# Interference and Wave Nature of Light

Student Learning Objectives
Lessons / Lecture Notes
Important Equations
Example Problems
Applets and Animations

Student Learning Objectives

• To recognize the experimental evidence for the wave nature of light.
• To understand how and why interference of light waves occurs.
• To understand how constructive and destructive interference are related to the path-length difference.
• To calculate the interference patterns of double slits.
• To understand the conditions for constructive and destructive interference in thin films.
• To study the spreading of waves due to diffraction.
• To understand how light diffracts through single slits and circular apertures.
• To understand how diffraction limits the resolution of optical instruments.

Lessons / Lecture Notes

The Physics Classroom (conceptual)

PY106 Notes from Boston University (algebra-based):

Introductory physics notes from University of Winnipeg (algebra-based):

HyperPhysics (calculus-based)

PHY2049 notes from Florida Atlantic University (calculus-based):

• Photons (middle portion of notes)

PHY2044 notes from Florida Atlantic University (calculus-based)

• Photons (middle portion of notes)

General Physics II notes from ETSU (calculus-based)

Important Equations

Example Problems

Problem 1
Light with a wavelength of 646 nm passes through two slits and forms an interference pattern on a screen 8.75 m away. The distance between the central bright fringe and the first-order (m = 1) bright fringe is 5.16 cm. (a) What is the separation between the slits? (b) What will be the distance between the central bright fringe and the second-order (m = 2) minimum? (Solutions)

Problem 2
Light reflected from a thin film of oil (n = 1.40) floating on water (n = 1.33) constructively interferes at a wavelength of  &lambda = 550 nm.  (a) Sketch the situation and indicate which of the reflected rays undergo a phase shift. (b) Find the minimum thickness of the film that could produce this constructive interference. (Solutions)

Applets and Animations
 Wave Interference Make waves with a dripping faucet, audio speaker, or laser! Add a second source or a pair of slits to create an interference pattern. Two Source Interference The Two Source Interference model displays the interference pattern on a screen due to two point sources.  The simulation allows an arbitrarily superposition of the two sources and shows both the current intensity and running average of the intensity on the screen. Optics Interference The Optics Interference program simulates a ripple tank by showing the intensity of waves produced by a point source. Adding multiple point sources creates easily observable interference patterns showing constructive and destructive interference. Users can add point sources, move them around and change their wavelength. Double Slit Interference This applet shows the interference of light on a screen from double slit interference. The user can control the wavelength and slit spacing. Young's Double Slit Interference This applet also shows the interference of light on a screen from double slit interference. The user can control the wavelength, slit spacing, and distance to the screen. Single Slit Diffraction This applet also shows the diffraction of light by a single slit. The user can control the wavelength and slit width. Multiple Slit Diffraction The Multiple Slit Diffraction model allows the user to simulate Fraunhofer diffraction through single or multiple slits. The user can modify the number of slits, the slit width, the slit separation and the wavelength of the incident light. The scale of the diffraction pattern can also be changed and a plot of the light intensity can be toggled on and off with a checkbox. Two-Color Multiple Slit Diffraction The Two-Color Multiple Slit Diffraction Model allows users to explore multiple slit diffraction by manipulating characteristics of the aperture and incident light to observe the resulting intensity.  An exploration of resolving power in spectroscopy is included in the model. Optical Resolution The Optical Resolution model computes the image from two point sources as seen through a circular aperture such as a telescope or a microscope.  The simulation allows the user to vary the distance between the light sources and the diameter of the aperture, as well as the intensity of the light source.