Single-Slit Diffraction Pattern

This Demonstration shows the intensity distribution of one-slit diffraction over a wide range of slit widths so that both Fraunhofer and Fresnel diffraction are covered. You can produce an interference pattern as it would be seen on a screen and the vector sum for any position on the screen. The results are derived from Feynman's method of "integrating over paths" and can be proven experimentally if the light source is a He-Ne laser and the screen is 1 m distance from the slit.


  • [Snapshot]
  • [Snapshot]
  • [Snapshot]


The aperture of the slit is divided into points, each of which can be considered the origin of a wave. The wave vectors are summed up at a point on the screen. At a given point each wave has a different distance to travel, which results in a different phase angle . Let be the distance between the slit and the screen, the distance of the point on the screen relative to the optic axis and the space between one of the points in the slit to the optic axis. The length of a path is then . Because it is approximately . In the case of Fraunhofer diffraction where the slit width it can be further approximated to , which means that and hence depend linearly on . The sum of the wave vectors gives a line of constant curvature, a circle. It is completed for the first time in the first minima. When becomes greater, cannot be neglected and the phase angle between two neighboring wave vectors is no longer constant. The result of the vector sum is now the so-called Cornu1 spiral, which is an important tool for investigating Fresnel diffraction.
1After the French physicist Alfred Cornu (1841-1902).
R. P. Feynman, QED: The Strange Theory of Light and Matter, Princeton: Princeton University Press, 1985.
    • Share:

Embed Interactive Demonstration New!

Just copy and paste this snippet of JavaScript code into your website or blog to put the live Demonstration on your site. More details »

Files require Wolfram CDF Player or Mathematica.

Mathematica »
The #1 tool for creating Demonstrations
and anything technical.
Wolfram|Alpha »
Explore anything with the first
computational knowledge engine.
MathWorld »
The web's most extensive
mathematics resource.
Course Assistant Apps »
An app for every course—
right in the palm of your hand.
Wolfram Blog »
Read our views on math,
science, and technology.
Computable Document Format »
The format that makes Demonstrations
(and any information) easy to share and
interact with.
STEM Initiative »
Programs & resources for
educators, schools & students.
Computerbasedmath.org »
Join the initiative for modernizing
math education.
Step-by-Step Solutions »
Walk through homework problems one step at a time, with hints to help along the way.
Wolfram Problem Generator »
Unlimited random practice problems and answers with built-in step-by-step solutions. Practice online or make a printable study sheet.
Wolfram Language »
Knowledge-based programming for everyone.
Powered by Wolfram Mathematica © 2018 Wolfram Demonstrations Project & Contributors  |  Terms of Use  |  Privacy Policy  |  RSS Give us your feedback
Note: To run this Demonstration you need Mathematica 7+ or the free Mathematica Player 7EX
Download or upgrade to Mathematica Player 7EX
I already have Mathematica Player or Mathematica 7+