# Interference & Diffraction

## Interference

Definition for two sources of traveling waves with the same frequency separated by some distance. Conditions for constructive and destructive interference; nodes and maxima; interference patterns.

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## Demonstration: Interference in Water

Creating an interference pattern in a pool of water by tapping on the surface at two points. Also includes a slide of a butterfly in a pond.

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• Watch {}video clip from Lecture 33 (11:29 - 16:28)

## Conditions for Constructive and Destructive Interference

Conditions in terms of angle θ between the center of the two sources and the point at which the interference is being measured.

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• Watch {}video clip from Lecture 33 (16:28 - 23:27)

## Demonstration: Interference of Sound Waves

Finding locations in the lecture hall where constructive and destructive interference occurs from two speakers placed at the front of the room.

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• Watch {}video clip from Lecture 33 (23:27 - 32:32)

## Young's Double Slit Experiment

The original experiment used to demonstrate that light was a wave, performed here by shining a red laser through two small slits.

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• Watch {}video clip from Lecture 33 (32:32 - 40:35)

Shows the setup of the double slit experiment and uses the geometry to determine the interference pattern from the phase difference of the waves.

• 8.02 Physics II: Electricity and Magnetism, Spring 2007
Prof. John Belcher, Dr. Peter Dourmashkin, Prof. Robert Redwine, Prof. Bruce Knuteson, Prof. Gunther Roland, Prof. Bolek Wyslouch, Dr. Brian Wecht, Prof. Eric Katsavounidis, Prof. Robert Simcoe, Prof. Joseph Formaggio, Andy Neely, Matthew Strafuss, Prof. Eric Hudson, Dr. Sen–Ben Liao

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## Interference with Different Colors of Light

Comparing interference patterns for red, blue, and white light, including a slide showing all three.

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• Watch {}video clip from Lecture 33 (40:35 - 44:31)

Tracking the interference pattern from two sources of radar waves using a receiver that slides along a track.

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• Watch {}video clip from Lecture 33 (44:31 - 51:37)

## Multi–Slit Interference

Conditions for constructive and destructive interference for light shining through N slits.

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• Watch {}video clip from Lecture 34 (0:00 - 7:48)

## Demonstration: Multi–Slit Interference

Interference pattern for a red laser and a white light shining through a fine grating.

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• Watch {}video clip from Lecture 34 (7:48 - 17:04)

## Demonstration: Multi–Slit Interference with a Lens

Using a lens to see an interference pattern at a much closer distance. Demonstration uses the lens of the eye and an individual grating to view the pattern for a white light and a neon light.

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• Watch {}video clip from Lecture 34 (17:04 - 23:08)

## Diffraction

Definition, with conditions for maxima and minima of this single–slit interference and a plot of the diffraction pattern.

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Introduction to Huygens's Principle, where every point on a wavefront acts as a source of spherical waves, and shows how this makes diffraction patterns possible; defines Fraunhofer diffraction.

• 8.02 Physics II: Electricity and Magnetism, Spring 2007
Prof. John Belcher, Dr. Peter Dourmashkin, Prof. Robert Redwine, Prof. Bruce Knuteson, Prof. Gunther Roland, Prof. Bolek Wyslouch, Dr. Brian Wecht, Prof. Eric Katsavounidis, Prof. Robert Simcoe, Prof. Joseph Formaggio, Andy Neely, Matthew Strafuss, Prof. Eric Hudson, Dr. Sen–Ben Liao

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## Demonstration: Diffraction Pattern

Showing that for a narrower slit the diffraction pattern becomes wider using a variable width slit and a green laser.

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• Watch {}video clip from Lecture 34 (30:08 - 36:08)

## Angular Resolution

Diffraction for a circular opening, and discussion of angular resolution for distinguishing between two light sources. Includes the Rayleigh criterion and discussion of angular resolution for telescopes on earth and in space.

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## Angular Resolution of the Human Eye

Testing the eye's angular resolution by looking at a series of pairs of pinholes with different separations to see which ones appear as two distinct light sources.

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• Watch {}video clip from Lecture 34 (45:58 - 51:30)

## Superposition and Interference of Waves

Introduces constructive and destructive interference that arise from superposing coherent, monochromatic waves with a phase difference.

• 8.02 Physics II: Electricity and Magnetism, Spring 2007
Prof. John Belcher, Dr. Peter Dourmashkin, Prof. Robert Redwine, Prof. Bruce Knuteson, Prof. Gunther Roland, Prof. Bolek Wyslouch, Dr. Brian Wecht, Prof. Eric Katsavounidis, Prof. Robert Simcoe, Prof. Joseph Formaggio, Andy Neely, Matthew Strafuss, Prof. Eric Hudson, Dr. Sen–Ben Liao

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## Single Slit Diffraction

Calculates the interference pattern of a single finite slit due to Fraunhofer diffraction.

• 8.02 Physics II: Electricity and Magnetism, Spring 2007
Prof. John Belcher, Dr. Peter Dourmashkin, Prof. Robert Redwine, Prof. Bruce Knuteson, Prof. Gunther Roland, Prof. Bolek Wyslouch, Dr. Brian Wecht, Prof. Eric Katsavounidis, Prof. Robert Simcoe, Prof. Joseph Formaggio, Andy Neely, Matthew Strafuss, Prof. Eric Hudson, Dr. Sen–Ben Liao

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## Diffraction Grating

Shows qualitatively the patterns that arise from many–slit diffraction gratings, and the pattern dependence on the number of slits.

• 8.02 Physics II: Electricity and Magnetism, Spring 2007
Prof. John Belcher, Dr. Peter Dourmashkin, Prof. Robert Redwine, Prof. Bruce Knuteson, Prof. Gunther Roland, Prof. Bolek Wyslouch, Dr. Brian Wecht, Prof. Eric Katsavounidis, Prof. Robert Simcoe, Prof. Joseph Formaggio, Andy Neely, Matthew Strafuss, Prof. Eric Hudson, Dr. Sen–Ben Liao

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## Analyzing Interference Fringes

When an unknown slit pattern is illuminated with red laser light, it produces the illustrated interference fringes; what are the width and/or separation of the slits? Solution is included after problem.

• 8.02 Physics II: Electricity and Magnetism, Spring 2007
Prof. John Belcher, Dr. Peter Dourmashkin, Prof. Robert Redwine, Prof. Bruce Knuteson, Prof. Gunther Roland, Prof. Bolek Wyslouch, Dr. Brian Wecht, Prof. Eric Katsavounidis, Prof. Robert Simcoe, Prof. Joseph Formaggio, Andy Neely, Matthew Strafuss, Prof. Eric Hudson, Dr. Sen–Ben Liao

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## Double–Slit Interference Maxima

How many interference maxima lie within a given angular range in a two–slit interference setup? Solution is included after problem.

• 8.02 Physics II: Electricity and Magnetism, Spring 2007
Prof. John Belcher, Dr. Peter Dourmashkin, Prof. Robert Redwine, Prof. Bruce Knuteson, Prof. Gunther Roland, Prof. Bolek Wyslouch, Dr. Brian Wecht, Prof. Eric Katsavounidis, Prof. Robert Simcoe, Prof. Joseph Formaggio, Andy Neely, Matthew Strafuss, Prof. Eric Hudson, Dr. Sen–Ben Liao

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## Double–Slit Phase Difference

Find various relationships between phase difference, path length difference, and screen position for a two–slit interference setup. Solution is included after problem.

• 8.02 Physics II: Electricity and Magnetism, Spring 2007
Prof. John Belcher, Dr. Peter Dourmashkin, Prof. Robert Redwine, Prof. Bruce Knuteson, Prof. Gunther Roland, Prof. Bolek Wyslouch, Dr. Brian Wecht, Prof. Eric Katsavounidis, Prof. Robert Simcoe, Prof. Joseph Formaggio, Andy Neely, Matthew Strafuss, Prof. Eric Hudson, Dr. Sen–Ben Liao

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## Constructive Interference Condition

Coherent light is incident from an angle onto a plane containing two slits; find the relationship between the incidence angle, d, λ, and the screen position angle for a point that is an interference maximum. Solution is included after problem.

• 8.02 Physics II: Electricity and Magnetism, Spring 2007
Prof. John Belcher, Dr. Peter Dourmashkin, Prof. Robert Redwine, Prof. Bruce Knuteson, Prof. Gunther Roland, Prof. Bolek Wyslouch, Dr. Brian Wecht, Prof. Eric Katsavounidis, Prof. Robert Simcoe, Prof. Joseph Formaggio, Andy Neely, Matthew Strafuss, Prof. Eric Hudson, Dr. Sen–Ben Liao

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## Determining Wavelength from Double–Slit Interference

Determine the wavelength of light in a two–slit interference setup based on the setup geometry and the distance between the central maximum and the second–order bright fringe. Solution is included after problem.

• 8.02 Physics II: Electricity and Magnetism, Spring 2007
Prof. John Belcher, Dr. Peter Dourmashkin, Prof. Robert Redwine, Prof. Bruce Knuteson, Prof. Gunther Roland, Prof. Bolek Wyslouch, Dr. Brian Wecht, Prof. Eric Katsavounidis, Prof. Robert Simcoe, Prof. Joseph Formaggio, Andy Neely, Matthew Strafuss, Prof. Eric Hudson, Dr. Sen–Ben Liao

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## Conceptual Interference and Diffraction Questions

Conceptual questions about the conditions for interference and how two–slit and finite–slit interference patterns depend on setup parameters.

• 8.02 Physics II: Electricity and Magnetism, Spring 2007
Prof. John Belcher, Dr. Peter Dourmashkin, Prof. Robert Redwine, Prof. Bruce Knuteson, Prof. Gunther Roland, Prof. Bolek Wyslouch, Dr. Brian Wecht, Prof. Eric Katsavounidis, Prof. Robert Simcoe, Prof. Joseph Formaggio, Andy Neely, Matthew Strafuss, Prof. Eric Hudson, Dr. Sen–Ben Liao

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## Double–Slit Interference Fringe Positions

For a two–slit interference setup with given parameters, find the spacing between adjacent fringes and the position of the third order bright fringe.

• 8.02 Physics II: Electricity and Magnetism, Spring 2007
Prof. John Belcher, Dr. Peter Dourmashkin, Prof. Robert Redwine, Prof. Bruce Knuteson, Prof. Gunther Roland, Prof. Bolek Wyslouch, Dr. Brian Wecht, Prof. Eric Katsavounidis, Prof. Robert Simcoe, Prof. Joseph Formaggio, Andy Neely, Matthew Strafuss, Prof. Eric Hudson, Dr. Sen–Ben Liao

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## Interference–Diffraction Pattern Fringes

How many bright fringes are in the central diffraction maximum of the interference pattern from two finite slits?

• 8.02 Physics II: Electricity and Magnetism, Spring 2007
Prof. John Belcher, Dr. Peter Dourmashkin, Prof. Robert Redwine, Prof. Bruce Knuteson, Prof. Gunther Roland, Prof. Bolek Wyslouch, Dr. Brian Wecht, Prof. Eric Katsavounidis, Prof. Robert Simcoe, Prof. Joseph Formaggio, Andy Neely, Matthew Strafuss, Prof. Eric Hudson, Dr. Sen–Ben Liao

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## Three–Slit Interference

Confirm the condition for the positions of interference maxima in a three–slit interference pattern, and find the spacing between adjacent maxima.

• 8.02 Physics II: Electricity and Magnetism, Spring 2007
Prof. John Belcher, Dr. Peter Dourmashkin, Prof. Robert Redwine, Prof. Bruce Knuteson, Prof. Gunther Roland, Prof. Bolek Wyslouch, Dr. Brian Wecht, Prof. Eric Katsavounidis, Prof. Robert Simcoe, Prof. Joseph Formaggio, Andy Neely, Matthew Strafuss, Prof. Eric Hudson, Dr. Sen–Ben Liao

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## Interference–Diffraction Parameter Determination

In a two finite slit diffraction pattern, characterize the relationship between slit width and separation based on the number of bring fringes in the central diffraction maximum.

• 8.02 Physics II: Electricity and Magnetism, Spring 2007
Prof. John Belcher, Dr. Peter Dourmashkin, Prof. Robert Redwine, Prof. Bruce Knuteson, Prof. Gunther Roland, Prof. Bolek Wyslouch, Dr. Brian Wecht, Prof. Eric Katsavounidis, Prof. Robert Simcoe, Prof. Joseph Formaggio, Andy Neely, Matthew Strafuss, Prof. Eric Hudson, Dr. Sen–Ben Liao

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## Graphical Interference Question

Distinguish constructive and destructive interference of illustrated waves.

• 8.02 Physics II: Electricity and Magnetism, Spring 2007
Prof. John Belcher, Dr. Peter Dourmashkin, Prof. Robert Redwine, Prof. Bruce Knuteson, Prof. Gunther Roland, Prof. Bolek Wyslouch, Dr. Brian Wecht, Prof. Eric Katsavounidis, Prof. Robert Simcoe, Prof. Joseph Formaggio, Andy Neely, Matthew Strafuss, Prof. Eric Hudson, Dr. Sen–Ben Liao

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## Angular Resolution of Telescopes

Finding angular resolution for single telescope, then two telescopes as interferometer.

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## Resolving Power of Optical Telescopes

Finding angular resolution for ground–based and space–based telescopes.

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## Two–Dimensional Waves

Applet showing the propagation of waves in two dimensions to illustrate the properties of interference, diffraction, and reflection.

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