1. Electromagnetic Waves
Chapter 33
Today’s information age is based almost entirely on the physics of electromagnetic waves. The connection between electric and magnetic fields to produce light is one of the greatest achievements produced by physics, and electromagnetic waves are at the core of many fields in science and engineering.
In this chapter we introduce fundamental concepts and explore the properties of electromagnetic waves.
Electromagnetic Waves
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2. When the amplitude of the oscillator in a series RLC circuit is doubled:
the impedance is doubled.
B. the voltage across the capacitor is halved
C. the capacitive reactance is halved
D. the power factor is halved
E. the current amplitude is doubled

3. Maxwell’s Rainbow
The wavelength/frequency range in which electromagnetic (EM) waves (light) are visible is only a tiny fraction of the entire electromagnetic spectrum
Fig. 33-2
Fig. 33-1
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4. The Travelling Electromagnetic (EM) Wave, Qualitatively
An LC oscillator causes currents to flow sinusoidally, which in turn produces oscillating electric and magnetic fields, which then propagate through space as EM waves
Fig. 33-3
Next slide
Oscillation Frequency:
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5. The Travelling Electromagnetic (EM) Wave, Qualitatively
Fig. 33-4
EM fields at P looking back toward LC oscillator
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6. Mathematical Description of Travelling EM Waves
Electric Field:
Wave Speed:
Magnetic Field:
All EM waves travel a c in vacuum
Fig. 33-5
Wavenumber:
Angular frequency:
Vacuum Permittivity:
Vacuum Permeability:
EM Wave Simulation
Amplitude Ratio:
Magnitude Ratio:
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7. A Most Curious Wave
Unlike all the waves discussed in Chs. 16 and 17, EM waves require no medium through/along which to travel. EM waves can travel through empty space (vacuum)!
Speed of light is independent of speed of observer! You could be heading toward a light beam at the speed of light, but you would still measure c as the speed of the beam!
= ft/ns
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8. The Travelling EM Wave, Quantitatively
Induced Electric Field
Changing magnetic fields produce electric fields, Faraday’s law of induction
Fig. 33-6
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9. The Travelling EM Wave, Quantitatively
Induced Magnetic Field
Changing electric fields produce magnetic fields, Maxwell’s law of induction
Fig. 33-7
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10. Energy Transport and the Poynting Vector
The magnitude of S is related to the rate at which energy is transported by a wave across a unit area at any instant (inst). The unit for S is (W/m2)
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11. Energy Transport and the Poynting Vector
Instantaneous
energy flow rate:
Note that S is a function of time. The time-averaged value for S, Savg is also called the intensity I of the wave.
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12. Variation of Intensity with Distance
Consider a point source S that is emitting EM waves isotropically (equally in all directions) at a rate PS. Assume energy of waves is conserved as they spread from source.
Fig. 33-8
How does the intesnity (power/area) change with distance r?
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13. Radiation Pressure
EM waves have linear momentum as well as energylight can exert pressure
Total absorption:
Total reflection
Back along path:
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14. Polarization
The polarization of light is describes how the electric field in the EM wave oscillates.
Vertically plane-polarized (or linearly polarized)
Fig
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15. Polarized Light
Fig
Unpolarized or randomly polarized light has its instantaneous polarization direction vary randomly with time
One can produce unpolarized light by the addition (superposition) of two perpendicularly polarized waves with randomly varying amplitudes. If the two perpendicularly polarized waves have fixed amplitudes and phases, one can produce different polarizations such as circularly or elliptically polarized light.
Polarized Light Simulation
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16. Polarizing Sheet
Fig I0 I
Only electric field component along polarizing direction of polarizing sheet is passed (transmitted), the perpendicular component is blocked (absorbed)
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17. Intensity of Transmitted Polarized Light
Fig
Intensity of transmitted light,
unpolarized incident light:
Since only the component of the incident electric field E parallel to the polarizing axis is transmitted
Intensity of transmitted light,
polarized incident light:
For unpolarized light, q varies randomly in time
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18. Reflection and Refraction
Although light waves spread as they move from a source, often we can approximate its travel as being a straight line  geometrical optics
Fig
What happens when a narrow beam of light encounters a glass surface?
Law of Reflection
Reflection:
Snell’s Law
Refraction:
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n is the index of refraction of the material

19. Sound Waves For light going from n1 to n2 n2 = n1  q2 = q1
Fig
For light going from n1 to n2
n2 = n1  q2 = q1
n2 > n1  q2<q1, light bent towards normal
n2 < n1  q2 > q1, light bent away from normal
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20. Chromatic Dispersion
The index of refraction n encountered by light in any medium except vacuum depends on the wavelength of the light. So if light consisting of different wavelengths enters a material, the different wavelengths will be refracted differently  chromatic dispersion
Fig
Fig
n2blue>n2red
Chromatic dispersion can be good (e.g., used to analyze wavelength composition of light) or bad (e.g., chromatic aberration in lenses)
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21. Chromatic Dispersion
Chromatic dispersion can be good (e.g., used to analyze wavelength composition of light)
Fig
prism
or bad (e.g., chromatic aberration in lenses)
lens
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22. Fig
Rainbows
Sunlight consists of all visible colors and water is dispersive, so when sunlight is refracted as it enters water droplets, is reflected off the back surface, and again is refracted as it exits the water drops, the range of angles for the exiting ray will depend on the color of the ray. Since blue is refracted more strongly than red, only droplets that are closer the the rainbow center (A) will refract/reflect blue light to the observer (O). Droplets at larger angles will still refract/reflect red light to the observer.
What happens for rays that reflect twice off the back surfaces of the droplets?
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23. Total Internal Reflection
For light that travels from a medium with a larger index of refraction to a medium with a smaller medium of refraction n1>n1  q2>q1, as q1 increases, q2 will reach 90o (the largest possible angle for refraction) before q1 does. n2
Fig
Critical Angle: n1
When q2> qc no light is refracted (Snell’s Law does not have a solution!) so no light is transmitted  Total Internal Reflection
Total internal reflection can be used, for example, to guide/contain light along an optical fiber
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24. Polarization by Reflection
When the refracted ray is perpendicular to the reflected ray, the electric field parallel to the page (plane of incidence) in the medium does not produce a reflected ray since there is no component of that field perpendicular to the reflected ray (EM waves are transverse).
Fig
Applications
Perfect window: since parallel polarization is not reflected, all of it is transmitted
Polarizer: only the perpendicular component is reflected, so one can select only this component of the incident polarization
Brewster’s Law
Brewster Angle:
In which direction does light reflecting off a lake tend to be polarized?
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25. The Sun is about 1.5 × 1011 m away. The time for light to travel this distance is about:
A. 4.5 × 1018 s
B. 8 s
C. 8 min
D. 8 hr
E. 8 yr