Search research articles

ABOUT JoVE

Overview Leadership Blog JoVE Help Center

AUTHORS

Publishing Process Editorial Board Scope & Policies Peer Review FAQ Submit

LIBRARIANS

Testimonials Subscriptions Access Resources Library Advisory Board FAQ

RESEARCH

JoVE Journal Methods Collections JoVE Encyclopedia of Experiments Archive

EDUCATION

JoVE Core JoVE Business JoVE Science Education JoVE Lab Manual Faculty Resource Center Faculty Site

Terms & Conditions of Use

Related Concept Videos

Reflective Property of Parabolas

Reflective Property of Parabolas

A parabola is a basic type of conic section that results from the intersection of a plane with a double-napped cone in a direction parallel to one of the cone's sides. This U-shaped curve has a distinctive reflective property: all incoming rays parallel to its axis of symmetry are directed toward a single point, known as the focus. This property is widely utilized in optical and communication technologies that require precise signal concentration.In analytic geometry, a parabola is defined as...

Reflection of Waves

Reflection of Waves

When a wave travels from one medium to another, it gets reflected at the boundary of the second medium. A common example of this is when a person yells at a distance from a cliff and hears the echo of their voice. The sound waves (longitudinal waves) traveling in the air are reflected from the bounding cliff. Similarly, flipping one end of a string whose other end is tied to a wall causes a pulse (transverse wave) to travel through the string, which gets reflected upon reaching the wall. In...

Trigonometric Identities II

Trigonometric Identities II

Double-angle and half-angle trigonometric identities are derived from the fundamental sum and difference formulas and serve as essential tools for simplifying expressions, solving equations, and evaluating integrals. These identities reduce the complexity of trigonometric functions by relating functions of a multiple or fractional angle to functions of a single angle. Their applications extend across mathematics, physics, and engineering, particularly in Fourier analysis, wave mechanics, and...

Surface Area Calculations

Surface Area Calculations

Surface area calculations for a graph z = f(x, y) are fundamental in engineering applications involving curved structures such as satellite dishes. A parabolic dish reflects communication signals efficiently, but engineers must determine its exact curved surface area to estimate coating materials, fabrication costs, and structural requirements. Since the rim of the dish forms a circular boundary, the surface area is calculated over a circular domain in the xy-plane.Parametric Representation of...

Transmission-Line Differential Equations

Transmission-Line Differential Equations

Transmission lines are essential components of electrical power systems. They are characterized by the distributed nature of resistance (R), inductance (L), and capacitance (C) per unit length. To analyze these lines, differential equations are employed to model the variations in voltage and current along the line.
Line Section Model
A circuit representing a line section of length Δx helps in understanding the transmission line parameters. The voltage V(x) and current i(x) are measured from the...

Trigonometric Equations

Trigonometric Equations

Trigonometric equations involve one or more trigonometric functions and arise frequently in mathematical modeling. These equations may be either identities, which are valid for all values of the variable, or conditional equations, which hold true only for specific values. The process of solving trigonometric equations typically involves both algebraic techniques and the use of fundamental properties of trigonometric functions.Some trigonometric equations resemble standard algebraic forms and...

You might also read

Related Articles

Articles linked to this work by shared authors, journal, and citation graph.

Sort by

Same author

Mie scattering near the Fröhlich mode.

Journal of the Optical Society of America. A, Optics, image science, and vision·2025

Same author

Surface contribution to the electric dipole moment near an interface, and its effect on power emission.

Journal of the Optical Society of America. A, Optics, image science, and vision·2021

Same author

Propagation of magnetic dipole radiation through a medium.

Journal of the Optical Society of America. A, Optics, image science, and vision·2016

Same author

Photon statistics of resonance fluorescence in the limit of separated spectral lines.

The journal of physical chemistry. A·2014

Same author

Theory of field attenuation in photon detection, with an application to resonance fluorescence.

Journal of the Optical Society of America. A, Optics, image science, and vision·2013

Same author

Damping of the dipole vortex.

Journal of the Optical Society of America. A, Optics, image science, and vision·2011

Search research articles

Related Experiment Video

Updated: Jul 6, 2026

Shaping the Amplitude and Phase of Laser Beams by Using a Phase-only Spatial Light Modulator

Shaping the Amplitude and Phase of Laser Beams by Using a Phase-only Spatial Light Modulator

Published on: January 28, 2019

Integral equation formulation for reflection by a mirror.

Henk F Arnoldus¹

¹Department of Physics and Astronomy, Mississipi State University, Mississipi State, Mississipi 39762-5167, USA. arnoldus@ra.msstate.edu

Journal of the Optical Society of America. A, Optics, Image Science, and Vision

|April 3, 2008

Summary

This study presents a new method for calculating surface current density on mirrors when light is incident. The approach simplifies obtaining the reflected field and constructing image sources for various current distributions.

Related Experiment Videos

Last Updated: Jul 6, 2026

Shaping the Amplitude and Phase of Laser Beams by Using a Phase-only Spatial Light Modulator

Shaping the Amplitude and Phase of Laser Beams by Using a Phase-only Spatial Light Modulator

Published on: January 28, 2019

Area of Science:

Electromagnetism
Optics
Surface Physics

Background:

Light incident on a mirror induces surface current density, which generates the reflected field.
Existing methods for calculating reflected fields can be complex.

Purpose of the Study:

To derive a simplified integral equation for the Fourier-transformed surface current density.
To develop a method for constructing image sources for arbitrary current distributions.
To provide an alternative approach to the method of images for calculating reflected fields.

Main Methods:

Derivation of an integral equation for the Fourier-transformed surface current density.
Representation of the incident field using an angular spectrum.
Solving the integral equation to find the surface current density.
Construction of image sources based on the derived solutions.

Main Results:

A relation between surface current density and source current density was derived.
The approach provides a simple method for obtaining surface current density.
Image sources were constructed for electric and magnetic dipoles and an electric quadrupole.
An expression for the reflected field was derived as an integral over the source current distribution.

Conclusions:

The presented integral equation approach offers a simplified method for calculating surface current density and reflected fields.
This method allows for the construction of image sources for various current distributions, serving as an alternative to the traditional method of images.