EE119 Introduction to Optical EngineeringSpring 2003Final ExamName: _____________________________________________SID: __________________________EE119 Introduction to Optical Engineering Spring 2003 Final Exam Name: _____________________________________________ SID: __________________________ CLOSED BOOK. THREE 8 1/2” X 11” SHEETS OF NOTES, AND SCIENTIFIC POCKET CALCULATOR PERMITTED. TIME ALLOTTED: 180 MINUTES Fundamental constants you might need: Planck’s constant, h = 6.62 x 10-34 J-s Boltzmann’s constant, k = 1.38 x 10-23 J/K Permittivity of free space, εο = 8.85 x 10-12 F/m Permeability of free space, µο = 1.26 x 10-6 H/m Speed of light in vacuum, c = 2.998 x 108 m/s Electron charge, e = 1.6 x 10-19 C Free electron mass, mo = 9.1 x 10-31 kg Electron volt, 1 eV = 1.6 x 10-19 J 1 radian = 57.3 degrees Total 200points Page 1 of 131. True or False. (30points, 2 points for each question) ____ A) For normal dispersion, the index of refraction is smaller for blue light than for red light. ____ B) 12,000Å = 1.20 µm ____ C) For a polarizing prism, such as the Nicol or Glan Air Prism, the transmitted component is p-polarized, and the reflected component is s-polarized. ____ D) The chief ray always passes through the exact center of the exit window of an imaging system. ____ E) For a light beam of given wavelength and average power, the signal/noise ratio due to shot noise from a PIN photodiode will increase as the quantum efficiency increases. ____ F) In contrast to a photomultiplier tube, a channel electron multiplier can be operated in air. ____ G) A camera exposure setting with shutter speed of 1/256 sec and aperture setting f/4 gives an equivalent film exposure to 1/64 sec shutter speed and f/2 aperture setting. ____ H) The minimum gain required for a laser to reach threshold and begin to oscillate depends on whether the laser transition is homogeneously or inhomogeneously broadened. ____ I) In myopia, the power of the eye is too large, and the sufferer cannot focus at infinity. ____ J) Right-hand circularly polarized light is incident on a linear polarizer. 50% of the incident power is transmitted. ____ K) Light incident on a glass plate at Brewster's angle will have 100% transmission for s-polarization. ____ L) Hyperopia is corrected using a positive lens. ____ M) The main function of the illuminator in a projection system is to make sure that the image is sharp. ____ N) A CCD chip consists of an array of p-i-n diodes. ____ O) In a photodiode, only photons that are absorbed within the diode depletion region contribute to the photocurrent. (Assume a depletion approximation model.) Page 2 of 132. Short questions. (30points, 3 points for each question) A) Write down mathematical expressions for a plane wave and a spherical wave. B) Write down a mathematical expression for the transverse intensity variation of a Gaussian laser beam. Give a definition in words for each of the parameters that you use. C) When light passes through two polarizers whose axes of transmission are parallel, a photodetector reads 30units. If the second polarizer is then turned through 30degrees, what will the detector read? D) A HeNe laser, operating at 633 nm wavelength, has a cavity length of 20 cm. The laser is operating in a single longitudinal mode. If the cavity length is increased by 2%, what will be the fractional change in the output wavelength and in which direction (shorter or longer wavelength)? E) Give a brief description of laser “Q-switching”. F) How many wavelengths wide must a single slit be if the first Fraunhofer diffraction minimum occurs at an angular distance of 30 degrees from the optic axis? G) Write down one advantage of PIN photodetector over a simple pn junction detector. H) Eddy’s father has worn glasses for years. As he is getting older he has trouble reading, and he has a habit of peeking under his glasses to read better. What was his original problem (near-sighted or far-sighted), and are his old glasses made with positive or negative lenses? I) State the gain threshold condition for steady-state laser oscillation in words. J) Give the definition for a “marginal ray” in an optical imaging system. Page 3 of 13Page 4 of 133. Light guide. (15 points) A glass rod of rectangular cross-section is bent into the shape shown as the figure below. A parallel beam of light falls perpendicularly on the flat surface A. Determine the minimum values of the ratio R/d for which all light entering the glass through surface A will emerge from the glass through surface B. The index of refraction of the glass is 1.5. Page 5 of 134. GRIN lens. (20 points) A gradient index lens, shown below, is made from a glass disk of constant thickness in which there is an index of refraction variation in the radial direction, n(r). Given a disk of radius a, and thickness d, find the radial variation of the index that will produce the equivalent of a conventional lens of focal length, f. [Hints: Assume a suitable thin-lens approximation. Try to duplicate the thin-lens phase shift derived in class for a conventional lens in the paraxial approximation.] d r2a Page 6 of 135. Diffraction theory of a lens (15 points) Consider a 100 mm focal length lens with a 1 cm square aperture (instead of a circular one). For a plane wave incident on this lens with 500 nm wavelength, sketch the intensity pattern at the focus. Show two sketches, one a 2D sketch of the pattern, and the second being a plot of intensity vs. position along a horizontal line through the center of the pattern. Give the dimensions of the central lobe of the pattern. Page 7 of 136. Optical fibers. (15points) An optical fiber has cladding index n1 = 1.42, and core index n2 = 1.45. It is used with a laser at wavelength 1.3 µm. The core d = 8.5 µm. A) Is this fiber single-mode for the given wavelength? If not, how many modes does it support? [5 points] B) What is the maximum d for single mode operation at this wavelength? [5 points] C) For the given d = 8.5 µm, what is the minimum wavelength for single mode operation? [5 points] Page 8 of 137. Microscope (15 points). A compound microscope has magnification of 600 (viewing with a fully relaxed eye). The microscope has standardized tube-length, and a 100X objective lens with NA=0.75. A) What is the focal length of the objective lens? [5 points] B) What is the focal length of the
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