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In a region of homogeneous density, a spherical embedded lens would correspond to the symmetric concentration of a spherical locality's mass into a smaller sphere (or a point) at its center. For a cosmological lens, if the universe has a non-vanishing cosmological constant Λ, then Λ is required to be the same inside and outside of the void.
[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 ...
In weak lensing by large-scale structure, the thin-lens approximation may break down, and low-density extended structures may not be well approximated by multiple thin-lens planes. In this case, the deflection can be derived by instead assuming that the gravitational potential is slowly varying everywhere (for this reason, this approximation is ...
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.
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. In the figure at right, [ 8 ] the points A and B are where parallel lines of radii of curvature R 1 and R 2 meet the lens surfaces.
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.
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.
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. Such gradual variation can be used to produce lenses with flat surfaces, or lenses that do not have the aberrations typical of traditional ...