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Related Concept Videos

Spherical Coordinates01:23

Spherical Coordinates

Spherical coordinate systems are preferred over Cartesian, polar, or cylindrical coordinates for systems with spherical symmetry. For example, to describe the surface of a sphere, Cartesian coordinates require all three coordinates. On the other hand, the spherical coordinate system requires only one parameter: the sphere's radius. As a result, the complicated mathematical calculations become simple. Spherical coordinates are used in science and engineering applications like electric and...
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Focusing of Light in the Eye

Light rays enter the eye through the cornea, a transparent dome-shaped tissue that is the eye's outermost layer. The cornea bends or refracts, light rays traveling to the pupil. The shape of the cornea determines how much of the light is bent and whether the image will be focused correctly on the retina at the back of the eye. Once the light has passed through both refraction layers, it converges into a single focal point onto a small area. This is where photoreceptors start transforming...
Gravitation Between Spherically Symmetric Masses01:14

Gravitation Between Spherically Symmetric Masses

The gravitational potential energy between two spherically symmetric bodies can be calculated from the masses and the distance between the bodies, assuming that the center of mass is concentrated at the respective centers of the bodies.
Design of Prismatic Beams for Bending01:23

Design of Prismatic Beams for Bending

The design of prismatic beams, structural elements with a uniform cross-section, focuses on ensuring safety and structural integrity under load. The design process begins by determining the allowable stress, either from material properties tables, or by dividing the material's ultimate strength by a safety factor. This safety factor is essential for accommodating uncertainties, and varies depending on the material—timber, steel, or concrete—with each having unique strength and stress...
Gravity between Spherical Bodies01:27

Gravity between Spherical Bodies

Newton's law of gravitation describes the gravitational force between any two point masses. However, for extended spherical objects like the Earth, the Moon, and other planets, the law holds with an assumption that masses of spherical objects are concentrated at their respective centers.
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Gauss's Law: Spherical Symmetry01:26

Gauss's Law: Spherical Symmetry

A charge distribution has spherical symmetry if the density of charge depends only on the distance from a point in space and not on the direction. In other words, if the system is rotated, it doesn't look different. For instance, if a sphere of radius R is uniformly charged with charge density ρ0, then the distribution has spherical symmetry. On the other hand, if a sphere of radius R is charged so that the top half of the sphere has a uniform charge density ρ1 and the bottom half has a uniform...

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Updated: Jun 15, 2026

Shaping the Amplitude and Phase of Laser Beams by Using a Phase-only Spatial Light Modulator
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Published on: January 28, 2019

Beam expander telescope design utilizing fast spherical primaries.

W H Southwell

    Applied Optics
    |March 9, 2010
    PubMed
    Summary
    This summary is machine-generated.

    This study presents telescope secondary mirror designs that perfectly recollimate light beams for Cassegrain and Gregorian telescopes. These designs can optimize energy distribution, enhancing beam uniformity for applications like Gaussian beams.

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    Published on: January 28, 2019

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    Area of Science:

    • Optical Engineering
    • Telescope Design

    Background:

    • Fast concave spherical mirrors present challenges in beam collimation.
    • Accurate recollimation is crucial for optimal telescope performance.

    Purpose of the Study:

    • To derive precise profiles for telescope secondary mirrors.
    • To achieve perfect beam recollimation for incident light on fast concave spherical mirrors.

    Main Methods:

    • Utilized exact geometrical ray analysis.
    • Developed analytical solutions for secondary mirror profiles.

    Main Results:

    • Derived specific secondary mirror profiles for both Cassegrain and Gregorian telescope configurations.
    • Demonstrated that high magnification designs can redistribute energy profiles.
    • Showcased the potential for uniforming Gaussian beams.

    Conclusions:

    • The derived secondary mirror profiles ensure perfect beam recollimation.
    • Telescope secondary mirror design can be tailored to optimize beam characteristics.
    • This work offers practical solutions for advanced telescope optics.