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

Download Midterm Exam 1 Questions - Light Matter Interaction | OSE 5312 and more Exams Chemistry in PDF only on Docsity! OSE 5312 FUNDAMENTALS OF OPTICAL SCIENCE Spring 2008 Mid Term Exam 1 Wednesday, Feb 20. 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 Score 1 /20 2 /15 3 /20 4 /15 5 /30 Total % Fundamental Physical Constants — Frequently used constants Relative std. Quantity Symbol Value Unit uncert. u, speed of light in vacuum eco 299 792458 ms? (exact) magnetic constant po An x 1o-7 NA? =12.566370614.. x 10-7 NA? (exact) electric constant 1/s1o¢" 0 8.854 187817... x 1071? Fm? (exact) Newtonian constant of gravitation G 6.6742(10) x 1071 mkets-? 1.5% 10-4 Planck constant A 6.626 0603(11) « 10-84 Ts LT «10-7 hon fi 1.054 57168(18) x 10-84 Ts LT «10-7 elementary charge e 1.60217653(14) x 10-1 8.5 x 1o7§ magnetic flux quantum /i/2e Do 2.067 83372(18) x 10-78 Wh 8.5 x 1078 conductance quantum 2¢2/h Go 7.748 091 733(26) x 10-& 8. 3.3 1079 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 1075 33x 107% inverse fine-structure constant a7! 137.035 999 11 (46) 3.3 x 10-9 Rydberg constant a2m.c/2h Roo 10973 731.568 525(73) mt 6.6 x 10-12 Avogadro constant Na,E 6.0221415(10) x 10°% mol-! LT x 10-7 Faraday constant Nye F 96 485.3383(83) C molt 8.6 x 1078 molar gas constant R 8.314472 15) Tmol"' Ko! 1.7 1078 Boltzmana constant RIN, k 1.380 6505/24) « 10-** Ik 18 x to-® Stefan-Boltzmann constant (60) kV Re? o 5.670400/40) x 1078 Wm?K-! 7.0 107% Non-SI units accepted for use with the SI electron volt: (e/C) J eV 1.60217653(14) x w-8 oy 8.5 ~ 10-8 (unified) atomic mass unit Lu= my =pm("C) u 1.66053886(28) x 107°" ke L7 «10-7 = 1073 ke mol“1/Nq 2. Define in one or two sentences, the following concepts: (5 points each) a. Local field. b. Inhomogeneous broadening c. Kramers Kronig relation for for refractive index and absorption. 3. At a frequency of 200THz, a material has dielectric susceptibility χ = 3 + 3i (a) What wavelength does 200 THz correspond to, in vacuum? What is the corresponding frequency, ν , in wavenumbers, and what is the photon energy in eV? (6 points) (b) What are the real and imaginary parts of the refractive index? (7 points) (c) What is the absorption coefficient? (3 points) (d) What is the reflectance from the surface on this material, in air? (4 points) 4. (a) Write down the equation of motion for an electron in an ideal (Drude) metal with damping Γ (rad/s). From this, obtain expressions for the real and imaginary parts of the dielectric function, ε′(ω) and ε″(ω). Sketch graphs of n(ω) and κ(ω)versus frequency for Γ << ωp. (But not for Γ=0.) Label your sketch to show all details you deem important. (10 points)