Phys0175 - Practice Exam 3Spring 2012 - Instructor: Matteo Broccio(1) Monochromatic blue light travels at a speed vp= 1.935∙108 m/s inside a transparent plastic slab and approximately at speed c (light speed in vacuum) in air. (a) Calculate the critical angle for blue light at the plastic-to-air boundary.(b) If the angle of incidence was θi = π/6, at what angles (measured from the normal to the plastic/air interface) would light emerge from the boundary?(c) If the angle of incidence was θi = π/3, at what angles (measured from the normal to the plastic/air interface) would light emerge from the boundary?(2) A circular parallel-plate capacitor, made of two metal discs of radius R facing each other, is being charged with a current i (see drawing). Let r be the radial distance from the axis joining plate centers. In the following, neglect any fringe effects on the capacitor plates.(a) Write the appropriate equation of electromagnetism linking induced magnetic field B and charging current i (explaining all the symbols).(b) Find the magnitude of the maximum magnetic field induced within the capacitor.(c) Find the magnitude of the magnetic field induced at r=R/4.(3) Monochromatic em radiation passes through two straight slits of width a and separation distance d and light intensity is detected at a distant screen. Let the angle θ be measured with respect to the line joining the midpoint between slits and the photosensitive screen.(a) Write the expression for the detected intensity I relative to its absolute maximum Imax, as a function of angle θ, slit width a, and slit separation distance d. Explain the physical meaning of each factor.(b) Consider the case in which the wavelength of the em radiation is much larger than the slit width, yet comparable to the separation distance between slits. Write an approximate expression for the detected intensity in this case, explaining the physical meaning of your answer.(c) Under the same approximation as in (b), at angle θ1= 0.55 rads, the detected intensity I(θ1) is exactly Imax/2. The slit separation distance is 1.08 μm. Find the radiation wavelength in question.(4) Ultraviolet light with a frequency of 3.50∙1015 Hz strikes a metal surface and ejects electrons whose maximum kinetic energy is 5.30 eV. What is the work function of the metal?A. 5.30 eV B. 9.18 eV C. 38.4 eV D. 12.7 eV E. 188 eV(5) White sunlight in air shines on an oil (n=1.50) film floating on a water (n=1.33) puddle. Looking straight down at the film, the reflected light is red with a wavelength λ = 636 nm. What is the minimum possible thickness of the oil film? A. 189 nm B. 285 nm C. 218 nm D. 106 nm E. 67 nm(6) Unpolarized monochromatic light in air impinges on a slab with a temperature-dependent index of refraction n(T)= 1.728 - (0.007 K-1)(T - T0), where T0 = 293 K. The angle of incidence of light with respect to the boundary normal is varied until at 58.06 degrees, reflected light is 100% linearly polarized. What is the current temperature of the slab?A. 303.5 K B. 441.8 K C. 18.2 K D. 274.8 K E. 310.7 K(7) Look at the figure below, in which a light beam travels through three parallel layers of different media. Based on the trajectory, deduce relations between the indices of refraction of media a, b, and c.A. a>b, b>c B. a>b, b<c C. a<b, b>c D. a<b, b<c E. a=b,
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