PHYSICS 213 PRACTICE EXAM 3* *The actual exam will contain EIGHT multiple choice quiz-type questions covering concepts from lecture (16 points), ONE essay-type question covering an important fundamental principle from lecture (4 points), and FOUR problems similar to the problems that follow (80 points). NAME (printed) SIGNATURE Student Number SECTION INSTRUCTIONS Wait for oral instructions before starting the test. Remember to show (in English) your problem solving steps for FULL CREDIT. A calculator and a one-sided 8½X11 student reference sheet are permitted. Your reference sheet may contain equations, graphs, and notes; however, quiz questions and worked out problems CANNOT be included. Cell phones/communication devices must be put away. For the graders: Q1-9 P1 P2 P3 P4 TOTAL
Electromagnetic Waves [20 Points] A large parabolic solar detector with radius 25.0 m is mounted to a solar probe with total mass 2500 kg which is placed in space near the Earth s orbit. The solar detector absorbs solar radiation with intensity 1340 W/m 2. a) Find the amplitude of the electric field for the solar radiation? [5 points] Answer: E = 1005 V/m b) Find the amplitude of the magnetic field for the solar radiation? [4 points] Answer: B = 3.35 µt c) Determine the solar power absorbed by the solar detector. [3 points] Answer: P = 2.63 MW d) Ignoring all gravitational effects, determine the acceleration of the solar probe due to the soar radiation pressure. [4 points] Answer: a = 3.51 x 10-6 m/s 2 e) Find the probe s speed as it reaches Mars 7.80 x 10 10 m away. Ignore all gravitational effects and assume the probe starts from rest and the solar intensity remains constant. [4 points] Answer: v = 740 m/s
Snell s Law [20 Points] A beam of light passes through different layers of materials with different indices of refraction as shown in the figure. a) If the beam emerges at θ 2 = 50, find the incident angle θ 1. [8 Points] Answer: θ 1 = 28.6 b) What must be the incident angle θ 1 in order to have total internal reflection occur at the bottom surface between the medium with n = 1.20 and the medium with n = 1.00? [6 Points] Answer: θ 1 = 38.7 c) If total internal reflection occurs at the bottom and top surfaces (when the incident angle is what you calculated in part b), how many reflections will occur between the top and bottom surfaces if all layers are 5.00 m in length and 25.0 cm in width? [6 Points] Answer: N = 6.00 reflections
Dispersion and Total Internal Reflection [20 Points] As shown below, white light is incident normally on a face of a 30 o -60 o -90 o flint prism (n 1 = 1.655 for violent light and n 1 = 1.595 for red light), that is immersed in water (n 2 = 1.333). The ray undergoes total internal reflection at point P. 60 n 2 n 2 P n 1 n 2 θ a) Determine the exit angle θ for red and violet light. What is the dispersion of the prism? [14 Points] Answer: θ red = 36.7, θ violet = 38.4, and Δθ = 1.7 b) A substance is dissolved in the water to increase the index of refraction. At what value of n 2 of the mixture will total internal reflection cease at point P for red and violet light? [6 Points] Answer: n 2 = 1.381 (red) and n 2 = 1.433 (violet)
Mirrors [20 Points] I) High school kids are always worried about pimples. When I was an adolescent, I had one of those magnifying shaving mirrors with which I perused my physiognomy diligently. If you place your face 15 cm from the mirror, what focal length is required to provide a magnification of 1.33? Draw the convenient type of mirror (concave or convex) and draw the rays. [10 Points] Answer: 60 cm and concave mirror II) An object is placed at a distance of p = 20 cm in front of a convex mirror of focal length f = -10 cm as shown. a) Where is the image located with respect to the mirror? Is the image virtual or real? Inverted or upright? [6 Points] Answer: 6.67 cm behind the mirror, virtual, upright b) What is the magnification of the mirror? [4 Points] Answer: M = 0.333
Combination of Lenses [20 Points] The object is placed 60 cm in front of a diverging lens with a focal length of -15 cm. A converging lens of focal length 20 cm is placed 10 cm behind the first lens. a) Make a diagram indicating the position of the lenses, the object and final image, and the corresponding distances measured from the origin. Assume the optical system is along the x-axis and take x = 0, as the position of the diverging lens. [10 Points] Answer: Final image is real, inverted at 230 cm. Diagram is shown. b) Find the magnification of the two lens system. [4 Points] Answer: M = -2 c) Repeat parts a) and b) for the case when the object is placed 10 cm in front of the diverging lens. [6 Points] Answer: Final image is virtual, upright at -70 cm with M = 3
Interference [20 Points] An airplane is traveling 100 m above two radio transmitters with the same height and a distance d = 5.00 m apart. The radio signal emitted from both transmitters has a wavelength of λ = 75.0 cm. The signal received by the airplane can be used to determine the location of the airplane with respect to the midpoint between the two transmitters. a) Determine how far the airplane is from the midpoint between the two transmitters if the radio signal received is at the third maximum? [8 Points] Answer: 112 m b) Determine how much further the airplane must travel horizontally to reach the next maximum. [6 Points] Answer: 24.6 m c) Suppose the space in which the waves are traveling is replaced with seawater of refractive index n = 1.35 and the airplane is replaced by a submarine. What would be the answer to parts a) and b)? [6 Points] Answer: 106 m, 14.3 m
Diffraction [20 Points] The emission of light from an excited gas is focused and passed through a diffraction grating with 3000 lines/cm, as shown. First order and second order spectral lines are observed. a) Four first-order spectral lines are observed at 7.07, 7.48, 8.38, and 11.3. Find the wavelengths of these four spectral lines. [8 Points] Answer: λ 1 = 410 nm, λ 2 = 434 nm, λ 3 = 486 nm, and λ 4 = 656 nm b) At what angles are the second-order spectral lines observed? [7 Points] Answer: θ 1 = 14.2, θ 2 = 15.1, θ 3 = 17.0, and θ 4 = 23.2 c) Suppose the diffraction grating is replaced with another having twice the number of gratings/cm. Find the angular separation observed between the second-order spectral lines. [5 Points] Answer: Δθ = 22.5
Polarization [20 Points] Three polarizing plates whose planes are parallel are centered on a common axis. The directions of the transmission axes relative to the common vertical direction are shown in the figure. A linearly polarized beam of light with plane of polarization parallel to the vertical reference direction is incident from the left onto the first disk with intensity I i = 100 W/m 2. a) Determine the transmitted intensity I f when θ 1 = 10.0, θ 2 = 30.0, and θ 3 = 60.0. [7 Points] Answer: I f = 64.2 W/m 2 b) What is the ratio I f /I i of the final transmitted intensity to the incident intensity if θ 1 = 30.0, θ 2 = 60.0, and θ 3 = 90.0? [7 Points] Answer: I f /I i = 27/64 c) If θ 1 = 0 and θ 2 = 45.0, what should θ 3 be in order to make I f /I i = 3/8? [6 Points] Answer: θ 3 = 75.0