Understanding Maxwell's Equations and Electromagnetic Waves

2. Chapter 31Maxwell’s Equations and Electromagnetic Waves

3. 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:

4. 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.

5. 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:

6. 31-8 Energy in EM Waves; the Poynting Vector This energy is transported by the wave.

7. 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:

8. 31-8 Energy in EM Waves; the Poynting Vector . Typically we are interested in the average value of S:

9. 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·m2 (= 1350 W/m2). Assume that this is a single EM wave, and calculate the maximum values of E and B.

10. 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:

11. 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/m2. Estimate the pressure and force exerted by the Sun on your outstretched hand.

12. 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?

13. 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.

14. 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):

15. 31-10 Radio and Television; Wireless Communication Second, by using the signal to modify the frequency of the carrier (FM):

16. 31-10 Radio and Television; Wireless Communication At the receiving end, the wave is received, demodulated, amplified, and sent to a loudspeaker.

17. 31-10 Radio and Television; Wireless Communication The receiving antenna is bathed in waves of many frequencies; a tuner is used to select the desired one.

18. 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.

19. 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.

20. ConcepTest 31.3TV Antennas 1) the circular one 2) the straight one 3) both equally; they were straight and circular for different reasons Before the days of cable, televisions often had two antennae on them, one straight and one circular. Which antenna picked up the magnetic oscillations?

21. ConcepTest 31.3TV Antennas 1) the circular one 2) the straight one 3) both equally; they were straight and circular for different reasons 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.

22. ConcepTest 31.4Radio Antennas 1) vertical 2) horizontal 3) doesn’t matter If a radio transmitter has a vertical antenna, should a receiver’s antenna be vertical or horizontal to obtain the best reception?

23. E field of wave E field of wave ConcepTest 31.4Radio Antennas 1) vertical 2) horizontal 3) doesn’t matter If a radio transmitter has a vertical antenna, should a receiver’s antenna be vertical or horizontal to obtain the best reception? If a wave is sent out from a vertical antenna, the electric field oscillates up and down. Thus, the receiver’s antenna should also bevertical so that the arriving electric field can set the charges in motion.

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

25. 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.

26. 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:

27. Chapter 35Diffraction and Polarization

28. 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.

29. 35-11 Polarization Polarized light will not be transmitted through a polarized film whose axis is perpendicular to the polarization direction.

30. 35-11 Polarization When light passes through a polarizer, only the component parallel to the polarization axis is transmitted. If the incoming light is plane-polarized, the outgoing intensity is:

31. 35-11 Polarization This means that if initially unpolarized light passes through crossed polarizers, no light will get through the second one.

32. 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.

33. 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?

34. 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%: .

35. 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?

36. 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.

37. 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.

38. 1 2 3 ConcepTest 35.3Polarization 1) only case 1 2) only case 2 3) only case 3 4) cases 1 and 3 5) all three cases If unpolarized light is incident from the left, in which case will some light get through?

39. 1 2 3 ConcepTest 35.3Polarization 1) only case 1 2) only case 2 3) only case 3 4) cases 1 and 3 5) all three cases If unpolarized light is incident from the left, in which case will some light get through? 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.