Chapter 31 Maxwells Equations and Electromagnetic Waves Copyright

31 -7 Measuring the Speed of Light The speed of light was known to

31 -7 Measuring the Speed of Light Over the years, measurements have become more

31 -8 Energy in EM Waves; the Poynting Vector Energy is stored in both

31 -8 Energy in EM Waves; the Poynting Vector This energy is transported by

31 -8 Energy in EM Waves; the Poynting Vector The energy transported through a

31 -8 Energy in EM Waves; the Poynting Vector Typically we are interested in

31 -8 Energy in EM Waves; the Poynting Vector Example 31 -6: E and

31 -9 Radiation Pressure In addition to carrying energy, electromagnetic waves also carry momentum.

31 -9 Radiation Pressure Example 31 -7: Solar pressure. Radiation from the Sun that

31 -9 Radiation Pressure Example 31 -8: A solar sail. Proposals have been made

31 -10 Radio and Television; Wireless Communication This figure illustrates the process by which

31 -10 Radio and Television; Wireless Communication The mixing of signal and carrier can

31 -10 Radio and Television; Wireless Communication Second, by using the signal to modify

31 -10 Radio and Television; Wireless Communication At the receiving end, the wave is

31 -10 Radio and Television; Wireless Communication The receiving antenna is bathed in waves

31 -10 Radio and Television; Wireless Communication A straight antenna will have a current

31 -10 Radio and Television; Wireless Communication Example 31 -9: Tuning a station. Calculate

Concep. Test 31. 3 Before the days of cable, televisions often had two antennae

Concep. Test 31. 4 If a radio transmitter has a vertical antenna, should a

Summary of Chapter 31 • Maxwell’s equations are the basic equations of electromagnetism: Copyright

Summary of Chapter 31 • Electromagnetic waves are produced by accelerating charges; the propagation

Summary of Chapter 31 • The wavelength and frequency of EM waves are related:

35 -11 Polarization Light is polarized when its electric fields oscillate in a single

35 -11 Polarization Polarized light will not be transmitted through a polarized film whose

35 -11 Polarization When light passes through a polarizer, only the component parallel to

35 -11 Polarization This means that if initially unpolarized light passes through crossed polarizers,

35 -11 Polarization Example 35 -13: Two Polaroids at 60°. Unpolarized light passes through

35 -11 Polarization Conceptual Example 35 -14: Three Polaroids. When unpolarized light falls on

35 -11 Polarization Light is also partially polarized after reflecting from a nonmetallic surface.

35 -11 Polarization Example 35 -15: Polarizing angle. (a) At what incident angle is

35 -12 Liquid Crystal Displays (LCD) Liquid crystals are unpolarized in the absence of

35 -13 Scattering of Light by the Atmosphere Skylight is partially polarized due to

Concep. Test 35. 3 Polarization If unpolarized light is incident 1) only case 1

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31 -7 Measuring the Speed of Light The speed of light was known to be very large, although careful studies of the orbits of Jupiter’s moons showed that it is finite. One important measurement, by Michelson, used a rotating mirror: Copyright © 2009 Pearson Education, Inc.

31 -7 Measuring the Speed of Light Over the years, measurements have become more and more precise; now the speed of light is defined to be c = 2. 99792458 × 108 m/s. This is then used to define the meter. Copyright © 2009 Pearson Education, Inc.

31 -8 Energy in EM Waves; the Poynting Vector Energy is stored in both electric and magnetic fields, giving the total energy density of an electromagnetic wave: Each field contributes half the total energy density: Copyright © 2009 Pearson Education, Inc.

31 -8 Energy in EM Waves; the Poynting Vector The energy transported through a unit area per unit time is called the intensity: Its vector form is the Poynting vector: Copyright © 2009 Pearson Education, Inc.

31 -8 Energy in EM Waves; the Poynting Vector Example 31 -6: E and B from the Sun. Radiation from the Sun reaches the Earth (above the atmosphere) at a rate of about 1350 J/s·m 2 (= 1350 W/m 2). Assume that this is a single EM wave, and calculate the maximum values of E and B. Copyright © 2009 Pearson Education, Inc.

31 -9 Radiation Pressure In addition to carrying energy, electromagnetic waves also carry momentum. This means that a force will be exerted by the wave. The radiation pressure is related to the average intensity. It is a minimum if the wave is fully absorbed: and a maximum if it is fully reflected: Copyright © 2009 Pearson Education, Inc.

31 -9 Radiation Pressure Example 31 -7: Solar pressure. Radiation from the Sun that reaches the Earth’s surface (after passing through the atmosphere) transports energy at a rate of about 1000 W/m 2. Estimate the pressure and force exerted by the Sun on your outstretched hand. Copyright © 2009 Pearson Education, Inc.

31 -9 Radiation Pressure Example 31 -8: A solar sail. Proposals have been made to use the radiation pressure from the Sun to help propel spacecraft around the solar system. (a) About how much force would be applied on a 1 km x 1 km highly reflective sail, and (b) by how much would this increase the speed of a 5000 -kg spacecraft in one year? (c) If the spacecraft started from rest, about how far would it travel in a year? Copyright © 2009 Pearson Education, Inc.

31 -10 Radio and Television; Wireless Communication This figure illustrates the process by which a radio station transmits information. The audio signal is combined with a carrier wave. Copyright © 2009 Pearson Education, Inc.

31 -10 Radio and Television; Wireless Communication The mixing of signal and carrier can be done two ways. First, by using the signal to modify the amplitude of the carrier (AM): Copyright © 2009 Pearson Education, Inc.

31 -10 Radio and Television; Wireless Communication A straight antenna will have a current induced in it by the varying electric fields of a radio wave; a circular antenna will have a current induced by the changing magnetic flux. Copyright © 2009 Pearson Education, Inc.

31 -10 Radio and Television; Wireless Communication Example 31 -9: Tuning a station. Calculate the transmitting wavelength of an FM radio station that transmits at 102. 3 MHz. Copyright © 2009 Pearson Education, Inc.

Concep. Test 31. 3 Before the days of cable, televisions often had two antennae on them, one straight and one circular. Which antenna picked up the magnetic oscillations? TV Antennas 1) the circular one 2) the straight one 3) both equally; they were straight and circular for different reasons

Concep. Test 31. 3 Before the days of cable, televisions often had two antennae on them, one straight and one circular. Which antenna picked up the magnetic oscillations? The varying B field in the loop means the flux is changing and therefore an emf is induced. TV Antennas 1) the circular one 2) the straight one 3) both equally; they were straight and circular for different reasons

Concep. Test 31. 4 If a radio transmitter has a vertical antenna, should a receiver’s antenna be vertical or horizontal to obtain the best reception? Radio Antennas 1) vertical 2) horizontal 3) doesn’t matter If a wave is sent out from a vertical antenna, antenna the electric field oscillates up and down Thus, the receiver’s E field antenna should also be vertical so of wave that the arriving electric field can set the charges in motion. E field of wave

Summary of Chapter 31 • Electromagnetic waves are produced by accelerating charges; the propagation speed is given by • The fields are perpendicular to each other and to the direction of propagation. Copyright © 2009 Pearson Education, Inc.

Summary of Chapter 31 • The wavelength and frequency of EM waves are related: • The electromagnetic spectrum includes all wavelengths, from radio waves through visible light to gamma rays. • The Poynting vector describes the energy carried by EM waves: Copyright © 2009 Pearson Education, Inc.

35 -11 Polarization Light is polarized when its electric fields oscillate in a single plane, rather than in any direction perpendicular to the direction of propagation. Copyright © 2009 Pearson Education, Inc.

35 -11 Polarization When light passes through a polarizer, only the component parallel to the polarization axis is transmitted. If the incoming light is planepolarized, the outgoing intensity is: Copyright © 2009 Pearson Education, Inc.

35 -11 Polarization Example 35 -13: Two Polaroids at 60°. Unpolarized light passes through two Polaroids; the axis of one is vertical and that of the other is at 60° to the vertical. Describe the orientation and intensity of the transmitted light. Copyright © 2009 Pearson Education, Inc.

35 -11 Polarization Conceptual Example 35 -14: Three Polaroids. When unpolarized light falls on two crossed Polaroids (axes at 90°), no light passes through. What happens if a third Polaroid, with axis at 45° to each of the other two, is placed between them? Copyright © 2009 Pearson Education, Inc.

35 -11 Polarization Light is also partially polarized after reflecting from a nonmetallic surface. At a special angle, called the polarizing angle or Brewster’s angle, the polarization is 100%: . Copyright © 2009 Pearson Education, Inc.

35 -11 Polarization Example 35 -15: Polarizing angle. (a) At what incident angle is sunlight reflected from a lake plane-polarized? (b) What is the refraction angle? Copyright © 2009 Pearson Education, Inc.

35 -12 Liquid Crystal Displays (LCD) Liquid crystals are unpolarized in the absence of an external voltage, and will easily transmit light. When an external voltage is applied, the crystals become polarized and no longer transmit; they appear dark. Liquid crystals can be found in many familiar applications, such as calculators and digital watches. Copyright © 2009 Pearson Education, Inc.

35 -13 Scattering of Light by the Atmosphere Skylight is partially polarized due to scattering from molecules in the air. The amount of polarization depends on the angle that your line of sight makes with the Sun. Google: “Sunstones” … not now! After class. Copyright © 2009 Pearson Education, Inc.

Concep. Test 35. 3 Polarization If unpolarized light is incident 1) only case 1 from the left, in which case will 2) only case 2 some light get through? 3) only case 3 4) cases 1 and 3 5) all three cases In cases 1 and 3, light is blocked by the adjacent horizontal and vertical polarizers. However, in case 2, the intermediate 45° polarizer allows some light to get through the last vertical polarizer.