Chapter 35 Interference Power Point Lectures for University

Goals for Chapter 35 • To consider interference of waves in space • To

Introduction • Why do soap bubbles show vibrant color patterns, even though soapy water

Wave fronts from a disturbance • Figure 35. 1 at the right shows a

Constructive and destructive interference • Figure 35. 2 at the right shows two coherent

Interfering Sources Copyright © 2012 Pearson Education Inc.

Two-source interference of light • Figure 35. 5 below-right shows Young’s double-slit experiment with

Interference from two slits • Projection of two-slit interference on to a screen. •

Two-slit interference • Example 35. 1: Given the measurements in the figure, what is

Broadcast pattern of a radio station • Example 35. 2: Radiation pattern of two

Intensity in interference patterns • Consider two interfering waves with phase different by phase

Intensity in interference patterns • What is the phase difference, f, at various angles

Interference in thin films • Fundamentally, the interference is due to path -length differences

Phase shifts during reflection • Follow the text analysis of thin-film interference and phase

Wedge between two plates • Read Problem-Solving Strategy 35. 1. • Follow Example 35.

Newton’s rings • Figure 35. 16 below illustrates the interference rings (called Newton’s rings)

Using interference fringes to test a lens • The lens to be tested is

Nonreflective coatings • The purpose of the nonreflecting film is to cancel the reflected

Michelson interferometer • The Michelson interferometer is used to make precise measurements of wavelengths

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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 Copyright © 2012 Pearson Education Inc.

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. Copyright © 2012 Pearson Education Inc.

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. Copyright © 2012 Pearson Education Inc.

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. Copyright © 2012 Pearson Education Inc.

Interference from two slits • 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. ym q R • Here, R is distance to screen, d is separation of slits, and m is the “order” of the fringe. Copyright © 2012 Pearson Education Inc.

Broadcast pattern of a radio station • Example 35. 2: Radiation pattern of two radio towers, 400 m apart, operating at 1500 k. Hz, oscillating in phase. In what directions is the intensity greatest? Copyright © 2012 Pearson Education Inc.

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 • • • Intensity is related to the square of the electric field through the Poynting vector But so Copyright © 2012 Pearson Education Inc. • The maximum intensity is • And in terms of the maximum

Intensity in interference patterns • What is the phase difference, f, at various angles q from the slits? • Think about the path difference r 2 – r 1. Whenever this path difference increases by a wavelength, the phase difference increases by 2 p. Thus • But the path difference for a slit separation d is just • Finally, then, the intensity pattern is • Since • Follow Example 35. 3. , Copyright © 2012 Pearson Education Inc.

Interference in thin films • Fundamentally, the interference is due to path -length differences for two coherent sources. Any arrangement that causes such a pathlength difference will show interference phenomena, as long as the • Figure 35. 12 (below) shows interference of an air wedge. Copyright © 2012 Pearson Education Inc.

Wedge between two plates • Read Problem-Solving Strategy 35. 1. • 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. Copyright © 2012 Pearson Education Inc.

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. Copyright © 2012 Pearson Education Inc.

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. Copyright © 2012 Pearson Education Inc.