Introductory Physics Volume Two

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154 Wave Optics 7.10 The reason that we care the wavelength has changed, is that when we use the result that ∆r = m λ 2 we need to use the wavelength where the path difference ∆r occurs. In the case considered above, the extra bit of path occurs within the oil, so we need to use the wavelength in the oil. In order to understand the root cause of the second complication, consider a soap bubble again. If you make a soap bubble and watch it carefully, you will notice that just before it pops, it appears that the top of the bubble has a hole in it. There is not actually a hole, but the top of the bubble looks like it has a hole because when the bubble gets very thin, no light is reflected from the surface of the bubble. Let us consider what our prediction would be for a very thin bubble. From our work with the oil film we expect that we will get a maximum reflection when 2t = mλ/2, and m is even. Recall also that m = 0 gives a maximum, so t ≈ 0 should give a maximum for all wavelengths. Thus we expect the soap bubble to reflect very well when the film of bubble juice gets very thin. The truth is just the opposite. The key to this puzzle is to understand that when a wave is reflected it can be inverted, that is the direction of the displacement can be reversed. But a reversal is the same as a π phase shift. Fact: Reflection Phase Shift When a wave is reflected at an interface between two media there will be a π phase shift in the reflected wave if the index of refraction of the incident medium is lower than the index of refraction of the reflecting medium. If the incident medium has a higher index, there is no phase shift. ⊲ Problem 7.11 Explain using the reflection phase shift why a thin soap bubble reflects no light. § 7.10 Single Slit Diffraction If a wave is passed through a rectangular hole that is much narrower in one direction than the other we find that we get an interference pattern like we do with a two source. Such a hole is usually referred to as a slit since it is so narrow in one direction.
7.11 Homework 155 Second Min First Min Source θ Central Max Fact: Single Slit Diffraction If light is passed through a single slit of width a, then the angle between the central maximum and the first minimum is given by a sin θ = λ § 7.11 Homework ⊲ Problem 7.12 A pair of speakers is configured as shown, with a microphone placed directly in front of one of the speakers. Sound waves having a wavelength 10 cm are coming from the speakers. The speakers are in phase with each other. What is the minimum distance d between the speakers so that no sound is heard at the microphone labeled P ? 1 m P d ⊲ Problem 7.13 A material having an index of refraction of 1.30 is used to coat a piece of glass (n = 1.50). What should be the minimum thickness of this film to minimize reflection of 500nm light? ⊲ Problem 7.14 A soap bubble of index of refraction 1.33 strongly reflects both the red and the green components of white light. What film thickness allows this to happen? (In air, λ red = 700nm, λ green = 500nm.)
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1 Introductory Physics Volume Two S
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1.1 Electric Charge 3 Demo 1 Electr
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1.1 Electric Charge 5 Then charge a
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- - - - - 1.2 Coulomb’s Law 7 How
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1.2 Coulomb’s Law 9 Example Consi
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1.3 Electric Field 11 + - Compute t
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1.3 Electric Field 13 points a well
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1.3 Electric Field 15 Look back now
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1.5 Continuous Charge Distributions
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1.6 Gauss’s Law 19 § 1.6 Gauss
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1.6 Gauss’s Law 21 Suppose that y
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1.7 More Examples 23 ⊲ Problem 1.
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1.7 More Examples 25 The net force
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1.7 More Examples 27 out the net fo
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1.7 More Examples 29 -4q +2q -q E -
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1.7 More Examples 31 The area vecto
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1.8 Homework 33 ⊲ Problem 1.14 Ri
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1.9 Summary 35 § 1.9 Summary Defin
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2.1 Electric Potential 37 2 Electri
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2.1 Electric Potential 39 Example S
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2.2 Equipotentials 41 ⊲ Problem 2
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2.3 Conductors in Equilibrium 43
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2.4 Capacitors 45 § 2.4 Capacitors
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2.5 Energy in an Electric Field 47
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2.7 More Examples 49 ⊲ Problem 2.
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2.7 More Examples 51 The resulting
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2.8 Homework 53 add up potential du
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2.8 Homework 55 ⊲ Problem 2.27 Ho
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3.2 Electric Current 57 3 Circuits
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3.3 Ohm’s Law 59 Some materials,
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3.5 Kirchhoff’s Rules 61 ⊲ Prob
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3.6 Resistors in Combination 63 par
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3.8 Capacitor Circuits 65 Theorem:
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3.9 More Examples 67 Note that the
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3.9 More Examples 69 This mean that
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3.9 More Examples 71 15Ω 5Ω 10Ω
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3.9 More Examples 73 First combine
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3.10 Homework 75 ⊲ Problem 3.16 B
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3.10 Homework 77 4 µF + - 2 µF +
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3.11 Summary 79 § 3.11 Summary Def
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4.2 Magnetic Force on a Current 81
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4.3 Trajectories Under Magnetic For
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4.4 Lorentz Force 85 with a charge
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4.5 Hall Effect 87 But this charge
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4.6 More Examples 89 -e F E v F B =
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4.6 More Examples 91 The force on t
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4.7 Homework 93 Imagine the closed
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4.7 Homework 95 circular orbits. Wr
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5.1 Sources of Magnetic Field 97 5
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5.1 Sources of Magnetic Field 99
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5.2 Ampere’s Law 101 and ⃗ dr s
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Page 111 and 112: 5.5 Homework 111 The magnetic force
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Page 115 and 116: 6.2 Faraday’s Law 115 6 Time Vary
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Page 137 and 138: 7.1 Maxwell Equations 137 7 Wave Op
Page 139 and 140: 7.2 Describing Oscillations 139 tio
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Page 161 and 162: 8.2 Reflection 161 8 Geometric Opti
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Page 185 and 186: A Hints 185 7.26 The distance from
Page 187 and 188: B Index 187 † Ohm’s Law: Resist
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Page 191 and 192: C Power Series Expansions 191 The F
Page 193: D Unit Prefixes 193 § D.3 Fundamen
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