4500T206 - Lit-kw oaqu 10. ll. 12. 13. 14. 15. General...

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Unformatted text preview: Lit-kw oaqu 10. ll. 12. 13. 14. 15. General Questions (20) Name Thick Lens (20) (Please Print) ' Microscope (20) Polarization (20) Refractive Index (20) E C E 4500 Second Hour Examination April 5, 2005 Rules for exam: 1. :The time allowed is 60 minutes. The test will start at 9:00am (rather than at 9:05am) and end at 10:00am (rather than at 9:55am). . Answer all questions. The value of each question is given in parentheses by the question. There are a total of 100 points possible. . All work must be shown for full credit. . Put your final answers in the locations specified. . You may use six new single-sided 8 1/2" x 11“ information sheets that you have prepared in your own handwriting. Your information sheets may not include photocopied material. You may also use the six single—sided information sheets that you prepared for the first examination. Some physical constants are given below. . You may use one "book of math tables" or calculus textbook. . You may use a "pocket calculator“ that can be put in a nonnal-size pocket and requires no external electrical power. Graphing calculators and programmable calculators are acceptable. You may not use portable, hand-held, lap—top, or notebook computers or wireless or network connections. . You may not use any reference materials other than those listed above. Therefore, you may not use the class notes, any textbooks, homework problems, reprints of papers, journals, prayer books, etc. There is to be no sharing of anything. , If e‘xcess information is given in a question, ignore the unneeded information. If too little information is given in a question, assume the information needed and clearly note this with your work. Any changes to the examination will be written on the board. Check the board periodically during the examination. Any acts of dishonesty will be referred to the Dean of Students without prior discusSion. The official written Institute procedures on academic honesty (entitled "Maintaining Academic Honesty" and available from the Dean of Students Office) will be followed in all cases. Have a happy exam! = 6.6260755 x 10'34joule-sec 2.99792458 x 108 meter / sec 1.6021773349 x 10"9cou1 = 1.38065812x10'23j0ule/K ' W005 General Optical Engineering Questions 1. Modern refractive/diffractive photographic lenses have been introduced in order to reduce which optical aberration? Circle the one best answer. a) Spherical aberration b) Coma ‘ I c) Astigmatism d) Chromatic aberration e) Distortion f) None of the above. 2. A Weierstrass solid immersion lens is pictured below. Such a lens is used for reading compact disks ’8). —~l=fl- “2 For paraxial rays h), what is the transverse linear magnification m? Circle the one best answer. _h a) E - m h b) 112 R .111 c) n2 2 "1 d) ng e) 1 + 3—2 l f) None of the above. , 3. Linearly polarized light of freespace wavelength A in the visible part of the spectrum is propagating in a block of glass (not a waveguide) of refractive index n. This electro— magnetic wave has a radian frequency w and a wavevector magnitude Is. For this wave, what is the phase velocity? Circ1e the one best answer. ‘ a) d_“’ ‘ dk _ c b __ ) n-Ag—Ri wA c) 21m c d __ ) Z—Zw+n ) 192 e n2dk f) None of the above. 4. Linearly polarized light of freespace wavelength A in the visible part of the spectrum I is propagating in a block of glass (not a waveguide) of refractive index n. This electro— magnetic wave has a radian frequency w and a wavevector magnitude k. For this wave, what-is the group velocity? Circle the one best ansWer. U.) a.) E c b _ ) .n ' w Q 2wn c- d ) gfiw+n ) £d_" e n2dk ' f) None of the ab0ve. 5. For light in the visible part of the spectrum in the above block of glass (not a wave- guide), What statement; can be made about the phase velocity relative to the group ve— locity? Circle the one best answer. a) Phase velocity is greater than the group velocity. b) Phase velocity is equal to the group velocity. e) Phase velocity is less than the group velocity. d) Cannot be determined: from the above information. e) None of the above. Thick Lens Imaging and Ray Tracing A particular wide-angle lens has a focal legth of 20.4 mm and a minimum f-no of 3.5. It is composed of eleven separate lens elements. An optical diagram of this lens is shown below. A point object is a distance of 10.3 mm to the left of the left-most glass surface (front) of the lens as measured along the axis of the lens. The point object is a distance of 20 mm above the centerline axis of the lens. A diagram showing F, H, H’, and F’ and the point object is given below. For this point object, calculate, showingall work, the location of the image of this object point. The image location should be specified by 1) the distance along the axis as measured from the right-most glass surface (positive for an image to the right and nega- tive for an image to the left) and 2) the distance above (positive) or below (negative) the centerline axis of the lens. Express your answers accurately to four significant figures. - Put your final answers in the spaces provided. Distance of imagefrom right—most glass 2 mm sign Distance of image from centerline axis : mm Sign For the above point object, trace the parallel ray and the focal ray through the opti— cal system as depicted in the second diagram. Label the parallel ray and the focal ray. Show the image in your ray—trace diagram and label it. _ Microscope Operation A microscope is to be used to make an accurate length measurement- The mi- crosCope objective has engraved markings on it as follows: “Achro” and “20 / 0.50’.’ and “160 / 0.17.” The eyepiece has engraved. markings on it as follows: ‘_‘R15X.” The field stop in this Ramsden eyepiece is 15.0mm in diameter. The outside of‘ the eyepiece tube is a standard 23.2 mm diameter. Calculate, showing all work, the focal length of the objective. Express your an— swer in mm accurately to three significant figures. Calculate, showing all work, the focal length of the eyepiece. Specify the length of microscope tube (from back focal plane of object to front focal plane of eyepiece) intended for this objective and eyepiece._ Express your answer in mm accurately to three significant figures. Calculate, showing all work, the angular magnification of the resulting microscope. Calculate, showing all work, the diameter of the magnified area of a sample object that is seen when viewing through the microscope. Express your answer in pm accurately to three significant figures. Put your ansWers in the spaces provided below. 7 FOcal length of objective = ' . ' mm ' - Focal length of eyepiece 2 mm -Length of microscope tube = ' mm ll Angular magnification of microscope Diameter ofarea of sample object as seen through the microscope | | pm Polarization of Laser» An engineer has an operating laser. The laser light is red in color. The polariza- tion of the laser is unknown. In addition to the laser, the engineer has only 1) tan ob- serving screen, 2) unmarkedpolarizer, and 3) a. glass microscope slide of unknown refractive index as shown in the .figure. No other equipment is available. Observing Screen {3 (3 Gloss Microscope Slide Describe a complete step-by—step logical procedure by which the engineer can de- termine if the laser is linearly polarized. Write one or more complete sentences (subject, verb, punctuation, etc.) for each step. Put your sentences by the step numbers below. Use whatever number of steps are needed and ignore the extra step numbers. . . . V _ _,_.__._.__,___ . v“... From the above steps, assume that the laser is found to be linearly polarized. Based on the fact that the laser is linearly polarized, describe a complete step—by~step logical procedure by which, the engineer can determine the unique orientation of the lin— ear polarization. Again, the engineer has only 1) an observing screen, 2) an unmarked polarizer, and 3) a glass microscope slide of unknown refractive index. No other equip— ment is available. Write one or more complete sentences (subject, verb, punctuation, etc.) for each step. As your last step, uniquely specify the orientation of the polariza— tion. Put your sentences by the step numbers below. 'Use whatever number of steps are needed and ignore the extra step numbers. _ Unknown Refractive Index - Light is propagating in a lossless isotropic dielectric of unknown refractive index 714. The light is incident upon a planar interface with air (122 = 1.00). The electric field 'E 'of this eleCtromagnetic wave lies in the plane of the page as "shown in the figure. The fraction of the power reflected and fraction of the power transmitted are experimen- tally measured. These measurementsare repeated as a function of angle of incidence 6. The results of these extensive experimental measurements are shown the figure below. ,_ Some measured values are indicated on the figure. Reflected and Transmitted Powers 60 80 Angle of Incidence (degrees) From the above information, What is the description of the polarization of the inCident light? Check the one best statement in the list.. TE polarized. TM polarized. Circularly polarized. Elliptically polarized. Not enough information to determine polarization. None of the above. From the measurements shown in the figure, which statement below can be made about the unknown refractive index? Check the one best statement in the list. n1 < n2 m 2 n2 n1 > n2 n1 is complex real'and imaginary parts). Not enough information to determine 711 relative to n2. None of the above. It is desired to determine the unknown refractive index n1. Using the experimen— tal measurements shown in the above figure, show three independent methods for cal- culating the value of the unknown refractive index m. In each of the three cases, give an analytical expression for n1. Define all quantities in your expression. In each of the three cases, use the analytical expression to calculate a numerical value of m. Put your answers in the spaces provided. Method N0. 1 Analytical expression: n1 : ll Numerical value: n1 Definitions of quantities in above analytical expression: Method No. 2 Analytical expression: n1 2 - Numerical value: my 2 ' Definitions of quantities in above analytical expression: Method N0. 3 Analytical expression: n1 : Numerical value: n1 = Definitions of quantities in above analytical expression: General Optical Engineering Questions 1. Modern refractive/diffractive photographic lenses have been introduced in order to reduce d) Chromatic aberration 2. A Weierstrass solid immersion lens has a transverse linear magnification m of 2 EL d>2 "2 3. The phase velocity of light propagating in a block of glass is C) w)‘ 27m 4. The groupvelocity of light propagating in a block of glass is C dn dww+n d)' 5. For light in the Visible part of the spectrum a) Phase velocity is greater than the group velocity. Thick‘Lens Imaging and Ray 'fl'acing f = 20.4 mm A point object is a distance of 10.3 mm to the left of the left—most glass surface and a distance of 20 mm above the centerline axis of the lens. Left-most glass-to—F distance = 63.5 mm + 38.2 mm — 84.8 mm = 16.9 mm Left-most glass-th distance = 16.9 mm + 20.4 mm = 37.3 mm Object distance, 3 = 10.3 mm + 37.3mm = 47.6mm Lens equation 1+l_1 s s'-f s, _ sf _ 47.6x20.4 s—f mmm = Right-most glass-to—image distance = 38.2 mm — 20.4 mm + 35.7 mm = 53.5 mm Linear magnification _ s’ ‘ 35.7- m -‘= —Ts‘ = —4—i‘é = Distance from centetline d = —0.75x20mm = —15mm Microscope Operation The linear magnification of the objective is- m0 = —£ 2 -20.0 f0 Since L = 160 mm, then f0 278.0 mm. The eyepiece adjusted for infinity focus has anglular magnification 250mm ' Me 2 f6 = 15.0 and so f5 = 16.67mm Length of microscope tube : 160 mm. Angular magnification of microscope, M : mo Me : (20)(15) = 300 The field stop has (1 = 15.0 mm and it located at the image plane of the objective. The diameter of the field Viewed is ' D: i :750pm m Polarization of Laser To determine if laser is linearly polarized: 1) Position the observing screen so that laser beam is incident upon the screen. 2) Insert the polarizer at a right angle into laser beam. 3) Rotate the polarizer about the axis of the laser beam as you observe the intensity upon the observing screen. 4) If, for some angular orientation of the polarizer, the intensity on the observing screen goes to zero, then the laser is linearly polarized. To determine the orientation of the linear polarization: 1) Insert the glass microscope slide into the laser beam so that the angle of incidence upon the slide is approximately 45° and the reflected laser beam propagates vertically upward. 2) Position the observing screen so that the reflected laser beam is incident upon the screen. 3) Rotate the glass microscope slide back and forth about the axis that lies in the plane of the microscope slide that is perpendicular to the incident beam while observing the intensity upon the observing screen. Thus, the angle of incidence is being changed. 4) Stop the angle of incidence rotation when the intensity appears to be minimum. 5) Rotate the glass microscope slide by a small amount about the axis of the laser beam and repeat steps 3 and 4. 6) Stop the rotation of the glass microsope slide when the minimum of step 4 becomes zero. At this orientation of the slide, the linear polarization lies in the plane of incidence (TM polarization). The anlge of incidence is the Brewster angle. 7) The linear polarization of the laser is perpendicular to the laser beam lying in the plane containing the laser beam and the normal to the surface of the microscope slide. Unknown Refractive Index 112 = 1.00 TM polarization Since total internal reflection occurs, m > n2 Method No. 1, Brewster Angle tanBB = :13 n1 n1 : nz/tcmGB = 1/tan(31.69deg) ‘ n1 2 1.61977 63 is the Brewster angle. Method No. 2, Critical Angle sinac = B “1 n1 : ng/sinQC = 1/sin(38.12deg) n1 = 1.61993 6c is the critical angle for total internal reflection. Method No. 3, Reflectance ni—nz 2 R 2 (7114-712 (n1+n2)R1/2 = (“1 —n2) 712 (RI/2 + 1) = n1(1— R1/2) m 2 n2 (1%) 1 — RV2 For R = 0.0560 n1 : 1.6200 R is the fraction of the power reflected at normal incidence. Method No. 4, Transmittance T = ( 2m 2’13 714 +112 m T : 4n1n2 (n1+n2)2 T(n¥+2n1n2 +ng) : 4n1n2 T713 +2n1(T—2)n2 +Tn¥ = 0 n1 2 2T n _ —~2n1(T—2) nt‘2nl[4(1—T)]1/2 1 ’ 2T 7 n _ —2n1 (T —‘2) i 4n1[(1 —T)]1/2 1 — 2T For T = 0944 n1 2 0.617281 not physical n1 = 1.620006 T is the fraction of the power transmitted at normal incidence. ...
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This note was uploaded on 04/29/2008 for the course ECE 4500 taught by Professor Gaylord during the Spring '08 term at Georgia Institute of Technology.

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4500T206 - Lit-kw oaqu 10. ll. 12. 13. 14. 15. General...

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