9. A laser beam is incident at an angle of 30.0° to the vertical onto a solution of corn syrup in water. If the beam is refracted to 19.24° to the vertical, (a) what is the index of refraction of the syrup solution? Suppose the light is red, with vacuum wavelength 632.8 nm. Find its (b) wavelength, (c) frequency, and (d) speed in the solution. 10. Find the speeds of light in (a) flint glass, (b) water, and (c) zircon. 12. Light of wavelength 436 nm in air enters a fishbowl filled with water, then exits through the crown-glass wall of the container. Find the wavelengths of the light (a) in the water and (b) in the glass. 13. A ray of light is incident on the surface of a block of clear ice at an angle of 40.0° with the normal. Part of the light is reflected and part is refracted. Find the angle between the reflected and refracted light. 14. A narrow beam of sodium yellow light (λ0 = 589 nm) is incident from air on a smooth surface of water at an angle of θ1 = 35.0°. Determine the angle of refraction θ2 and the wavelength of the light in water. 15. A beam of light, traveling in air, strikes the surface of mineral oil at an angle of 23.1° with the normal to the surface. If the light travels at 2.17 x 108 m/s through the oil, what is the angle of refraction? 17. How many times will the incident beam shown in Figure P22.17 be reflected by each of the parallel mirrors?

Figure P22.17

18. A ray of light strikes a flat, 2.00-cm-thick block of glass (n = 1.50) at an angle of 30.0° with the normal (Fig. P22.18). Trace the light beam through the glass and find the angles of incidence and refraction at each surface.

Figure P22.18

20. Find the time required for the light to pass through the glass block shown above. 21. The light beam shown in Figure P22.21 makes an angle of 20.0° with the normal line NN' in the linseed oil. Determine the angles θ and θ'. (The refractive index for linseed oil is 1.48.)

Figure P22.21

27. 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 the bottom of the tank. How deep is the tank? 30. A certain kind of glass has an index of refraction of 1.650 for blue light of wavelength 430 nm and an index of 1.615 for red light of wavelength 680 nm. If a beam containing these two colors is incident at an angle of 30.00° on a piece of this glass, what is the angle between the two beams inside the glass?

32. The index of refraction for violet light in silica flint glass is 1.66 and that for red light is 1.62. What is the angular dispersion of visible light passing through an equilateral prism of apex angle 60.0° if the angle of incidence is 50.0°? (See Fig. P22.32.)

Figure P22.32

34. For 589-nm light, calculate the critical angle for the following materials surrounded by air: (a) diamond and (b) flint glass. 35. Repeat Problem 34 when the materials are surrounded by water. 36. A beam of light is incident from air on the surface of a liquid. If the angle of incidence is 30.0° and the angle of refraction is 22.0°, find the critical angle for the liquid when surrounded by air. 38. Determine the maximum angle θ for which the light rays incident on the end of the light pipe in Figure P22.38 are subject to total internal reflection along the walls of the pipe. Assume that the light pipe has an index of refraction of 1.36 and that the outside medium is air.

Figure P22.38

Answers: 9) 1.52; 417nm; 4.74E14Hz;1.98E8m/s 10) 1.81E8 m/s; 2.25E8 m/s; 1.56E8 m/s 12) 327nm; 287nm 13) 111o; 14) 25.5o; 442nm 15) 16.5o 17) left mirror 6 times right mirror 5 times 18) 30o; 19.5o; 30o 20)1.06E-10s 21) 0.388cm 27) 3.39m 30) 0.40o 32) 4.6o 34) 24.4o; 37o 35) 33.4o; 53.4o 36) 48.5o 38) 67.2o 43) 27.5o 47) 53.1o; 38.7o 49) 38.5o; 1.44

43. The light beam in Figure P22.43 strikes surface 2 at the critical angle. Determine the angle of incidence θi.

Figure P22.43

47. Figure P22.47 shows the path of a beam of light through several layers of different indices of refraction. (a) If θ1 = 30.0°, what is the angle θ2 of the emerging beam? (b) What must the incident angle θ1 be in order to have total internal reflection at the surface between the n = 1.20 medium and the n = 1.00 medium?

Figure P22.47

49. As shown in Figure P22.49, a light ray is incident normally on one face of a 30°-60°-90° block of dense flint glass (a prism) that is immersed in water. (a) Determine the exit angle θ4 of the ray. (b) A substance is dissolved in the water to increase the index of refraction. At what value of n2 does total internal reflection cease at point P?

Figure P22.49