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

Copyright © 2012 Pearson Education Inc. 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. Interfering Sources

Copyright © 2012 Pearson Education Inc. Interfering Sources

Copyright © 2012 Pearson Education Inc. Two-source interference of light Figure 35.5 below-right shows Young’s double-slit experiment with geometric analysis.

Copyright © 2012 Pearson Education Inc. 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  ymym R

Copyright © 2012 Pearson Education Inc. Two-slit interference Example 35.1: Given the measurements in the figure, what is the wavelength of the light?

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 kHz, 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 . 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

Copyright © 2012 Pearson Education Inc. Intensity in interference patterns What is the phase difference, , at various angles  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 . 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. Interfering Sources

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 path-length difference will show interference phenomena, as long as the Figure (below) shows interference of an air wedge.

Copyright © 2012 Pearson Education Inc. Phase shifts during reflection Follow the text analysis of thin-film interference and phase shifts during reflection. Use Figure below.

Copyright © 2012 Pearson Education Inc. Wedge between two plates Read Problem-Solving Strategy Follow Example 35.4, having air between the plates. Use Figure below. Follow Example 35.5, having water between the plates. Follow Example 35.6, another variation on the plates.

Copyright © 2012 Pearson Education Inc. Newton’s rings Figure below illustrates the interference rings (called Newton’s rings) resulting from an air film under a lens.

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 at the right.

Copyright © 2012 Pearson Education Inc. Nonreflective coatings The purpose of the nonreflecting film is to cancel the reflected light. (See Figure at the right.) Follow Example 35.7.

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 below.