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Related Concept Videos

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...
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...
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,...
Triple Integrals in Spherical Coordinates01:27

Triple Integrals in Spherical Coordinates

Triple integrals in spherical coordinates provide an efficient method for evaluating volumes over regions with central symmetry, such as spheres. Instead of describing points by rectangular coordinates, spherical coordinates use three variables: 𝜌, 𝜃, and 𝜑. Here, 𝜌 is the distance from the origin, 𝜃 is the angle in the xy-plane measured from the positive x-axis, and 𝜑 is the angle measured downward from the positive z-axis.To derive the volume of a sphere, the solid region can be divided...
Spherical and Cylindrical Capacitor01:26

Spherical and Cylindrical Capacitor

A spherical capacitor consists of two concentric conducting spherical shells of radii R1 (inner shell) and R2 (outer shell). The shells have equal and opposite charges of +Q and −Q, respectively. For an isolated conducting spherical capacitor, the radius of the outer shell can be considered to be infinite.
Conventionally, considering the symmetry, the electric field between the concentric shells of a spherical capacitor is directed radially outward. The magnitude of the field, calculated by...
Cylinders in Three-Dimensional Space01:28

Cylinders in Three-Dimensional Space

A cylindrical surface is generated when a two-dimensional profile curve is translated along a straight line in three-dimensional space. The translated copies of the curve form a surface composed of parallel rulings, each oriented in the same fixed direction. This construction allows many three-dimensional forms to be described using relatively simple planar equations.In Cartesian coordinates, a cylindrical surface is often recognized by an equation that omits one of the three variables. For...

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Related Experiment Video

Updated: Jun 14, 2026

Indoor Experimental Assessment of the Efficiency and Irradiance Spot of the Achromatic Doublet on Glass (ADG) Fresnel Lens for Concentrating Photovoltaics
09:00

Indoor Experimental Assessment of the Efficiency and Irradiance Spot of the Achromatic Doublet on Glass (ADG) Fresnel Lens for Concentrating Photovoltaics

Published on: October 27, 2017

Cladded radially inhomogeneous sphere lenses.

K Kikuchi, T Morikawa, J Shimada

    Applied Optics
    |March 24, 2010
    PubMed
    Summary

    Researchers minimized spherical transverse aberration in sphere lenses by adding a refractive-index medium. This allows for diffraction-limited imaging with small, high-numerical-aperture (N.A.) lenses.

    Area of Science:

    • Optics and Photonics
    • Materials Science

    Background:

    • Aberrations limit the performance of optical systems, particularly in small lenses.
    • Achieving diffraction-limited imaging requires precise control over optical aberrations.

    Purpose of the Study:

    • To minimize spherical transverse aberration in radially inhomogeneous sphere lenses.
    • To design sphere lenses capable of diffraction-limited imaging for small-diameter optics.
    • To explore applications in imaging, Fourier transforms, and optical disk reading.

    Main Methods:

    • Cladding a radially inhomogeneous sphere with a specific refractive-index medium.
    • Numerical design and analysis of sphere lenses with approximately 0.4 numerical aperture (N.A.).
    • Evaluating lens performance for point source imaging.

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    Convergent Polishing: A Simple, Rapid, Full Aperture Polishing Process of High Quality Optical Flats & Spheres
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    Convergent Polishing: A Simple, Rapid, Full Aperture Polishing Process of High Quality Optical Flats & Spheres

    Published on: December 1, 2014

    Development of Whispering Gallery Mode Polymeric Micro-optical Electric Field Sensors
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    Development of Whispering Gallery Mode Polymeric Micro-optical Electric Field Sensors

    Published on: January 29, 2013

    Related Experiment Videos

    Last Updated: Jun 14, 2026

    Indoor Experimental Assessment of the Efficiency and Irradiance Spot of the Achromatic Doublet on Glass (ADG) Fresnel Lens for Concentrating Photovoltaics
    09:00

    Indoor Experimental Assessment of the Efficiency and Irradiance Spot of the Achromatic Doublet on Glass (ADG) Fresnel Lens for Concentrating Photovoltaics

    Published on: October 27, 2017

    Convergent Polishing: A Simple, Rapid, Full Aperture Polishing Process of High Quality Optical Flats & Spheres
    13:07

    Convergent Polishing: A Simple, Rapid, Full Aperture Polishing Process of High Quality Optical Flats & Spheres

    Published on: December 1, 2014

    Development of Whispering Gallery Mode Polymeric Micro-optical Electric Field Sensors
    08:32

    Development of Whispering Gallery Mode Polymeric Micro-optical Electric Field Sensors

    Published on: January 29, 2013

    Main Results:

    • Successful minimization of spherical transverse aberration.
    • Achieved diffraction-limited spot size for millimeter-scale lenses.
    • Demonstrated design examples for imaging, Fourier transform, and optical disk reading applications.

    Conclusions:

    • The cladding technique effectively corrects aberrations in sphere lenses.
    • These optimized sphere lenses offer potential for advanced optical applications.
    • Further uses are envisioned, highlighting the versatility of this lens design.