. An atom (not a hydrogen atom) absorbs a photon whose associated wavelength is 235 nm and immediately emits a photon whose associated wavelength is 590 nm. How much net energy (in terms of eV) is absorbed by the atom in this process? (______eV)
67. What are the (a) energy (in eV), (b) magnitude of the momentum, and (c) wavelength (in nm) of the photon emitted when a hydrogen atom undergoes a transition from a state with n = 5 to a state with n = 3?
68. An atom (not a hydrogen atom) absorbs a photon whose associated frequency is 6.9 x 1014 Hz. By what amount does the energy (in terms of eV) of the atom increase? (_____eV)
69. What is the intensity of a traveling plane electromagnetic wave if Bm is 1.1 x 10-5 T?_____ W/m^2
70. Assume (unrealistically) that a TV station acts as a point source broadcasting isotropically at 1.2 MW. What is the intensity of the transmitted signal reaching a nearby star that is 18 ly away. (An alien civilization at that distance might be able to watch X Files.) A light-year (ly) is the distance light travels in one year. _______ W/m^2
71. A plane electromagnetic wave has a maximum electric field of magnitude 2.98 x 10-6 V/m. Find the maximum magnetic field amplitude. ______T
72. In a plane radio wave the maximum value of the electric field component is 6.83 V/m. Calculate (a) the maximum value of the magnetic field component and (b) the wave intensity.
b. ______ W/m^2
73. The maximum electric field 10 m from a point light source is 1.6 V/m. What are (a) the maximum value of the magnetic field and (b) the average intensity of the light there? (c) What is the power of the source?
b. ______ W/m^2
74. High-power lasers are used to compress a plasma (a gas of charged particles) by radiation pressure. A laser generating radiation pulses with peak power 2200 MW is focused onto 0.99 mm2 of high-electron-density plasma. Find the pressure exerted on the plasma if the plasma reflects all the light beams directly back along their paths. _______units
75. It has been proposed that a spaceship might be propelled in the solar system by radiation pressure, using a large sail made of foil. How large must the surface area (in m2) of the sail be if the radiation force is to be equal in magnitude to the Sun’s gravitational attraction? Assume that the mass of the ship + sail is 1400 kg, that the sail is perfectly reflecting, and that the sail is oriented perpendicular to the Sun’s rays. (With a larger sail, the ship is continuously driven away from the Sun.) The rate at which the Sun emits energy is 3.90 × 1026 W. The Sun’s mass is 1.99 × 1030 kg. Gravitational constant is 6.67 × 10-11 N•m2/kg2. _______units
76. When the rectangular metal tank in the figure is filled to the top with an unknown liquid, observer O, with eyes level with the top of the tank, can just see corner E. A ray that refracts toward O at the top surface of the liquid is shown. If D = 93.4 cm and L = 2.30 m, what is the index of refraction of the liquid? ______units
77. Light in vacuum is incident on the surface of a slab of transparent material. In the vacuum the beam makes an angle of 37.8° with the normal to the surface, while in the slab it makes an angle of 22.7° with the normal. What is the index of refraction of the transparent material? _______units
78. The figure shows light reflecting from two perpendicular reflecting surfaces A and B. Find the angle (in o) between the incoming ray i and the outgoing ray r’. ______units
79. In the figure, light is incident at angle θ1 = 42.0˚ on a boundary between two transparent materials. Some of the light travels down through the next three layers of transparent materials, while some of it reflects upward and then escapes into the air. If n1 = 1.28, n2 = 1.42, n3 = 1.30 and n4 = 1.43, what is the value of (a) θ4 and (b) θ5?
80. A point source of light is 65.3 cm below the surface of a body of water. Find the diameter of the circle at the surface through which light emerges from the water. Water has an index of refraction of 1.33.______cm
81. In the figure, a ray of light is perpendicular to the face ab of a prism (n = 1.41). Find the largest value for the angle so that the ray is totally reflected at face ac if the prism is immersed (a) in air and (b) in water (n=1.33).
82. A lens is made of a transparent material having an index of refraction of 1.5. One side of the lens is flat, and the other convex with a radius of curvature of 25 cm. (a) Find the focal length of the lens. (b) If an object is placed 110 cm in front of the lens, where will the image be located?
83. A movie camera with a (single) lens of focal length 70 mm takes a picture of a person standing 35 m away. If the person is 160 cm tall, what is the height of the image in millimeters on the film? _______mm
84. You produce an image of the Sun on a screen using a thin lens whose focal length is 17.3 cm. What is the diameter of the image in millimeters? (Take the radius of the Sun to be 6.96 x 108 m and its distance to Earth to be 1.5 x 1011 m.) ________mm
85. An illuminated slide is held 75 cm from a screen. How far from the slide (between the slide and the screen) must a lens of focal length 6.7 cm be placed to form an image of the slide’s picture on the screen? (Give the smaller of the two possible answers.) _______cm
86. In the figure, a real inverted image I of an object O is formed by a certain lens (not shown); the object-image separation is d = 31.4 cm, measured along the central axis of the lens. The image is just 1/2 the size of the object. (a) How far from the object must the lens be placed? (b) What is the focal length of the lens?
87. In a microscope of the type shown in the figure, the focal length of the objective is 5.89 cm, and that of the eyepiece is 9.98 cm. The distance between the lenses is 25.1 cm. (a) What is the tube length s? (b) If image I in the figure is to be just inside focal point F’1, how far from the objective should the object be? What then are (c) the lateral magnification m of the objective, (d) the angular magnification mθ of the eyepiece, and (e) the overall magnification M of the microscope?