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Wave Optics

Particle or wave?. Wave Optics. Interference and other Mysteries Explained. You Predict. What happens when a pitcher throws lots of fastballs at two holes? What pattern do you see on the wall beyond?. Predict This. What happens when a beam of light goes through two tiny slits?

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Wave Optics

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  1. Particle or wave? Wave Optics Interference and other Mysteries Explained

  2. You Predict • What happens when a pitcher throws lots of fastballs at two holes? • What pattern do you see on the wall beyond?

  3. Predict This • What happens when a beam of light goes through two tiny slits? • What pattern do you expect on the screen beyond?

  4. Double Slit Interference Applet • What if light from two slits interferes? • http://www.ece.gatech.edu/research/ccss/education/Java/1998.Winter/Projects/pierce-woods/project/bin/projApp.htm • Experiment performed by Young in 1801 • Convincing evidence for wave nature of light • Another Double Slit Applet

  5. Double Slit Derivation • http://noether.physics.ubc.ca/Teaching/Physics101/StudySheets/Double.html

  6. Understanding Path Difference • dsinq = Dd is the path difference for waves traveling to a given point on the fringe pattern • If path difference is an integer number of wavelength, interference is constructive (bright fringe) • If path difference is a half integer number of wavelengths, interference is destructive (dark fringe)

  7. Line Spacing • d sinq = ml m =0, 1, 2 constructive • d sinq = (m +1/2) l m =0, 1, 2 destructive • x = Lq = Lml/d for bright fringes using sinq ~q q in radians x q~ tanq = x/L q d L

  8. What Will Happen to the Fringe Spacing… • x = Lml/d • …if the wavelength increases? • …if the distance to the screen increases? • …if the slit width increases?

  9. Find l • x = Lml/d l = dx/Lm = 6.12 x 10 –7 m = 612 nm • x = 2.5 mm • L= 2.6 m • d = 0.6 mm l = 5.78 x 10 –7 m = 578 nm

  10. Varying the Slit Separation Courtesy of Siltec Ltd. http://www.infoline.ru/g23/5495/Physics/English/feedback.htm

  11. x = Lml/d l=xd/L for adjacent fringes= 4x10-3 x 5x10-4 2.6 = 7.7 x 10-7 = 770 nm

  12. Problem • When white light passes through two slits 0.50mm apart an interference pattern appears on a screen 2.5m away. The fringe separation is 2.5 mm for the violet light. Find the wavelength of this light. Hint: solve x = Lml/d for l L dx/mL = dx/L = 5.0 x 10-7 m = 500nm

  13. Single Slit Interference • Also called diffraction • Fringes are larger • Size of fringes decreases out from center of pattern • Derivation http://oldsci.eiu.edu/physics/DDavis/1160/Ch25WO/Diff.html

  14. Homework • Ch 24 Problems • 3,5,7,9,10(613 nm), 11

  15. More On Single Slit Interference • Pattern dominated by central maximum • Called central diffraction maximum • Width measured from minimum to minimum • Twice as wide as other fringes • Much brighter than other fringes

  16. Single Slit Diffraction- Varying the Slit Width • Fringes get bigger as slit gets smaller

  17. Double d sinq = ml bright d sinq = (m +1/2) l Dark modest central maximum m=0,1,2,etc Single d sinq = ml dark d sinq = (m +1/2) l bright Dominant central maximum Fringes usually larger m=1,2,3, etc Double Slit vs. Single Slit

  18. Single Slit Problem • 500 nm light is incident on a slit of width 0.001 mm which is 1.0 m from a screen. Find the width (2q ) of the central diffraction maximum. (hint: use dsinq = ml ) • 60 degrees

  19. Dispersion • Spreading of white light into spectrum of wavelengths

  20. Why Dispersion Occurs • Index of refraction, n, depends on wavelength l • Typically n decreases as l increases • Exit angle from prism depends on l White light

  21. Forming a Rainbow • Java Applet

  22. Diffraction Gratings • Diffraction Grating has thousands of lines per cm cut into glass plate • Light from each slit interferes with light from all other slits • Analysis like Double Slit • Sin q = ml/d principal maxima (bright) • Lines very close so maxima occur at large angles • Q = 900 is maximum possible so only a few maxima (“orders”)exist

  23. Courtesy http://fermi.bgsu.edu/~stoner/P202/interfere/sld015.htm

  24. Grating Set-Up • Mercury lamp • Spectrometer • Gratings Courtesy http://physics.okstate.edu/courses/experiments/o5.html

  25. How Grating Works in Practice • Purpose is to analyze spectrum of light from source such as unknown gas or a star

  26. Spectrum Produced by Grating

  27. Diffraction Grating Problem • A grating contains 5000 lines per cm • Find the slit separation (d) in meters • 500 nm light is incident on the grating. • At what angles will the first, second and third orders be observed? Is there a fourth order? • Hint: use Sin q = ml/d 2 x 10-6 m = 0.5x10-6m/2x10-6 m=1 14.40 ;m=2 300 ; m=3 48.60 ; m=4 900 not visible

  28. Thin Film Interference Let film thickness = t Assume no net phase change on reflection 2t = ml m=0, 1, 2 Condition for bright 2t = (m+1/2) l Condition for dark For one hard reflection 2t =ml becomes condition for dark

  29. SOFT beam exits higher n material No phase shift on reflection HARD beam enters higher n material Phase shift of l/2 on each reflection Complication #1Soft and Hard Reflections Air n=1.0 Coating n=1.38 Glass n=1.52

  30. Complication #2What Wavelength to Use • Use ln =l/n where n is the index of refraction in the medium where refraction occurs (the film) • Example: green 500nm light leaves air and enters a thin layer of oil n=1.25 floating on water. What wavelength should be used to find the minimum thickness of oil for the oil to appear green? ln = l/1.25 = 500nm/1.25 = 400nm

  31. Oil On Water How many hard reflections are there? What is the total phase shift due to reflections? 1 l/2 = 180 Whatl should you use? ln = l/1.50 Courtesty of http://physics.bu.edu/~duffy/PY106/Diffraction.html

  32. What Really Happens This shows why the wavelength must be divided by n in the film – to get the two reflected waves to interfere completely destructively

  33. Anti-reflective Coating

  34. Problem • A coating of MgF on glass has an index of refraction of 1.38. What is the minimum thickness of this coating to prevent reflection of 550 nm light? 2t =(m+1/2) ln For m = 0 t = ln/4 t=l/1.38/4 t = 100nm

  35. Puzzle • If the two reflected beams interfere destructively, what happens to their energy? It is transmitted! That’s the point of an antireflective coating.

  36. Multi Coating Super-Multi-Coating (SMC) - Pentax's unique seven layer coating applied to each lens element of the lens to increase light transmission, increase color saturation and to help prevent flare.

  37. Polarization • Intensity varies as polarizer is rotated Courtesy Siltec Ltd.

  38. Polarization In linear Polarization light vibrations become confined to a single linear plane Courtesy of 3M Corporation

  39. Polarization Analogy

  40. Two Polarizers • What will happen if the polarized beam hits another polarizer rotated 900 from the first?

  41. Propagation of a Linearly Polarized Electromagnetic Wave Animation Courtesy Siltec Ltd. http://www.infoline.ru/g23/5495/Physics/English/feedback.htm

  42. Courtesy: http://webug.physics.uiuc.edu/courses/phys112/summer97/lectures/lect24/sld014.htm

  43. n = c/v

  44. Link to Interference Applet • In ripple tank • link

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