4/24/2012. PHY 114 A General Physics II 11 AM 12:15 PM TR Olin 101

Transcription

1 PHY 4 A General Phsics II AM :5 PM TR Olin Plan for Lecture (Chapter 38): Diffraction of light. Diffraction gratings. X ra diffraction 3. Other properties of light PHY 4 A Spring Lecture PHY 4 A Spring Lecture Part of SPS zone 5 conference April, Offer point extra credit for attendance* *After the lecture, me that ou attended. In the following exchange ou will be asked to answer one question about the lecture. PHY 4 A Spring Lecture 3

2 3 rd exam solutions Solutions posted on web xam review session?? Would ou like to attend an exam review session? (A) es (B) no If ou would like a review session, can ou meet (A) Toda Tuesda at PM (here) (B) Toda Tuesda at 5 PM Olin 7 (C) Tomorrow Wed. at PM Olin 7 (D) Tomorrow Wed. at PM Olin 7 () Other? Similar problems ma appear on final exam PHY 4 A Spring Lecture 4 Fourth exam scheduled during the week of April 3 (evenings 6 PM) Note: Content mostl on material in Chapters 35 38, optics, diffraction, plus possibl some ideas of Quantum Mechanics and possibl some topics from xam 3 Which of these times are ou likel to prefer: A. Monda 4/3 B. Tuesda 4/4 C. Wednesda 4/5 D. Thursda 4/6. Frida 4/7 PHY 4 A Spring Lecture 5 Wave phenomena associated with light Plane polarized electromagnetic wave at an instant of time: π ( x, vt λ k Superposition of two electromagnetic waves (electric field portion) tot ( x, ( x, ( x, tot ( x, π λ π λ vt sin vt vt cos π λ PHY 4 A Spring Lecture 6

3 Note that this result followsfrom the trigonometricidentit : A B A B sin( A) sin( B) cos A B Squared magnitude : sin( A) sin( B) 4sin cos In our case: tot Intensit of the M waves : I S avg c tot avg A PHY 4 A Spring Lecture 7 B π π ( x, vt vt λ λ π vt cos λ Constant in time 4 c Rapidl changing in time cos I cos xample: =.5 rad plotting snapshot of M wave xample: =3 rad plotting snapshot of M wave Intensit as a function of : /() PHY 4 A Spring Lecture 8 tot ( x, π λ π λ vt sin vt vt cos What is the significance of this result? π λ A. No significance onl an evil phsics professor could love such a result. B. Shows that an two electromagnetic waves can interfere C. Shows that two electromagnetic wave with the same amplitude, wavelength, and velocit can interfere if the have different phases PHY 4 A Spring Lecture 9 3

4 Young s double slit geometr: Mathematical analsis of bright fringes: r r δ d sin θ πr πr ( P, πft πft λ λ πr r πr r sin πft cos λ λ πr r intensit ima occur for mπ d sin θ λ λ m PHY 4 A Spring Lecture Diffraction pattern from a plane wave incident on a double slit: r r δ d sin θ πr πr ( P, πft πft λ λ πr r πr r sin πft cos λ λ πr r intensit ima occur for mπ d sin θ λ λ m PHY 4 A Spring Lecture I I cos d L ( P, πr πr πft πft λ λ πr r πr r sin πft cos λ λ r r d L tan L PHY 4 A Spring Lecture 4

5 Webassign hints: PHY 4 A Spring Lecture 3 Recall that the - slit intensit pattern has the form : d I I cos d sin m bright fringes when m sin d m d sin m dark fringes when sin d PHY 4 A Spring Lecture 4 Webassign hint: In illustration case : Constructive interference : Destructive interference : nt m nt m PHY 4 A Spring Lecture 5 5

6 Light intensit patterns seen on screen for ver thin double slit Assuming that d and L are the same which plot corresponds the the greater wavelength? > > PHY 4 A Spring Lecture 6 Ideal infinitel thin slit pattern Finite thickness slit pattern I I a d cos L L a L d slit separation a slit width PHY 4 A Spring Lecture 7 ffects of diffraction when ou ma not want it images of small objects near the diffraction limit PHY 4 A Spring Lecture 8 6

7 nhancement of diffraction diffraction gratings πri ( P, πft i λ Nπd sin θ πrav λ sin πft λ πd sin θ λ PHY 4 A Spring Lecture 9 Diffraction pattern for N slits diffraction grating πri ( P, πft i λ Nπd sin θ πr λ sin Intensit ima at av πft λ πd sin θ d sin θ mλ λ PHY 4 A Spring Lecture Intensit pattern from multiple slit grating: I I N π d sin θ sin λ π d sin θ sin λ N= N=5 N= PHY 4 A Spring Lecture 7

8 Sanit check: If the intensit pattern for N slits is given b I I N π d sin θ sin λ π d sin θ sin λ what happened to the formula two slit intensit pattern? A. NVR trust our phsics professor B. More evidence that phsics does not make sense C. The formula look different, but are equivalent for N= PHY 4 A Spring Lecture N π d sin θ sin λ I I π d sin θ sin λ For N : I I πd sin θ sin λ πd sin θ sin λ I I I ' I ' sin sin sin cos cos cos π sin θ λ PHY 4 A Spring Lecture 3 d thin multiple slits fat single slit fat double slits thin double slits PHY 4 A Spring Lecture 4 8

9 Diffraction gratings in nature crstals Model of NaCl Tpical atomic distances a =.. nm PHY 4 A Spring Lecture 5 Recall form of diffraction pattern for grating : I I N d π sinθ λ πd sinθ λ ima when d m PHY 4 A Spring Lecture 6 X ra diffraction geometr: X - ra bright spots - - Bragg condition : d m PHY 4 A Spring Lecture 7 9

10 xample of X ra scattering for NaCl Note that in this case d=a/ PHY 4 A Spring Lecture 8 xample of X ra diffraction data at different temperatures PHY 4 A Spring Lecture 9 Constituents of Li GeP S : α * - Li3PS4 Pbcn H 8. ev * Li3PS4 Pnma H 8.8 ev * Li3PS4 Pmn H 8.36 ev S Li P Ge Li GeS 4 4 Pnma H.9 ev ** *K. Homma et al, Solid State Ionics 8, () **M. Muraama et al, Solid State Ionics 54 55, () PHY 4 A Spring Lecture 3

11 Polarization of light In this case, is polarized in direction. PHY 4 A Spring Lecture 3 General case reflection and refraction n For n n n R n n n n n For polarized in scattering plane nn cos n cos n n cos R R PHY 4 A Spring Lecture 3 For polarized out of scattering plane n cos n cos n cos n cos nn cos n cos n n cos n cos n cos n cos n cos General case reflection and refraction n n For polarized in scattering plane R R R Snell' s law : n cos n cos n cos n cos For polarized out of scattering plane R n cos n cos n cos n cos n sin n sin PHY 4 A Spring Lecture 33

12 Plot of reflectivit R versus perpendicular to scattering plane parallel to scattering plane Brewster s angle n tan P n PHY 4 A Spring Lecture 34