Chapter 34 – Electromagnetic Waves 1. (a) How long does it take a radio signal to travel 150 km from a transmitter to a receiving antenna? (b) We

see a full Moon by reflected sunlight. How much earlier did the light that enters our eye leave the sun? The Earth-Moon and Earth-Sun distances are 3.8 X 105 km and 1.5 X 108 km. (c) What is the round-trip travel time for light between Earth and a spaceship orbiting Saturn, 1.3 X 109 km distant? (d) The Crab nebula, which is about 6500 light-years (ly) distant, is thought to be the result of a supernova explosion recorded by Chinese astronomers in A.D. 1054. In approximately what year did the explosion actually occur?

5. On method for measuring the speed of light, based on

observations by Roemer in 1676, consisted of observing the apparent times of revolutions of one of the moons of Jupiter. The true period of revolution is 42.5 hours. (a) Taking into account the finite speed of light, how would you expect the apparent time for one revolution to change as Earth moves in its orbit from point x to point y in Fig. 34-38? (b) What observations would be needed to compute the speed of light? Neglect the motion of Jupiter in its orbit. Fig 34-38 is not drawn to scale.

7. What inductance must be connected to a 17 pF capacitor in an oscillator capable of generating 550 nm

electromagnetic wave? Comment on your answer. 12. Our closest stellar neighbor, Proxima Centauri, is 4.3 ly away. It has been suggested that TV programs from

our planet have reached this star and may have been viewed by the hypothetical inhabitants of a hypothetical planet orbiting it. Suppose a television station on Earth has a power of 21.0 MW. What is the intensity of its signal at Proxima Centauri?

16. Sunlight just outside Earth’s atmosphere has an intensity of 1.4 kW/m2. Calculate Em and Bm for sunlight

there, assuming it to be a plane wave. 18. Figure 34-40: Frank D. Drake, an investigator in the SETI

program, once said that the large radio telescope 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 enter is 2.2 X 104 lys away. Take the source as radiating uniformly in all directions.

24 A helium-neon laser of the type often found in physics labs has a beam power of 5.00 mW at a wavelength

of 633 nm. The beam is focused by a lens to a circular spot whose effective diameter may be taken to be equal to 2.00 wavelengths. Calculate (a) the intensity of the focused beam, (b) the radiation pressure exerted on a tiny perfectly absorbing sphere whose diameter is that of the focal spot, (c) the force exerted on this sphere, and (d) the magnitude of the acceleration imparted to it. Assume a sphere density of 5.00 X 103 kg/m3.

25. A plane electromagnetic wave, with wavelength 3.0 m, travels in vacuum in the positive x direction with its electric field , of amplitude 300 V/m, directed along the y axis. (a) What is the frequency “f” of the wave? (b) What are the direction and amplitude of the magnetic field associated with the wave? (c) What are the values of “k” and “ω” if E = Em sing (kx - ωt)? (d) What is the time-averaged rate of energy flow in watts per square meter associated with this wave? (e) If the wave falls on a perfectly absorbing sheet of area 2.0 m2, at what rate is momentum delivered to the sheet and what is the radiation pressure exerted on the sheet?

36. A beam of polarized light is sent through a system of two polarizing sheets. Relative to the polarization

direction of that incident light, the polarizing direction of the sheets are at angles θ for the first sheet and 900 from the second sheet. If 0.10 of the incident intensity is transmitted by the two sheets, what is θ?

37. A horizontal beam of vertically polarized light of intensity 43 W/m2 is sent through two polarizing sheets.

The polarizing direction of the first is 700 to the vertical, and that of the second is horizontal. What is the intensity of the light transmitted by the pair of sheets?

38. Suppose that in Problem 37 the initial beam is un-polarized, what then is the intensity of the transmitted

light? 40. At a beach the light is generally partially polarized owing to reflections off sand and water. At a particular

beach on a particular day near sundown, the horizontal component of the electric field vector is 2.3 times the vertical component. A standing sunbather puts on polarizing sunglasses; the glasses eliminate the horizontal field component. (a) What fraction of the light intensity received before the glasses were put on now reaches the sunbather’s eyes? (b) The sunbather, still wearing the lasses, lies on his side. What fraction of the light intensity received before the glasses were put on now reaches his eyes?

41. We want tot rotate the direction of polarization of a beam of polarized light through 900 by sending the

beam through one or more polarizing sheets. (a) What is the minimum number of sheets required? (b) What is the minimum number of sheets required if the transmitted intensity is to be more that 60 % of the original intensity?

49. Prove that a ray of light incident on the surface of a sheet of plate glass of

thickness “t” emerges from the opposite face parallel to its initial direction but displaced sideways, as in Fig. 34-47. Show that, for small angles of incidence θ, this displacement is given by , where n is the index of refraction of the glass and θ is measured in radians.

51. In Fig. 34-49, a ray is incident on one face of a triangular glass

prism in air. The angle of incidence θ is chosen so that the emerging ray also makes the same angle θ with the normal to the other face. Show that the index of refraction n of the class prism

is given by, ,where φ is the vertex angle of the

prism and ψ is the deviation angle, the total angle through which the beam is turned in passing through the prism. (Under these conditions the deviation angle ψ has the smallest possible value, which is called the angle of minimum deviation.)

58. Suppose the prism of Fig. 34-49 has apex angle φ = 600 and index of refraction n = 1.60. (a) What is the smallest angle of incidence θ for which a ray can enter the left face of the prism and exit the right face? (b) What angle of incidence θ is required for the ray to exit the prism with an identical angle θ for its refraction, as it does in Fig. 34-49? (See problem 51.)

59. In Fig. 34-52, light enters a 900 triangular prism at point “P” with incident angle

θ and then some of it refracts at point “Q” with an angle of refraction of 900. (a) What is the index of refraction of the prism in terms of θ? (b) What, numerically, is the maximum value that the index of refraction can have? Explain what happens to the light at “Q” if the incident angle at “Q” is (c) increased slightly and (d) decreased slightly.

62. Calculate the upper and lower limits of the Brewster angles for white light incident on fused quartz.

Assume that the wavelengths of the light are 400 and 700 nm.