This document provides an overview of electromagnetic waves and key concepts in physics including: - James Clerk Maxwell showed that electric and magnetic fields can form propagating electromagnetic waves. - Electromagnetic waves include visible light, ultraviolet rays, infrared rays, radio waves, x-rays and gamma rays. - The speed of electromagnetic waves in a vacuum is a constant at approximately 3×10^8 m/s. - Electromagnetic waves transport energy and the total energy density carried by a wave depends on the electric and magnetic field amplitudes.

1. Chapter 24 Electromagnetic Waves

2. AP Learning Objectives WAVES AND OPTICS Physical optics Dispersion of light and the electromagnetic spectrum Students should understand dispersion and the electromagnetic spectrum, so they can: Know the names associated with electromagnetic radiation and be able to arrange in order of increasing wavelength the following: visible light of various colors, ultraviolet light, infrared light, radio waves, x-rays, and gamma rays

3. Table of Contents The Nature of Electromagnetic Waves The Electromagnetic Spectrum The Speed of Light The Energy Carried by Electromagnetic Waves (AP?) The Doppler Effect and Electromagnetic Waves Polarization

4. Chapter 24: Electromagnetic Waves Section 1: The Nature of Electromagnetic Waves

5. Electromagnetic Waves In Section 13.3 we saw that energy is transported to us from the sun via a class of waves known as electromagnetic waves. Includes visible, ultraviolet, and infrared waves. The great Scottish physicist James Clerk Maxwell (1831–1879) showed that these two fields fluctuating together can form a propagating electromagnetic wave. We will now bring together our knowledge of electric and magnetic fields in order to understand this important type of wave.

6. Generating EM Waves Two straight wires connected to the terminals of an AC generator can create an electromagnetic wave . Only the electric wave traveling to the right is shown here. As the electrons are moved to one end of the wire, an electric field is created. As the electrons move back, the field disappears. The field propagates outward radially Like the ripples formed by dropping a pebble in a pond

7. Generating EM Waves As the electrons are moving, a magnetic field is also generated. The direction of the magnetic field is predicted by the right hand rule. Since the maximum field is when the electrons are moving the fastest The maximum field occurs when the electric field is at a minimum. The magnetic field also propagates away from the wire. Process occurs any time an electron is accelerated

8. EM Wave Propagation The speed of an electromagnetic wave in a vacuum is:

9. EM Wave Reception A radio wave can be detected with a receiving antenna wire that is parallel to the electric field.

10. 24.1 The Nature of Electromagnetic Waves With a receiving antenna in the form of a loop, the magnetic field of a radio wave can be detected.

11. 24.1.1. At a point far from an antenna, the electric field of a radio wave is directed in the positive y direction as the wave travels in the negative x direction. Which one of the following statements correctly describes the magnetic field component of the wave at that same location? a) The magnetic field component is out of phase with the electric field component and it is directed in the positive z direction. b) The magnetic field component is in phase with the electric field component and it is directed in the positive z direction. c) The magnetic field component is out of phase with the electric field component and it is directed in the negative z direction. d) The magnetic field component is in phase with the electric field component and it is directed in the negative z direction. e) The magnetic field component is out of phase with the electric field component and it is directed in the negative y direction.

12. 24.1.2. Which one of the following statements most closely describes how humans see objects? a) Light rays leave the eye, shine on an object, and are reflected back to the eye. b) All objects are sources of visible light and the eye is sensitive to that light. c) All objects are seen when visible light is scattered from them and into the eye. d) Some objects are sources of visible light and others are seen when visible light is scattered from them. e) The human eye is sensitive to all types of electromagnetic waves that are emitted from all objects.

13. 24.1.3. You are standing on the right side of a closed opaque box. There is a hole through which you can look inside. The drawing shows a small light bulb inside that is on. There is also a wall inside the box as shown. All of the surfaces of the box are rough surfaces that are painted black. As you look through the hole, what can you see? a) a bright beam of light from the bulb b) the light bulb c) the walls will appear to be the same color as the light bulb d) the black walls of the box e) nothing

14. Chapter 24: Electromagnetic Waves Section 2: The Electromagnetic Spectrum

15. Like all waves, electromagnetic waves have a wavelength and frequency, related by:

16. Example 1 The Wavelength of Visible Light Find the range in wavelengths for visible light in the frequency range between 4.0x10 14 Hz and 7.9x10 14 Hz.

17. Conceptual Example 2 The Diffraction of AM and FM Radio Waves Diffraction is the ability of a wave to bend around an obstacle or the edges of an opening. Would you expect AM or FM radio waves to bend more readily around an obstacle such as a building? Since AM radio waves have greater wavelengths than FM waves do, they exhibit greater diffraction and bend more readily around obstacles than FM waves do.

18. 24.2.1. Consider the region of space that you are occupying. Which of the following types of electromagnetic waves are present around you? a) visible light waves b) radio waves c) microwaves d) infrared waves e) all of the above

19. 24.2.2. For which one of the following properties do visible light and ultraviolet waves have the same value? a) wavelength b) frequency c) speed d) energy e) period

20. 24.2.3. What is the correct order, beginning with longest wavelength and extending to the shortest wavelength, of the following colors in the visible light spectrum: blue, green, red, violet, and yellow? a) red, yellow, green, blue, violet b) violet, blue, green, yellow, red c) red, blue, violet, green, yellow d) red, yellow, blue, green, violet e) violet, blue, yellow, red, green

21. Chapter 24: Electromagnetic Waves Section 3: The Speed of Light

22. Determining the speed of light The speed of light in a vacuum The minimum angular speed must be such that one side of the mirror rotates one-eighth of a revolution during the time it takes for the light to make the round trip between the mirrors

23. Conceptual Example 3 Looking Back in Time A supernova is a violent explosion that occurs at the death of certain stars. The figure shows a photograph of the sky before and after a supernova. Why do astronomers say that viewing an event like this is like looking back in time?

24. Early predictions Maxwell’s prediction of the speed of light in 1885  o is the electric permittivity of free space μ o is the magnetic permeability of free space

25. 24.3.1. About how many times faster is the speed of light when compared to the speed of sound? a) 100 times faster b) 1000 times faster c) 10 000 times faster d) 100 000 times faster e) 1 000 000 times faster

26. 24.3.2. In 1667, Galileo attempted to measure the speed of light by having two people hold covered lanterns on hills that were about 1.5 km apart. One person would measure time. One of the people with a lantern would uncover it. The other person would then uncover his lantern when he saw the light from the first lantern. Repeated attempts failed. To see why, determine the approximate time it takes light to travel the 1.5 km distance. a) 5  s b) 50  s c) 5 ms d) 50 ns e) 5 ns

27. Chapter 24: Electromagnetic Waves Section 4: The Energy Carried by Electromagnetic Waves (AP?)

28. Electromagnetic waves, like water waves, carry energy.

29. Total energy density carried by an EM wave

31. 24.4.1. Monochromatic electromagnetic radiation illuminates an area of a surface. The electric and magnetic fields of the waves are then doubled in magnitude. How is the total energy incident on the surface per unit time affected by this increase in the electric and magnetic fields? a) The total energy is not affected by this change. b) The total energy will increase by a factor of two. c) The total energy will increase by a factor of four. d) The total energy will decrease by a factor of two. e) The total energy will decrease by a factor of four.

32. 24.4.2. The amplitude of the magnetic field component of electromagnetic wave “one” is B . If the amplitude for wave “two” is 2 B , how does the intensity of wave two compare to that of wave one? a) The intensity of wave two is four times larger than that of wave one. b) The intensity of wave two is two times larger than that of wave one. c) The intensity of wave two is the same as that of wave one. d) The intensity of wave two is one half that of wave one. e) The intensity of wave two is one fourth that of wave one.

33. 24.4.3. The intensity of electromagnetic wave A is one fourth that of wave B. How does the magnitude of the electric field of wave A compare to that of wave B? a) The electric field amplitude of wave A is one fourth that of wave B. b) The electric field amplitude of wave A is one half that of wave B. c) The electric field amplitude of wave A is one half that of wave B. d) The electric field amplitude of wave A is two times that of wave B. e) The electric field amplitude of wave A is four times that of wave B.

34. 24.4.4. A laser beam has an intensity of 120 W/m 2 . What is the magnitude of the magnetic field component of the electromagnetic waves emitted by this laser? a) 2.2  10 9 N/C b) 4.2  10 6 N/C c) 4.5  10 4 N/C d) 1200 N/C e) 210 N/C

35. 24.4.5. How does the energy associated with the magnetic field of an electromagnetic wave compare to the energy associated with the electric field? a) All of the energy is carried by the magnetic field component of an electromagnetic wave. b) One-half of the energy is carried by the magnetic field component of an electromagnetic wave. c) None of the energy is carried by the magnetic field component of an electromagnetic wave. d) The energy carried by the magnetic field is a factor of c times larger than that carried by the electric field. e) The energy carried by the magnetic field is a factor of c times smaller than that carried by the electric field

36. Chapter 24: Electromagnetic Waves Section 5: The Doppler Effect and Electromagnetic Waves

37. Doppler Effect Electromagnetic waves also can exhibit a Dopper effect, but it differs for two reasons: Sound waves require a medium, whereas electromagnetic waves do not. For sound, it is the motion relative to the medium that is important. For electromagnetic waves, only the relative motion of the source and observer is important.

38. Example 6 Radar Guns and Speed Traps The radar gun of a police car emits an electromagnetic wave with a frequency of 8.0x10 9 Hz. The approach is essentially head on. The wave from the gun reflects from the speeding car and returns to the police car, where on-board equipment measures its frequency to be greater than the emitted wave by 2100 Hz. Find the speed of the car with respect to the highway. The police car is parked.

39. frequency “observed” by speeding car frequency observed by police car

40. 24.5.1. Hydrogen atoms in a laboratory can emit blue light that has a specific wavelength of 4.34  10  7 m. Hydrogen atoms in a distant galaxy far from Earth also emit this same light, but to an observer on Earth, the light appears to have a wavelength of 4.64  10  7 m. What is the relative velocity of this galaxy with respect to Earth? a) 2.80  10 7 m/s, toward the Earth b) 1.44  10 6 m/s, away from the Earth c) 4.10  10 5 m/s, away from the Earth d) 2.07  10 7 m/s, away from the Earth e) 3.00  10 5 m/s, toward the Earth

41. 24.5.2. The pilot of an airplane flying due south at a constant speed v observes three sources of electromagnetic waves. Each source emits light with the same frequency f . Source A is moving due south at a speed v , source B is moving due north at a speed v, and source C is moving due south at a speed 2 v . Rank the three frequencies of the observed waves in increasing order (smallest first, largest last) according to magnitude. a) A = C < B b) A = B < C c) B < A < C d) A < C < B e) B < C < A

42. Chapter 24: Electromagnetic Waves Section 6: Polarization

43. Linearly polarized wave on a rope. POLARIZED ELECTROMAGNETIC WAVES

44. In polarized light, the electric field fluctuates along a single direction.

45. Polarized light may be produced from unpolarized light with the aid of polarizing material.

46. MALUS’ LAW intensity before analyzer intensity after analyzer

47. Example 7 Using Polarizers and Analyzers What value of θ should be used so the average intensity of the polarized light reaching the photocell is one-tenth the average intensity of the unpolarized light?

48. When Polaroid sunglasses are crossed, the intensity of the transmitted light is reduced to zero.

49. IMAX 3D Movie Projector

50. 24.6.1. Unpolarized light with intensity I is incident on a series of polarizing sheets. The first sheet has its transmission axis oriented at 0  . A second polarizer has its transmission axis oriented at 45  and a third polarizer oriented with its axis at 90  . Determine the fraction of light intensity exiting the third sheet with and without the second sheet present. a) 0.5 I , I b) 0.5 I , zero c) 0.25 I , zero d) 0.25 I , 0.5 I e) I , 0.5 I

51. 24.6.2. Horizontally polarized light of intensity I is incident on a polarizer with its transmission axis oriented at 45  . Determine the fraction of light intensity exiting the polarizer. a) zero b) 0.25 I c) 0.5 I d) 0.71 I e) I

52. 24.6.3. Unpolarized light of intensity S is directed toward three polarizing sheets. The first sheet is polarized vertically; and the last sheet is oriented horizontally. If the middle sheet is also oriented vertically, what is the intensity of the light exiting the last polarizer? a) zero b) 0.25 S c) 0.5 S d) 0.71 S e) S

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