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Copyright � 2012 Pearson Education Inc.

PowerPoint Lectures for

University Physics, Thirteenth Edition

– Hugh D. Young and Roger A. Freedman

Lectures by Wayne Anderson

Chapter 35

Interference

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Goals for Chapter 35

• To consider interference of waves in space
• To analyze two-source interference of light
• To calculate the intensity of interference patterns
• To understand interference in thin films
• To use interference to measure extremely small distances

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Introduction

• Why do soap bubbles show vibrant color patterns, even though soapy water is colorless?
• What causes the multicolored reflections from DVDs?
• We will now look at optical effects, such as interference, that depend on the wave nature of light.

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Wave fronts from a disturbance

• Figure 35.1 at the right shows a “snapshot” of sinusoidal waves spreading out in all directions from a source.
• Superposition principle: When two or more waves overlap, the resultant displacement at any instant is the sum of the displacements of each of the individual waves.

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Constructive and destructive interference

• Figure 35.2 at the right shows two coherent wave sources.
• Constructive interference occurs when the path difference is an integral number of wavelengths.
• Destructive interference occurs when the path difference is a half-integral number of wavelengths.

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Interfering Sources

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Interfering Sources

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Two-source interference of light

• Figure 35.5 below-right shows Young’s double-slit experiment with geometric analysis.

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• Projection of two-slit interference on to a screen.
• The linear dimension of the separation of fringes obviously depends on the angle and the distance from the screen.
• Here, R is distance to screen, d is separation of slits, and m is the “order” of the fringe.

Interference from two slits

q

ym

R

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Two-slit interference

• Example 35.1: Given the measurements in the figure, what is the wavelength of the light?

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• Example 35.2:  Radiation pattern of two radio towers, 400 m apart, operating at 1500 kHz, oscillating in phase.  In what directions is the intensity greatest?

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Intensity in interference patterns

• Consider two interfering waves with phase different by phase angle f.
• By superposition, we find the resultant wave by simply adding.
• We use a phasor diagram to show the vector addition. Using the law of cosines
• But
• so

• Intensity is related to the square of the electric field through the Poynting vector
• The maximum intensity is
• And in terms of the maximum

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Intensity in interference patterns

• What is the phase difference, f, at various angles q from the slits?
• Think about the path difference r2r1.  Whenever this path difference increases by a wavelength, the phase difference increases by 2p.  Thus
• But the path difference for a slit separation d is just
• Finally, then, the intensity pattern is
• Since                ,

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Interfering Sources

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Interference in thin films

• Fundamentally, the interference is due to path-length differences for two coherent sources.  Any arrangement that causes such a path-length difference will show interference phenomena, as long as the
• Figure 35.12 (below) shows interference of  an air wedge.

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Phase shifts during reflection

• Follow the text analysis of thin-film interference and phase shifts during reflection. Use Figure 35.13 below.

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Wedge between two plates

• Follow Example 35.4, having air between the plates. Use   Figure 35.15 below.
• Follow Example 35.5, having water between the plates.
• Follow Example 35.6, another variation on the plates.

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Newton’s rings

• Figure 35.16 below illustrates the interference rings (called Newton’s rings) resulting from an air film under a lens.

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Using interference fringes to test a lens

• The lens to be tested is placed on top of the master lens. If the two surfaces do not match, Newton’s rings will appear, as in Figure 35.17 at the right.

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Nonreflective coatings

• The purpose of the nonreflecting film is to cancel the reflected light. (See Figure 35.18 at the right.)

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Michelson interferometer

• The Michelson interferometer is used to make precise measurements of wavelengths and very small distances.
• Follow the text analysis, using Figure 35.19 below.
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