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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...
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,...
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: 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...
Electric Field of a Non Uniformly Charged Sphere01:22

Electric Field of a Non Uniformly Charged Sphere

Gauss's law states that the electric flux through any closed surface equals the net charge enclosed within the surface. This law is beneficial for determining the expressions for the electric field for a particular charge distribution if the electric flux is known.
Consider a non-uniformly charged sphere, for which the density of charge depends only on the distance from a point in space and not on the direction. Such a sphere has a spherically symmetrical charge distribution. Here, the electric...
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.

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Related Experiment Video

Updated: Jun 12, 2026

Determining 3D Flow Fields via Multi-camera Light Field Imaging
14:25

Determining 3D Flow Fields via Multi-camera Light Field Imaging

Published on: March 6, 2013

On-axis light distribution in converging spherical fields: general case.

R Torroba, M Garavaglia

    Applied Optics
    |May 22, 2010
    PubMed
    Summary
    This summary is machine-generated.

    We derived a general formula for light distribution from spherical waves passing through a circular aperture. This solution accurately models the effects of aperture tilt across various Fresnel numbers (N).

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    Area of Science:

    • Optics and Photonics
    • Wave Diffraction Theory

    Background:

    • Understanding light distribution is crucial in optical systems.
    • Diffraction by circular apertures is a fundamental problem in optics.
    • Existing models may not fully capture the effects of aperture tilt or wide Fresnel number ranges.

    Purpose of the Study:

    • To derive a general analytical expression for on-axis light distribution.
    • To investigate the impact of aperture tilt on focal shift.
    • To analyze field symmetry relative to the focal plane for varying Fresnel numbers.

    Main Methods:

    • Development of a general mathematical expression for diffracted spherical waves.
    • Analysis of the derived expression for small and high Fresnel numbers (N).
    • Inclusion and analysis of aperture tilt effects.

    Main Results:

    • A unified solution for on-axis light distribution is obtained.
    • The influence of aperture tilt on focal shift, particularly for small N, is quantified.
    • Symmetry of the diffraction field concerning the geometrical focal plane is examined.

    Conclusions:

    • The derived expression provides a comprehensive model for on-axis diffraction.
    • Aperture tilt significantly affects focal shift and field symmetry.
    • The solution is applicable across a broad range of Fresnel numbers (N).