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Wave nature of light thin films, diffraction

Wave nature of light thin films, diffraction. Physics 123, Spring 2006. Intensity in Young’s experiment. E=E 1 +E 2 E=E 0 (sin( w t)+sin( w t+ d )). q =0  d =0: amplitude E( q =0)=2E 0 I( q =0)=4E 0 2 Amplitude E( q )=2E 0 cos( d /2) I( q )=4E 0 2 cos 2 ( d /2).

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Wave nature of light thin films, diffraction

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  1. Wave nature of lightthin films, diffraction Physics 123, Spring 2006 Lecture VI

  2. Intensity in Young’s experiment • E=E1 +E2 • E=E0 (sin(wt)+sin(wt+d)) • q=0 d=0: amplitude E(q=0)=2E0 • I(q=0)=4E02 • Amplitude E(q)=2E0cos(d/2) • I(q)=4E02 cos2(d/2) Lecture VI

  3. Intensity in Young’s experiment • I(q=0)=4E02 • I(q)=4E02 cos2(d/2) • Bright when cos=1, or -1 Lecture VI

  4. Young’s experiment • lr=700 nm • lb=400 nm • d=2000nm • L=20cm • First fringes (bright spots) yr, yb-? • m=1: • y=L l/d • yr=7cm • yb=4cm • Blue is closer to the center than red Lecture VI

  5. Young’s experiment • Two different - l1, l2 • Distance between slits – d • Multiple slits (diffractive grating) • same pattern, sharper lines • Interference pattern depends on l • Maxima: • d sinq1 = m l1 • d sinq2 = m l2 Lecture VI

  6. Coherence • Why do not we observe an interference pattern between two different light bulbs? • These two sources of light are incoherent: • What does it mean for two sources to be coherent? • Same (or close) frequency • Constant shift in phase (not necessarily zero) Lecture VI

  7. Light in a medium (refraction) • Huygens principle – each point forces oscillations with frequency f • f1=f2 • v1=c/n1 • v2=c/n2 • n1l1=n2l2 • E.g. go from air to medium n: • l l/n • ln=l/n n1 n2 Lecture VI

  8. Light in medium d1=k1x=(2p/l1)x=2p600/400=3p + - l=400nm x=600nm Destructive interference n=2 + - Extra phase d=d2-d1=3p ln=l/n=400/2=200nm d2=k2x=(2p/l2)x=2p600/200=6p Lecture VI

  9. Reflection of a transverse wave pulse • Reflection from fixed end –inverted pulse •  • Reflection from loose end – the pulse is not inverted. •  Lecture VI

  10. Reflection • Reflect from medium with highern2>n1  phase change byd=p • + - + + + - • Reflect from medium with lowern2<n1  no phase change d=0 • + + Lecture VI

  11. Soap film film is violet 2t=400nm/2/n t=70nm film is red 2t=700nm/2/n t=123nm Violet is thinner than red. • Soap film, air on both sides • Thickness t • n(soap)=1.42 • n(soap)>n(air)Ray 1 d=p at A • n(air)<n(soap)Ray 2 d=0 at B • Relative shiftd‘=p • Ray 2 travels ABC = extra 2t • d“=kDl=2p2t/ln= 4pt/ln • Relative shift d= d“-d’= 4pt/ln-p • If d=-p+2pm  4pt/ln=2pm or t(m=1)=ln/2 • Rays 1 and 2 are out of phase • Destructive interference • If d=2pm  4pt/ln-p=2pm or t(m=0)=ln/4 • Rays 1 and 2 are in phase • Constructive interference 1 2 B Lecture VI

  12. Diffraction on a single slit z Dl x 0 Slit size D, z=-D/2 to D/2 Observe diffraction at angle q Interference of wavescoming fromdz Lecture VI

  13. Diffraction on a single slit Integrate overdz z Dl x 0 Lecture VI

  14. Diffraction • Dark spot at • Except q=0 – must be bright spot: Lecture VI

  15. Diffraction • Single slit diffraction • Angular half width of the first peak: Lecture VI

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