radius of the lens itself.
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
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)}
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 ...