solutions417final

solutions417final - PHY 417 Final Exam NAME: Monday, June...

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Unformatted text preview: PHY 417 Final Exam NAME: Monday, June 4, 2007 Exam duration: 120 minutes Grading: Q1 Q2 Q3 Q4 —Q5 Q6 Q7 Q8 Total —/20 /20 /20 /20 /20 /20 /20 /20 Directions: Please solve the first question and any five of the remaining seven questions. If you attempt all questions, please indicate which ones you want graded clearly. You are allowed to use a 2—paqe, front and back, formula sheet. 1 Plane Electromagnetic Waves A 540—nm harmonic EM—Wave in vacuum Whose electric field is oscillating along the z—axis travels in the —:c direction. (a) What is the frequency of the wave? (b) Determine a) and k for this wave. ((3) If the electric field amplitude is 300 V/m7 What is the amplitude of the magnetic field? ((1) Write an expression for both E(t) and B(t), given that electric field strength is 150 V/m at a: = O and t z 0. (g ., A l o S 1 *M \‘t 1 saw Hf \5’ met/5 wl7/\¥ 2‘ 3a5xl0 7 ~i k7 ET g 9&3 Ié'c’mm -Q, w O C SLlO ' ' » l<X'——wJC+’jfl QUENEFH: [0 Cat 0 :{SO 3 3GB 0"“w' l ~—« :. f . A, , 1 ,~ Hie; 3m%)kfln (Liam x resins t 3) 4’ a l .r a a f"? 2 v E : B flbmaoma “\j TIL 3g 1? Fm ’ ._.,,_ A I s, m a ‘E(?lqb) :GKMGI j @(iJéxlo 7a KlO’éf- 3 2 Dispersion Equation Dispersion equation is given by Nq§( 1 (Some (.08 — LUZ n2(w) 2 1+ (1) (a) Explain the meaning of each variable: N, qg,w0,w, 60,7716 (b) Explain the simple model for light—matter interaction behind this equa— tion. (c) Which steps do you need to take from the simple model until you reach the dispersion equation briefly. (You do not need to derive explicitly, just write the steps.) at I (x a! 4W“ e .: WWW «r MW M6 : {lgcffion M49155 MO _, film Debt) "7 5?“ if ‘Wi grommet F6” Wt WW 3 Reflections at air-silicon interface The graphs shown display the amplitude coefficients for air~silicon interface for light at 632.8 nm coming from air into silicon. (a) Identify in each graph the transmission and reflection coefficients. Give your reasoning clearly. (b) Which graph represents the amplitude coefficients for polarization per— pendicular to the plane of incidence? Which one is the one for polarization in the plane of incidence? (c) What is the reflectance (reflected power divided by incident power) for unpolarized light at 632.8 11m, for 50° angle of incidence? Amplitude Caefflcimt \I: fo 7': a; 4 Wave plates and polarizers A 10—mW light beam polarized linearly along the vertical goes through a half- wave plate with slow axis along the horizontal, and then a quarter wave—plate with slow axis making 45° angle with the horizontal. Finally it goes through a linear polarizer with polarization axis along the vertical. Assume 10% optical power loss in each of the elements in the path of the beam because of the reflections and absorption. (a) What is the optical power of the beam after it goes through half—wave plate? (b) What is the polarization state of the beam after it goes through the half-wave plate? ((3) What is the optical power of the beam after it goes through quarter-wave plate? (d) What is the polarization state of the beam after it goes through the quarter—wave plate? (e) What is the optical power of the beam after it goes through the linear polarizer? (f) What is the polarization state of the beam after it goes through the linear “N polarizer? ‘ E y) . g I: C {All . (a) l03% lDSg we QUE/s gar lQrmW 1 WV: (' Fa ) Vb wrvUi L1 QWW , I 2 {\o \p o \oquaekm clAm/j/é 6 C can) 3' ‘HH QA/x can..in yam/02A «We «641142.12 : . U2; . 43 V} we“) 5 Thick lenses A convex—planar lens of index 1.50 has a thickness of 2.0 cm and a radius of curvature of 2.5 cm. (a) Determine the system matrix when light is incident on the planar surface. (13) If a light beam hits the planar surface 0.5 cm above the optical axis as shown in Fig. 5, Where will the light beam cross the optical axis on the other side of the lens? i «~43, 6 Group velocity and phase velocity An ionized gas or plasma is a dispersive medium for EM—Waves. The dispersion equation is given by w? = w; + czkz (2) where cup is the constant plasma frequency. (a) Determine an expression for the phase velocity. (b) Determine an expression for the group velocity. (c) Show that the product of phase and group velocities is c2. This means that if phase velocity is less than c then group velocity is greater than c, and vice versa. (d) What is the condition on frequency for phase velocity to be greater than c? (e) What is the condition on frequency for group velocity to be greater than c? (f) Explain briefly the physical meaning of phase / group velocity to be greater than 6. Why is this not a violation of the rinci e ativity? . i/w ’L - 1‘ k , ’) + l , (A) i p + c k _ e V C j,» (a) ‘1 ‘7: Z - ‘” Uf>c (a) (9 ) (:3:ch V U) KL, 2.. L Q” L}; >C : <0 "9 LL: F ¥ m. . «k . ‘ ,. . ' v “ {3 0x0 ’ _ - Q‘M/X \ . fired) :fiix’YW L” “H”; J‘Wfi _ /‘ NA, CR 2 nMJHmn . thwr pm“ M 9/5: ‘ ~ “ be / “I . <1 I LL Graeme VA} >Q HAM D a _. 1 x (97 MWWLQ Wfiam Mgfl Mafia hawk WUL Fix/b JAR? QM a}; MAW” ’L g; NM m ’ ‘ ‘kfi-C‘M I 4);" “\x ‘ I «(<6 weak JV) vd“ W1” W / 7 Thin film Lfiwa’lgfim A thin film of ethyl alcohol (71 = 1.36) spread mafiatwglaes—mg = 1.50) Web—— and illuminated with White light is found to reflect only green light (500 11111) strongly at normal incidence. How thick is the film? Li A//\ rangee’ ayaaa 8 Fraunhofer Difiraction You see a plot of intensity normalized to central maximum vs sin (9 for a diffrac— tion pattern as a light beam is sent towards a multiple—slit arrangement. a is the distance between the slits7 and b is the thickness of each slit. (a) What is the number of slits? Support your answer. ...
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solutions417final - PHY 417 Final Exam NAME: Monday, June...

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