Physics 4C Chapter 33: Electromagnetic Waves

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1 Physics 4C Chapter 33: Electromagnetic Waves Our greatest glory is not in never failing, but in rising up every time we fail. Ralph Waldo Emerson If you continue to do what you've always done, you'll continue to get what you've always got. Yogi Berra Failure is only the opportunity to begin again, this time more wisely. unknown "Keep in mind that neither success nor failure is ever final." Roger Ward Babson Reading: pages ; Outline: electromagnetic spectrum properties of electromagnetic waves intensity radiation pressure total absorption total reflection polarization one-half rule cosine-squared rule reflection and refraction law of reflection law of refraction total internal reflection polarization by reflection Brewster s law Problem Solving Techniques For an electromagnetic wave, you should know that and are perpendicular to each other, and that the direction of propagation is given by. The last statement implies that both and are perpendicular to the direction of propagation. You should know that intensity is the energy per unit area per unit time that crosses an area that is perpendicular to the direction of propagation. For a point source that radiates uniformly in all

2 directions, the intensity at a point is proportional to the inverse square of the distance from the P s source to the point, I = 2 4π r You should also know that when an object absorbs electromagnetic radiation, it receives momentum: p = U/c, where U is the energy absorbed. When the radiation is reflected back along the path of incidence, the momentum received is p = 2 U/c, where U is the reflected energy. For total absorption, the radiation pressure is p r = I/c and the force on the object is F = IA/c, where A is the area struck by radiation. If the radiation is reflected back on its path of incidence, the radiation pressure and force are both twice as great. Some problems deal with polarization. You should know how to identify the direction and plane of polarization. You should also know how to compute the intensity of radiation transmitted by a polarizing sheet. Remember that the exiting radiation is polarized in the polarizing direction of the sheet. Many problems deal with refraction at a single plane surface and with total internal reflection. For refraction problems, use Snell's law: n 1 sinθ 1 = n 2 sinθ 2. Remember to measure the angle from the surface normal. For total internal reflection, remember that n 1 sinθ > n 2, where n 1 is the index of refraction for the medium of incidence and n 2 is the index of refraction for the medium beyond the surface. Other problems ask you to calculate the Brewster angle. Use tanθ B = n 2 /n 1, where n 1 is the index of refraction for the medium of incidence and n 2 is the index of refraction for the medium of the refracted light. In some cases, you will also need to use geometry to trace rays. Questions and Example Problems from Chapter 33 Question 1 The figure shows the electric and magnetic fields of an electromagnetic wave at a certain instant. Is the wave traveling into the page or out of it? Question 2 Each part of the figure below shows light that refracts through an interface between two materials. The incident ray (shown gray in the figure) consists of red and blue light. The approximate index of refraction for visible light is indicated for each material. Which of the three parts show physically possible refraction?

3 Problem 1 About how far apart must you hold your hands for them to be separated by 1.0 nano-lightsecond? Problem 2 Frank D. Drake, an investigator in the SETI (Search for Extra-Terrestrial Intelligence) program, once said that the large radio telescope (see the figure below) in Arecibo, Puerto Rico, can detect a signal which lays down on the entire surface of the earth a power of only one picowatt. (a) What is the power that would be received by the Arecibo antenna for such a signal? The antenna diameter is 300 m. (b) What would be the power of a source at the center of our galaxy that could provide such a signal? The galactic center is ly away. Take the source as radiating uniformly in all directions. Problem 3 An airplane flying at a distance of 10 km from a radio transmitter receives a signal of intensity 10 µw/m 2. Calculate the total power of the transmitter assuming that the transmitter radiates uniformly in all directions.

4 Problem 4 In the figure to the right, a laser beam of power 4.60 W and diameter 2.60 mm is directed upward at one circular face (of diameter d < 2.60 mm) of a perfectly reflecting cylinder, which is made to hover by the beam's radiation pressure. The cylinder's density is 1.20 g/cm 3. What is the cylinder's height H? Problem 5 A point source of light emits isotropically with a power of 200 W. What is the force due to the light on a totally absorbing sphere of radius 2.0 cm at a distance of 20 m from the source?

5 Problem 6 In the figure below, initially unpolarized light is sent toward a system of three polarizing sheets. What fraction of the initial light intensity emerges from the system? Problem 7 An unpolarized beam of light is sent into a stack of four polarizing sheets, oriented so that the angle between the polarizing sheets is 30 o. What fraction of the incident intensity is transmitted by the system?

6 Problem 8 In the figure below, two light rays pass from air through five transparent layers of plastic whose boundaries are parallel, whose indexes of refraction are as given, and whose thicknesses are unknown. The rays emerge back into air at the right. With respect to a normal to the last interface, what is the angle of (a) emerging ray a and (b) emerging ray b? (c) What are your answers if there is glass, with n = 1.5, instead of air on the left and right sides of the plastic layers? (Hint: Save yourself much time by first solving the problems algebraically.) Problem 9 In the figure below, a 2.00-m-long vertical pole extends from the bottom of a swimming pool to a point 50.0 cm above the water. Sunlight is incident at angle θ = What is the length of the shadow of the pole on the level bottom of the pool?

7 Problem 10 A beam of light is emitted 8.0 cm beneath the surface of a liquid and strikes the surface 7.0 cm from the point directly above the source. If total internal reflection occurs, what can you say about the index of refraction of the liquid? Problem 11 In the figure below, light initially in material 1 refracts into material 2, crosses that material, and is then incident at the critical angle on the interface between materials 2 and 3. The indexes of refraction are n 1 = 1.60, n 2 = 1.40, and n 3 = (a) What is angle θ? (b) If θ is increased, is there refraction of light into material 3?

8 Problem 12 The figure below depicts a simplistic optical fiber: a plastic core (n 1 = 1.58) is surrounded by a plastic sheath (n 2 = 1.53). A light ray is incident on one end of the fiber at angle θ. The ray is to undergo total internal reflection at point A, where it encounters the core sheath boundary. (Thus there is no loss of light through that boundary.) What is the maximum value of θ that allows total internal reflection at A? Problem 13 (a) At what angle of incidence will the light reflected from water be completely polarized? (b) Does this angle depend upon the wavelength of the light?

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