Skip to ContentGo to accessibility pageKeyboard shortcuts menu
OpenStax Logo

Summary

4.1 Single-Slit Diffraction

  • Diffraction can send a wave around the edges of an opening or other obstacle.
  • A single slit produces an interference pattern characterized by a broad central maximum with narrower and dimmer maxima to the sides.

4.2 Intensity in Single-Slit Diffraction

  • The intensity pattern for diffraction due to a single slit can be calculated using phasors as
    I=I0(sinββ)2,I=I0(sinββ)2,

    where β=ϕ2=πasinθλβ=ϕ2=πasinθλ, a is the slit width, λλ is the wavelength, and θθ is the angle from the central peak.

4.3 Double-Slit Diffraction

  • With real slits with finite widths, the effects of interference and diffraction operate simultaneously to form a complicated intensity pattern.
  • Relative intensities of interference fringes within a diffraction pattern can be determined.
  • Missing orders occur when an interference maximum and a diffraction minimum are located together.

4.4 Diffraction Gratings

  • A diffraction grating consists of a large number of evenly spaced parallel slits that produce an interference pattern similar to but sharper than that of a double slit.
  • Constructive interference occurs when dsinθ=mλform=0,±1,±2,...,dsinθ=mλform=0,±1,±2,..., where d is the distance between the slits, θθ is the angle relative to the incident direction, and m is the order of the interference.

4.5 Circular Apertures and Resolution

  • Diffraction limits resolution.
  • The Rayleigh criterion states that two images are just resolvable when the center of the diffraction pattern of one is directly over the first minimum of the diffraction pattern of the other.

4.6 X-Ray Diffraction

  • X-rays are relatively short-wavelength EM radiation and can exhibit wave characteristics such as interference when interacting with correspondingly small objects.

4.7 Holography

  • Holography is a technique based on wave interference to record and form three-dimensional images.
  • Lasers offer a practical way to produce sharp holographic images because of their monochromatic and coherent light for pronounced interference patterns.
Order a print copy

As an Amazon Associate we earn from qualifying purchases.

Citation/Attribution

This book may not be used in the training of large language models or otherwise be ingested into large language models or generative AI offerings without OpenStax's permission.

Want to cite, share, or modify this book? This book uses the Creative Commons Attribution License and you must attribute OpenStax.

Attribution information
  • If you are redistributing all or part of this book in a print format, then you must include on every physical page the following attribution:
    Access for free at https://openstax.org/books/university-physics-volume-3/pages/1-introduction
  • If you are redistributing all or part of this book in a digital format, then you must include on every digital page view the following attribution:
    Access for free at https://openstax.org/books/university-physics-volume-3/pages/1-introduction
Citation information

© Jan 19, 2024 OpenStax. Textbook content produced by OpenStax is licensed under a Creative Commons Attribution License . The OpenStax name, OpenStax logo, OpenStax book covers, OpenStax CNX name, and OpenStax CNX logo are not subject to the Creative Commons license and may not be reproduced without the prior and express written consent of Rice University.