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Related Concept Videos

Interference and Diffraction02:18

Interference and Diffraction

Interference is a characteristic phenomenon exhibited by waves. When two electromagnetic waves interact with their peaks and troughs coinciding, a resulting wave with enhanced amplitude is produced. This is known as constructive interference. In this case, the two waves interacting are in phase with each other.
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...
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...
Interference: Path Lengths01:10

Interference: Path Lengths

Consider two sources of sound, that may or may not be in phase, emitting waves at a single frequency, and consider the frequencies to be the same.
Two special sources may be considered when they are in phase. This can be easily achieved by feeding the two sources from the same source. An example would be synchronizing the two speakers by feeding them with the same source, such as the sound waves produced by a tuning fork. This setup ensures that the two sources have the same frequency and are...
Induced Electric Fields: Applications01:27

Induced Electric Fields: Applications

An important distinction exists between the electric field induced by a changing magnetic field and the electrostatic field produced by a fixed charge distribution. Specifically, the induced electric field is nonconservative because it does not work in moving a charge over a closed path. In contrast, the electrostatic field is conservative and does no net work over a closed path. Hence, electric potential can be associated with the electrostatic field but not the induced field. The following...
Electric Field of a Charged Disk01:23

Electric Field of a Charged Disk

The simplest case of a surface charge distribution is the uniformly charged disk. Calculating its electric field also helps us calculate the electric field of a large plane of charge.
The system's symmetry is in the cylindrical directions across the plane of the charge. As a result, the electric fields created by various surface charge elements nullify each other in the direction parallel to the surface. Thereby, the resulting electric field is perpendicular to the plane. Since the disk is...

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Related Experiment Video

Updated: May 22, 2026

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

Far-field interference from a sphere and its applications.

Jianmin Li1, Ye Tian, Chongxiang Li

  • 1Institute of Modern Optics, Hebei North University, Zhangjiakou, China. lijianmin318@sina.com

Applied Optics
|May 23, 2012
PubMed
Summary

This study introduces a new method for measuring sphere diameters using laser interference patterns. The technique accurately determines sphere size by analyzing hyperbolic fringes formed by reflected laser beams.

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Last Updated: May 22, 2026

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Published on: January 28, 2019

Area of Science:

  • Optics and Photonics
  • Metrology

Background:

  • Far-field interference patterns are generated when coherent laser beams interact with spherical surfaces.
  • These interference fringes exhibit hyperbolic shapes and non-uniform density, requiring theoretical analysis.

Purpose of the Study:

  • To establish a theoretical model for far-field interference from a sphere.
  • To develop and demonstrate a method for precise sphere diameter measurement using optical interference.
  • To investigate the applicability of the method for measuring cylinder diameters.

Main Methods:

  • Derivation of a method to calculate path-length difference for parallel reflected light.
  • Analysis of the interference field and factors influencing fringe density.
  • Development of a formula for calculating the highest orders of interference fringes.
  • Experimental demonstration using a spectrometer, CCD camera, and computer.

Main Results:

  • A theoretical model for sphere interference was established and validated.
  • A practical method for measuring sphere diameter was demonstrated with high accuracy.
  • Experimental results showed strong agreement with measurements from an Abbe comparator.
  • The developed optical methods were found suitable for measuring smooth cylinder diameters.

Conclusions:

  • The theoretical model accurately describes far-field interference from spheres.
  • The proposed optical measurement technique provides a reliable and accurate method for determining sphere and cylinder diameters.
  • This research offers a valuable tool for precision metrology in optics and related fields.