4500T201 - General Questions(18 Name Thick Lens 14(Please Print Depth of Field(10 Polarized Light(18 Telescope(14 Waveguide(14 E C E 4500

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Unformatted text preview: General Questions (18) Name Thick Lens ( 14) (Please Print) Depth of Field (10) Polarized Light (18) Telescope (14) Waveguide (14) E C E 4500 Interference Filter ( 12) Second Examination April 25, 2001 Rules for exam: 1. may: cortex 10. 11. 12. 13. 14. 15. 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 the six new single—sided 8 l/ " x 11" information sheets that you have prepared. In addition, you may use the six information sheets that you prepared for the first examination. Some physical constants are given below. You may use one "book of math tables." . You may use a "pocket calculator" that can be put in a normal-size pocket and requires no external electrical power. You may not use portable, lap-top, or notebook computers nor 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 other textbooks, homework problems, reprints of papers, journals, prayer books, etc. There is to be no sharing of anything. If excess 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 chalk board. Check the chalk 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! c = 2.99792458x108meter/sec General Optical Engineering Questions 1. Given a lens of focal length f, an object distance of s, and an image distance of 3’, write Newton’s thin lens equation as a function of f, s, and s’. 2. In an optical system exhibiting spherical aberration, this aberration can be reduced by (Circle all correct responses.) a) decreasing the f—number b) increasing the f—number c) decreasing the field of view d) increasing the field of View e) none of the above 3. Of the aberrations coma and astigmatism, which is more important to be corrected in a telescope objective? (Circle one.) a) coma b) astigmatism c) none of the above 4. In the visible part of spectrum, losses in fused silica optical fibers are primarily due to (Circle one.) a) Mie scattering b) Rayleigh scattering c) none of the above 5. Compared to a multi—mode optical fiber, a single-mode optical fiber has (Circle all correct responses.) 3.) small numerical aperture b) large numerical aperture c) small core diameter d) large core diameter e) more dispersion f) less dispersion g) none of the above 6. If a slit of width a diffracts light whose wavelength is long compared to a, the diffrac— tion is called (Circle all correct responses.) a) Fraunhofer diffraction b) Fresnel diffraction c) Bragg diffraction d) Kirchhoff diffraction e) none of the above Thick Lens Imaging An object is placed to the left of the lens shown in the diagram below. All dimen— sions given are in mm. An image is formed that is 25% of the size of the object (mea- sured transversely to the axis of the optical system). 63.5 38.2 Calculate, showing all work, the distance of the object from the left-most glass surface. Calculate, showing all work, the distance of the image from the right—most glass surface. Express your answers in mm accurately to within :l:0.1 mm. Put your answers in the spaces provided. Distance of object from left—most glass = mm Distance of image from right—most glass 2 mm Depth of Field A camera lens has a focal length of 100 mm and a minimum f—number of 2 (max- imum aperture) and a maximum f-number of 22 (minimum aperture). It is used to im- age an object that is 2 m away. An f—number of 4 is used together with a shutter time of 1/60 sec. It is desired to double the depth of field in the image and simultaneously to keep the overall exposure energy the same. Complete the following sentences to describe how to accomplish this. The new f—number should be The new shutter time should be sec. Production of Polarized Light A randomly linearly polarized argon laser of freespace wavelength 488 nm (blue) has an output power of 250 milliwatts. It is desired to produce linearly polarized light from this beam. A quartz flat is the only item of optics available and it is to be used as shown in the drawing below to obtain linearly polarized light. At this wavelength, the quartz has a refractive index of 1.463. The laser and the quartz flat are in air. R 1) Calculate, showing all work, the required angle fl to produce linearly polarized light. Express your angle in degrees accurately to within i0.001°. Put your answer in the space provided. 2) Indicate which beam is linearly polarized. R T (circle one) 3) Calculate, showing all work, the power in the linearly polarized beam. Express your power in milliwatts accurately to within four significant figures. flz—‘a—-——O Power in linearly polarized beam 2 milliwatts Catadioptric Telescope A 3.5 inch diameter, 1300 mm focal length, f / 14.4 Questar brand Maksutov cata- dioptric telescope is used with a 12 mm focal length Erfle wide-field eyepiece to view dis- tant objects under room lighting conditions. Calculate, showing all work, the angular magnification obtained with this config- uration. Express your answer accurately to three significant figures. Calculate, showing all work, the minimum angle (measured from the telescope to the distant object) that can be resolved with this configuration. Express your answer in degrees accurately to three significant figures. Put your answers in the spaces provided. Angular magnification 2 Minimum angle resolved 2 Slab Waveguide A slab waveguide consists of a glass film of 5 pm thickness with a refractive index of 1.515. This film is surrounded by a substrate and cover both with a refractive index of 1.500. Light of freespace wavelength 1.00 pm is launched into the waveguide. The po— larization of the light is such that it excites TE modes in the waveguide. By solving the dispersion equation (using program SLWG), the TE modes are found to have character- istics be as listed below. For a freespace wavelength of 1.000 mm TEO, 6 = 87.103493°, N = 1.513064, 6 = 9.506864um—1 TEl, 6 = 84.313614°, N = 1.507545, 6 = 9.472183/rm‘1 TE2, 6 = 82.031273°, N = 1.500371, [3 = 9.427108um_1 For a freespace wavelength of 0.995 ,um TEO, 6 = 87.114479°, N = 1.513079, [3 = 9.554729pm‘1 TEl, 6 = 84.333702°, N = 1.507597, 6 = 9.520114,um_1 TEg, 6 = 82.045410°, N = 1.500423, 6 : 9.474808;rm_1 For a freespace wavelength of 1.005 pm TE), 6 : 87.092537°, N = 1.513050, 6 = 9.459475um"1 TEl, 6 = 84.293602°, N = 1.507492, 6 = 9.42473011771—1 TE2, 6 = 82.017838°, N = 1.500322, 6 = 9.379900,um"1 For the lowest-order TE mode, calculate, showing all work, the phase velocity and the group velocity. Give the velocity in m/ sec. Express your answers accurately to within five significant figures. Put your final answers in the spaces provided below. Phase velocity = m / sec Group velocity = m / sec Interference Filter One “half wavelength” thick interference filter is specified to pass 510nm wave- length light at normal incidence. Another is specified to pass 520nm wavelength light at normal incidence. By rotating the angle of incidence of one of these filters it is desired to pass only 514.5 nm green light from an argon laser as shown in the figure. The one “half wavelength” thick layers have a refractive index of 1.400. The surrounding regions have a refractive index of 1.500. Specify which filter should be used. Calculate, showing all work, the required an- gular rotation a in degrees that is required. Express your answer accurately to within :i:0.01°. Put your answer in the space provided. The filter to be used is 510 nm filter 520nm filter Circle one. General Optical Engineering Questions 1. Newton’s thin lens equation is (s - f ) (3/ -— f) = f2. 2. In an optical system exhibiting spherical aberration, this aberration can be reduced by b) increasing the finumber 3. Of the aberrations coma and astigmatism, which is more important to be corrected in a telescope objective? a) coma 4. In the visible part of spectrum, losses in fused silica optical fibers are primarily due to b) Rayleigh scattering 5. Compared to a multi-mode optical fiber, a single-mode optical fiber has a) small numerical aperture c) small core diameter f) less dispersion 6. If a slit of width a diffracts light whose wavelength is long compared to a, the diffrac- tion is called (Circle all correct responses.) a) Fi‘aunhofer diffraction Thick Lens Imaging . Real image, m < 0 Linear magnification, m ll —o.25 = —1/4 Focal length, f = 20.4 mm Object distance 1 ,s = (1 — E)f = 5f = 5(20.4mm) 2 102mm Distance of object from left—most glass = 102 -— (63.5 + 38.2 — 44 — 20.4) = 64.7mm Image distance I s = —m3 = —(-1/4) 102mm = 25.5mm Distance of image from right-most glass = 25.5 + (38.2 — 20.4) = 43.3 mm Depth of Field The new f-number should be 8. The new shutter time should be 1 / 15 sec. Production of Polarized Light Incidence should be at the Brewster angle 91 = tan'1(n2/n1) tan—1(1.463) = = ,6 The angle of refraction is 02 = (nl/n2)sin01 = 34.35366° The fraction of the TE amplitude reflected is : n100361—n200302 : _0.36313 Ei TE n1 cos 61 + 712 cos 62 The fraction of the TE power reflected is E 2 (mm = = 0.131865 The fraction of the total power reflected is (Pr)polam'zed = PTotal (PT)TE/2 = (250 771W) 0.065933 = 16.483 mW Catadioptric Telescope D = 35inch f0 2 1300mm f8 2 12mm M = fo/fe = W = 108.3X A 9min = 1.221)— Use A = 0.5 pm D = 3.5 in (25.4 mm/in) (1000 pm) = 88, 900 ,um 6mm 26.86 X 10‘6rad (180°/7rrad) = 3.93 X 10‘4 degrees Slab Waveguide h 2 5pm nf = 1.515 ns = nc = 1.500 A = 1.00pm The lowest-order TE mode is T E0 and it is characterized by 0 = 87.103493°, N = 1.513064, 6 = 9.506864pm"1. vph = $0 = 0.6609100 W = 1.981359 x 108m/sec The group velocity dw d 27rc 27rc dA 27m AA “ m = 2173(7): ‘VW “ —7\7A—fl /\ = 1.005um, fl = 9.459475pm‘1. A = 0.995pm, [3 = 9.554729pm‘1. and so 119? = 065962430 1.977527 X 108 m/sec. Interference Filter Use the 520 nm wavelength filter and tune it to the shorter wavelength of 514.5 nm. The tuning characteristic is 2 n d cos ,8 = m A For one half wavelength filters at normal incidence 2nd = A and so 2nd :2 520nm For tuning to 514.5 nm 14. c033 = -————5 5nm and so fl = 8.3407° 520nm Parallel. glass plates do not affect the ray direction in air. Thus from Snell’s law 1.03ina = 1.4sinfi and so a = 11.7172°. ...
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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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4500T201 - General Questions(18 Name Thick Lens 14(Please Print Depth of Field(10 Polarized Light(18 Telescope(14 Waveguide(14 E C E 4500

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