Chapter 34 20. A person looking into an empty container is able to see the far edge of the container’s bottom as shown in Figure P34.20a. The height of the container is h, and its width is d. When the container is completely filled with a fluid of index of refraction n and viewed from the same angle, the person can see the center of a coin at the middle of the container’s bottom as shown in Figure P34.20b. (a) Show that the ratio h/d is given by ℎ 𝑛2 − 1 =√ 𝑑 4 − 𝑛2 (b) Assuming the container has a width of 8.00 cm and is filled with water, use the expression above to find the height of the container. (c) For what range of values of n will the center of the coin not be visible for any values of h and d? Chapter 35 14. A ball is dropped at t = 0 from rest 3.00 m directly above the vertex of a concave spherical mirror that has a radius of curvature of magnitude 1.00 m and lies in a horizontal plane. (a) Describe the motion of the ball’s image in the mirror. (b) At what instant or instants do the ball and its image coincide? 45. The distance between an object and its upright image is 20.0 cm. If the magnification is 0.500, what is the focal length of the lens being used to form the image? Chapter 36 7. A student holds a laser that emits light of wavelength 632.8 nm. The laser beam passes through a pair of slits separated by 0.300 mm, in a glass plate attached to the front of the laser. The beam then falls perpendicularly on a screen, creating an interference pattern on it. The student begins to walk directly toward the screen at 3.00 m/s. The central maximum on the screen is stationary. Find the speed of the 50th-order maxima on the screen. 45. Figure P36.35 shows a radio-wave transmitter and a receiver separated by a distance d=50.0 m and both a distance h=35.0 m above the ground. The receiver can receive signals both directly from the transmitter and indirectly from signals that reflect from the ground. Assume the ground is level between the transmitter and receiver and a 180o phase shift occurs upon reflection. Determine the longest wavelengths that interfere (a) constructively and (b) destructively.
