Homework #9 Physics 11b Morii 4/21/2005 Due 4/29/2005, 4 PM in mailboxes outside Science Center 109 Read: Chapter 36, 37. Instructions: Please box your solutions. The homework problems are graded out of 3 points, and then the total re-scaled to 30. For each problem, in order to get full credit, you must also include a sentence explaining the most important idea you used in order to solve it. Do not summarize the whole solution, simply the one most important idea. HW Problems 1. Serway & Jewett 34.33 In Lecture #18, slide 12, I showed you a Hertz antenna (also known as a halfwave antenna, because its length is λ/2). Most AM radio stations, however, use a Marconi antenna, shown in the second picture on the slide, which consists of the top half of a Hertz antenna. The lower end of this (quarter-wave) antenna is connected to Earth ground, and the ground itself serves as the missing lower half. What are the heights of the Marconi antennas for radio stations broadcasting at (a) 560 kHz and (b) 1 600 kHz? 2. Serway & Jewett 34.40 Compute an order-of-magnitude estimate for the frequency of an electromagnetic wave with wavelength equal to (a) your height; (b) the thickness of this sheet of paper. How is each wave classified on the electromagnetic spectrum? 3. Serway & Jewett 34.44 An important news announcement is transmitted by radio waves to people sitting next to their radios 100 km from the station, and by sound waves to people sitting across the newsroom, 3.00 m from the newscaster. Who receives the news first? Explain. Take the speed of sound in air to be 343 m/s. 4. Serway & Jewett 34.50 Consider a small, spherical particle of radius r located in space a distance R from the Sun. (a) Show that the ratio Frad/Fgrav is proportional to 1/r, where Frad is the force exerted by solar radiation and Fgrav is the force of gravitational attraction. (b) The result of part (a) means that, for a sufficiently small value of r, the force exerted on the particle by solar radiation exceeds the force of gravitational attraction. Calculate the value of r for which the particle is in equilibrium under the two forces. (Assume that the particle has a perfectly absorbing surface and a mass density of 1.50 g/cm3. Let the particle be located 3.75 × 1011 m from the Sun, and use 214 W/m2 as the value of the solar intensity at that point.)5. Serway & Jewett 35.6 The two mirrors illustrated in the figure below meet at a right angle. The beam of light in the vertical plane P strikes mirror 1 as shown. (a) Determine the distance the reflected light beam travels before striking mirror 2. (b) In what direction does the light beam travel after being reflected from mirror 2? 6. Serway & Jewett 35.18 An opaque cylindrical tank with an open top has a diameter of 3.00 m and is completely filled with water. When the afternoon Sun reaches an angle of 28.0° above the horizon, sunlight ceases to illuminate any part of the bottom of the tank. How deep is the tank? 7. Serway & Jewett 35.21 + 35.22 When the light illustrated in the figure below passes through the glass block, it is shifted laterally by the distance d. (a) Taking n = 1.50, find the value of d. (b) Find the time interval required for the light to pass through the glass block. 8. Serway & Jewett 35.30 Light of wavelength 700 nm is incident on the face of a fused quartz prism at an angle of 75.0° (with respect to the normal to the surface). The apex angle of the prism is 60.0°. Use the value of n from Figure 35.20 and calculate the angle (a) of refraction at this first surface, (b) of incidence at the second surface, (c) of refraction at the second surface, and (d) between the incident and emerging rays.9. Serway & Jewett 35.38 Determine the maximum angle θ for which the light rays incident on the end of the pipe in Figure P35.38 are subject to total internal reflection along the walls of the pipe. Assume that the pipe has an index of refraction of 1.36 and the outside medium is air. (Don’t forget that the light refracts as it enters the pipe through the end!) 10. Serway & Jewett 35.41 A large Lucite cube (n = 1.59) has a small air bubble (a defect in the casting process) below one surface. When a penny (diameter 1.90 cm) is placed directly over the bubble on the outside of the cube, the bubble cannot be seen by looking down into the cube at any angle. However, when a dime (diameter 1.75 cm) is placed directly over it, the bubble can be seen by looking down into the cube. What is the range of the possible depths of the air bubble beneath the