EE119 Introduction to Optical EngineeringSpring 2002Final ExamName: _____________________________________________SID: __________________________CLOSED BOOK. FOUR 8 1/2” X 11” SHEETS OF NOTES, AND SCIENTIFIC POCKET CALCULATOR PERMITTED.TIME ALLOTTED: 180 MINUTESFundamental constants you might need:Planck’s constant, h = 6.62 x 10-34 J-sBoltzmann’s constant, k = 1.38 x 10-23 J/KPermittivity of free space, εο = 8.85 x 10-12 F/mPermeability of free space, µο = 1.26 x 10-6 H/mSpeed of light in vacuum, c = 2.998 x 108 m/sElectron charge, e = 1.6 x 10-19 CFree electron mass, mo = 9.1 x 10-31 kgElectron volt, 1 eV = 1.6 x 10-19 J1 radian = 57.3 degreesTotal 200pointsPage 1 of 101. True or False. (30points, 2 points for each question)____ A) At Brewster’s angle, the reflected light is fully polarized.____ B) A light beam that illuminates a perfectly reflecting surface exerts pressure upon that surface.____ C) A light beam inside a prism with n = 1.39, incident at an interface with air with an angle of incidence of 45 degrees will be totally reflected.____ D) An object placed 10 cm in front of a +5 diopter lens will form a virtual image 20 cm in front of the lens.____ E) An achromatic doublet lens perfectly cancels chromatic aberrations over a specified wavelength range.____ F) The ratio of the exit numerical aperture to the entrance numerical aperture of an imaging system is equal to the transverse image magnification.____ G) The effective lens power for two thin lenses in contact is equal to the sum of the individual powers of the two lenses.____ H) The fovea is the region within your field of vision that is most sensitive to low light levels.____ I) Visual accommodation refers to the ability of the eye to adapt to differing light levels.____ J) The retina contains about six billion rod cells.____ K) Myopia is corrected using a positive lens.____ L) A telescope that has a combination of reflecting and refracting elements is called a catadioptric system.____ M) A singlet lens with perfect spherical surfaces made from glass with homogeneous index of refraction and having a circular aperture stop cannot have any coma aberration for an on-axis image point.____ N) In offset-reference holography, the reconstruction beam must illuminate the hologram plate at the same angle as the reference wave used to record the hologram.____ O) Stimulated emission only occurs when a population inversion exists between the two atomic levels participating in the transition.Page 2 of 102. Short questions. (30points, 3 points for each question)A) A Mach-Zender interferometer (λ=632nm) is set up with a sample of gas placed in one of the optical paths. The gas is in a thin-walled, glass cube with 2cm dimensions. As the gas is heated to a new temperature, a detector records the passing of 2000 fringes. How much has the index of refraction of the gas changed?B) Suppose that the objective lens of a telescope has a diameter of 35mm. How far apart (in light-years) must two stars be before they are theoretically resolvable by the lens? Assume monochromatic wavelength of 550nm. The stars are near the center of our galaxy, about 30,000 light-years away.C) A He-Ne laser (633 nm) with a flat output coupler generates an output beam with Gaussian beam radius w of 1 mm at the output. What is the Gaussian beam radius of the beam at a distance of 7 meters?D) What causes dark current in a photomultiplier tube?E) Name four advantages of optical fibers compared to wires for transmitting information.F) Define the chief ray for a given object point in an imaging system.G) Define chromatic aberration.H) Define field curvature.I) Explain why people in their late 40s to early 50s who previously never required glasses start using “reading glasses”.J) Describe the polarization of the following transverse, monochromatic waves:i) E = x sin(ωt-kz) + y sin(ωt-kz +180)ii) E = x sin(ωt-kz) + y sin(ωt-kz + 90)Page 3 of 10Page 4 of 103. Fun with lenses. (15 points) A solid glass hemisphere is placed with its flat face down on a tabletop. The hemisphere has a radius of 10cm and a refractive index of 1.5. It is lit from above by a collimated beam 1cm in diameter centered on the hemisphere axis. What is the diameter of the circle of light on the table? [Hint: You can use the paraxial approximation.]Page 5 of 104. Lens-based color filter. (20points) Consider the arrangement of lenses and a small pinhole shown in the figure below. Lens 1 is made with Dense Flint glass, and Lens 2 is made with Spectacle Crown glass. The indices for these two glasses are indicated in the table. Both lenses are designed to have equal focal lengths at the ‘F’ wavelength (486 nm), they are separated by twice this focal length, and the pinhole is placed on the optical axis, halfway between the two lenses.Glass typenC (656 nm)nD (589 nm)nF (486 nm)nG (434 nm)Spectacle Crown1.520421.523001.529301.53435Dense Flint1.643571.649001.662001.67456For collimated white light, incident from the left on Lens 1, sketch the spectrum of the light that emerges from lens 2. Explain in words how the device works.Page 6 of 10Lens 1Lens 25. Illuminator. (15points) List three functions of the illuminator optics in a projection system.Page 7 of 106. Camera lens (30 points). A “telephoto” lens system for a camera consists of a convex lens of focal length12cm placed 8cm in front of a concave lens of focal length -6cm. The camera is focused on an object 6 meters in front of the convex lens.A) What will be the total length of the camera from convex lens to the photographic film when the image of the object is in focus.B) What magnification is achieved?Now, a single thin converging lens replaces this lens system. The focal length of this lens being so chosen that the same magnification results when the distance from the object to the lens remains at 6 meters. C) What is the focal length required?D) What will now be the total length of the camera when the image is in focus on the plate?Page 8 of 107. Lasers. (30 points) A) Calculate the longitudinal mode spacing for a He-Ne laser operating at 632 nm with 25 cm spacing between the mirrors. Assume n = 1 inside the He-Ne gas.B) Suppose the laser is operating in a single longitudinal mode with a