Midterm Exam 1 - Light Matter Interaction | OSE 5312, Exams of Chemistry

Download Midterm Exam 1 - Light Matter Interaction | OSE 5312 and more Exams Chemistry in PDF only on Docsity! OSE 5312 FUNDAMENTALS OF OPTICAL SCIENCE Spring 2007 Mid Term Exam 1 Wednesday, Feb, 21. This is a closed notes, closed book exam. Answer all questions. Try to use drawings & figures to help explain your answers. Clearly state all your assumptions, definitions and approximations. The number of points for each question is given in italics. Useful Physical Constants are given on the next page. ________________________________________________________________ Name: ___________________________________ Question Max points Score 1 15 2 10 3 15 4 20 5 20 6 20 Total 100 Fundamental Physical Constants — Frequently used constants Relative std. Quantity Symbol Value Unit uncert. u, speed of light in vacuum eco 299 792 458 ms? (exact) magnetic constant po an x 1o-7 NA? =12.566370614.. x 10-7 NA? (exact) electric constant 1/s1oe7 £0 8.854 187817... x 1071? Fm? (exact) Newtonian constant of gravitation G 6.6742(10) x 1071 me kets-2 1.5% 1074 Planck constant A 6.626 0603(11) « 10-84 Is L7 x 10-7 hjon fi 1.054 57168(18) x 10-4 Ts 17x 1077 elementary charge e 1.60217653(14) x 10-1 8.5 x 10-8 magnetic flux quantum f/2e Do 2.067 83372(18) x 10-778 Wh 8.5 x 1078 conductance quantum 2¢"/h Go 7.748 091 733(26) x 10-& 8. 3.3 x 10-9 electron mass me 9.109 3826/16) « 1078! kg LT x 10-7 proton mass mp 1.672621 71(29) x 10-77 keg LT x 10-7 proton-electron mass ratio mpim, 1836.15267261(85) 4.6% 197!" fine-structure constant e"/4meahie a 7.297 352568(24) x 107% 3.3 x 1079 inverse fine-structure constant a7! 137.035 999 11 (46) 3.3 x 10-9 Rydberg constant a?m.c/2h Roo 10973 731.568 525(73) m-t 6.6 x 10-12 Avogadro constant Na,E 6.0221415(10) x 10°% mol-! LT x 10-F Faraday constant Nye F 96 485.3383(83) C molt 8.6 x 10-8 molar gas constant R 8.314472 15) TImol"'K-! 1.7 1078 Boltzmana constant RN, k 1.380 6505/24) « 10-*% kt 18 = to-® Stefan-Boltzmann constant (re 60) kV Re? o 5.670400/40) x 10-8 Wm?K-! 7.0 107% Non-SI units accepted for use with the SI electron volt: (e/C) J eV 1L.60217653(14) x w-8 oy 8.5 x 10-8 (unified) atomic mass unit Lu=m, =pm("C) u 1.66053886(28) x 107°7 ke 17 1077 = 1073 ke mol“1/Nq  b % 1 10° (0? \ 10° WAVELENGTH : 10? (yam)  io . is! WAVELENGTH ! io? . io gum) —_— Absorption —__/\ 2600 4. (a) Write down the equation of motion for an electron in an ideal (Drude) metal with damping Γ (rad/s). From this, find expressions for the real and imaginary parts of the dielectric function, ε′(ω) and ε″(ω). Sketch graphs of ε′(ω) and ε″(ω)versus frequency. (15 points) (b) Indium Tin Oxide (ITO) may be considered as a Drude metal with low conduction electron density. If a film of ITO has an electron density of N=3·1026 m−3, sketch the reflectance of the film versus wavelength. Be sure to use a labeled wavelength scale. (5 points) (Total points Q4: 20) 5. Ruby is a crystal of Al2O3 (Sapphire) doped with Cr3+ ions. It has a strong absorption line with oscillator strength of f = 1 centered on a wavelength of 694 nm. In a particular Ruby crystal, the FWHM of the absorption line is 20 GHz and the Cr3+ density is 2 x 1023 m-3 If the refractive index of the Al2O3 host is 1.77, determine: a. The peak value of the imaginary part of the dielectric constant. (10 points) (Note: you may use the resonance approximation, where ( ) 222220 2)(" ωωω ωωωχ Γ+− Γ = p ) b. The absorption coefficient at λ = 694 nm. (5 points) c. The difference between the high frequency dielectric constant, ε∞, and the static dielectric constant of the ruby, assuming no other absorption resonances due to the Cr3+ ions. (5 points) (Total points Q5: 20)