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Related Concept Videos

Gauss's Law: Cylindrical Symmetry01:20

Gauss's Law: Cylindrical Symmetry

A charge distribution has cylindrical symmetry if the charge density depends only upon the distance from the axis of the cylinder and does not vary along the axis or with the direction about the axis. In other words, if a system varies if it is rotated around the axis or shifted along the axis, it does not have cylindrical symmetry. In real systems, we do not have infinite cylinders; however, if the cylindrical object is considerably longer than the radius from it that we are interested in,...
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...
Eccentric Axial Loading in a Plane of Symmetry01:16

Eccentric Axial Loading in a Plane of Symmetry

Eccentric axial loading occurs when an axial load is applied away from the centroidal axis of a structural member. This scenario is common in engineering, where structural elements may not be directly aligned due to various design or functional requirements.
Gauss's Law: Planar Symmetry01:27

Gauss's Law: Planar Symmetry

A planar symmetry of charge density is obtained when charges are uniformly spread over a large flat surface. In planar symmetry, all points in a plane parallel to the plane of charge are identical with respect to the charges. Suppose the plane of the charge distribution is the xy-plane, and the electric field at a space point P with coordinates (x, y, z) is to be determined. Since the charge density is the same at all (x, y) - coordinates in the z = 0 plane, by symmetry, the electric field at P...
General Case of Eccentric Axial Loading01:12

General Case of Eccentric Axial Loading

Unsymmetrical bending occurs when the bending moment applied to a structural member does not align with its principal axis. This misalignment leads to complex stress distributions and deflection patterns that differ from symmetrical bending, which are essential for designing structures to withstand different loading conditions.
Consider a member subjected to equal and opposite forces that are applied along a line that does not coincide with the member's neutral axis. In unsymmetrical bending,...
Geometry of Hyperbolas01:30

Geometry of Hyperbolas

A hyperbola consists of all points where the absolute difference of distances to two fixed points, called foci, remains constant. The standard equation isEach branch extends infinitely and approaches two asymptotes, which guide the curve’s behavior. The parameters a and b define key features: a measures the distance from the center to each vertex along the transverse axis, while b influences the slopes of the asymptotes. The asymptotes have equationsA rectangle centered at the origin with...

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Related Experiment Video

Updated: Jun 15, 2026

Sequential Application of Glass Coverslips to Assess the Compressive Stiffness of the Mouse Lens: Strain and Morphometric Analyses
07:56

Sequential Application of Glass Coverslips to Assess the Compressive Stiffness of the Mouse Lens: Strain and Morphometric Analyses

Published on: May 3, 2016

Axially symmetric geodesic lenses.

G E Betts, J C Bradley, G E Marx

    Applied Optics
    |March 6, 2010
    PubMed
    Summary
    This summary is machine-generated.

    A new procedure optimizes aspheric geodesic lenses for improved optical performance. This method allows independent control of refractive index, radius, and focal length for precise lens design.

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    Whole Mount Imaging to Visualize and Quantify Peripheral Lens Structure, Cell Morphology, and Organization
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    Whole Mount Imaging to Visualize and Quantify Peripheral Lens Structure, Cell Morphology, and Organization

    Published on: January 19, 2024

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    Last Updated: Jun 15, 2026

    Sequential Application of Glass Coverslips to Assess the Compressive Stiffness of the Mouse Lens: Strain and Morphometric Analyses
    07:56

    Sequential Application of Glass Coverslips to Assess the Compressive Stiffness of the Mouse Lens: Strain and Morphometric Analyses

    Published on: May 3, 2016

    Whole Mount Imaging to Visualize and Quantify Peripheral Lens Structure, Cell Morphology, and Organization
    05:45

    Whole Mount Imaging to Visualize and Quantify Peripheral Lens Structure, Cell Morphology, and Organization

    Published on: January 19, 2024

    Area of Science:

    • Optical Engineering
    • Lens Design

    Background:

    • Aspheric lenses offer advantages over spherical lenses but require precise design.
    • Geodesic lenses present unique design challenges for optimal performance.

    Purpose of the Study:

    • To develop an optimization procedure for corrected aspheric geodesic lenses.
    • To enable independent design parameters including refractive index, lens radius, and focal length.

    Main Methods:

    • A novel procedure was developed and applied for lens shape optimization.
    • The method was tested for F-numbers ranging from 3 to 15.

    Main Results:

    • Optimal shapes for corrected aspheric geodesic lenses were obtained.
    • The impact of shape perturbations on diffraction spot size and focal plane shift was quantified for F-numbers 3-10.

    Conclusions:

    • The developed procedure effectively optimizes aspheric geodesic lens design.
    • Understanding the effects of shape perturbations is crucial for lens manufacturing and application.