Book cover for Physics

Physics

Alan Giambattista, Betty McCarthy Richardson, Robert C. Richardson

ISBN #9780073404530

2nd Edition

2,795 Questions

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Summary
Learning Objectives
Key Concepts
Example Problems
Explanations
Common Mistakes

Summary

This chapter emphasizes the wave nature of light through interference and diffraction. It covers the conditions for constructive and destructive interference in systems such as double slits, single slits, and thin films. The text also explores how diffraction gratings, Rayleigh’s criterion, and Bragg’s Law determine the resolution of optical and x-ray instruments. Applications, including CD technology, antireflective coatings, and holography, illustrate the practical implications of these phenomena. Overall, understanding these concepts is essential for grasping how wave properties influence optical imaging and spectroscopic measurements.

Learning Objectives

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Key Concepts

CONCEPT

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Example Problems

Example 1

Constructive and Destructive Interference A $60-\mathrm{kHz}$ radio transmitter sends an electromagnetic wave to a receiver $21 \mathrm{km}$ away. The signal also travels to the receiver by another path where it reflects from a helicopter as shown. Assume that there is a $180^{\circ}$ phase shift when the wave is reflected. (a) What is the wavelength of this EM wave? (b) Will this situation give constructive interference, destructive interference, or something in between? (FIGURE CANNOT COPY)

Example 2

A steep cliff west of Lydia's home reflects a $1020-\mathrm{kHz}$ radio signal from a station that is $74 \mathrm{km}$ due east of her home. If there is destructive interference, what is the minimum distance of the cliff from her home? Assume there is a $180^{\circ}$ phase shift when the wave reflects from the cliff.

Example 3

Roger is in a ship offshore and listening to a baseball game on his radio. He notices that there is destructive interference when seaplanes from the nearby Coast Guard station are flying directly overhead at elevations of $780 \mathrm{m}, 975 \mathrm{m},$ and $1170 \mathrm{m} .$ The broadcast station is $102 \mathrm{km}$ away. Assume there is a $180^{\circ}$ phase shift when the EM waves reflect from the seaplanes. What is the frequency of the broadcast?

Example 4

Sketch a sinusoidal wave with an amplitude of $2 \mathrm{cm}$ and a wavelength of $6 \mathrm{cm} .$ This wave represents the electric field portion of a visible EM wave traveling to the right with intensity $I_{0}$. (a) Sketch an identical wave beneath the first. What is the amplitude (in centimeters) of the sum of these waves? (b) What is the intensity of the new wave? (c) Sketch two more coherent waves beneath the others, one of amplitude $3 \mathrm{cm}$ and one of amplitude $1 \mathrm{cm},$ so all four are in phase. What is the amplitude of the four waves added together? (d) What intensity results from adding the four waves?

Example 5

Draw a sketch like that of Problem 4 but this time draw the third wave $180^{\circ}$ out of phase with the others. (a) What is the amplitude of the sum of these waves? (b) What is the intensity for the four waves together? (c) Consider the case for the first three waves in phase and the fourth wave $180^{\circ}$ out of phase. What is the amplitude for the sum of these waves? (d) What is the intensity of the wave?
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