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Reflection, Refraction, Interference, Diffraction: Understanding Optics

This section explores the principles of reflection, refraction, interference, and diffraction in optics. Topics include the index of refraction, chromatic dispersion, interference patterns, thin film interference, and diffraction patterns.

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Reflection, Refraction, Interference, Diffraction: Understanding Optics

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  1. 11 反射、折射、干涉、繞射

  2. Sections • 反射 (reflection)與折射 (refraction) • 干涉 (interference) • 繞射 (diffraction)

  3. 11-1 Reflection and Refraction (反射與折射)

  4. 折射率

  5. Chromatic Dispersion – prisms and gratings

  6. Rainbows

  7. 11-2 Interference – (干涉) What produces the blue-green of a Morpho’s wing?  How do colorshifting inks shift colors?

  8. Huygens’ principle Fig. 35-2 All points on a wavefront serve as point sources of spherical secondary wavelets. After a time t, the new position of the wavefront will be that of a surface tangent to these secondary wavelets.

  9. Law of Refraction from Huygens’ principle

  10. Fig. 35-3 35-

  11. Index of Refraction: Law of Refraction: 35-

  12. Phase Difference, Wavelength and Index of Refraction

  13. Wavelength and Index of Refraction The frequency of light in a medium is the same as it is in vacuum 35-

  14. Phase Difference Fig. 35-4 Since wavelengths in n1 and n2 are different, the two beams may no longer be in phase 35-

  15. Ex.11-1 35-1 wavelength 550.0 nm n2=1.600 and L = 2.600 m

  16. Young’s Experiment

  17. Coherence Two sources to produce an interference that is stable over time, if their light has a phaserelationship that does not change with time: E(t)=E0cos(wt+f) Coherent sources: Phasefmust be well defined and constant. When waves from coherent sources meet, stable interference can occur － laser light (produced by cooperative behavior of atoms) Incoherent sources: fjitters randomly in time, no stable interference occurs － sunlight 35-

  18. Intensity and phase Fig. 35-13 Eq. 35-22 Eq. 35-23 35-

  19. Intensity in Double-Slit Interference E2 E1 35-

  20. Intensity in Double-Slit Interference Fig. 35-12 35-

  21. Ex.11-2 35-2 wavelength 600 nm n2=1.5 and m = 1 → m = 0

  22. Interference form Thin Films

  23. Reflection Phase Shifts n1 > n2 n1 < n2 n1 n1 n2 n2 Fig. 35-16 Reflection Reflection Phase Shift Off lower index 0 Off higher index 0.5 wavelength 35-

  24. Phase Difference in Thin-Film Interference Fig. 35-17 • Three effects can contribute to the phase difference between r1 and r2. • Differences in reflection conditions • Difference in path length traveled. • Differences in the media in which the waves travel. One must use the wavelength in each medium (l / n), to calculate the phase. 35-

  25. Equations for Thin-Film Interference ½ wavelength phase difference to difference in reflection of r1 and r2 35-

  26. Color Shifting by Paper Currencies,paints and Morpho Butterflies weak mirror soap film better mirror looking directly down ： red or red-yellow tilting ：green 35-

  27. 大藍魔爾蝴蝶

  28. 雙狹縫干涉之強度

  29. Ex.11-3 35-3 water film thickness 320 nm n2=1.33 m = 0, 1700 nm, infrared m = 1, 567 nm, yellow-green m = 2, 340 nm, ultraviolet

  30. Ex.11-4 35-4 anti-reflection coating

  31. Ex.11-5 35-5 thin air wedge

  32. Michelson Interferometer Fig. 35-23 35-

  33. Determining Material thickness L 35-

  34. 11-3 Diffraction and the Wave Theory of Light Diffraction Pattern from a single narrow slit. Side or secondary maxima Light Central maximum Fresnel Bright Spot. These patterns cannot be explained using geometrical optics (Ch. 34)! Light Bright spot 36-

  35. The Fresnel Bright Spot (1819) • Newton • corpuscle • Poisson • Fresnel • wave

  36. Diffraction by a single slit

  37. 單狹縫繞射之強度

  38. 雙狹縫與單狹縫 • Double-slit diffraction (with interference) • Single-slit diffraction

  39. Diffraction by a Single Slit: Locating the first minimum (first minimum) 36-

  40. (minima-dark fringes) Diffraction by a Single Slit: Locating the Minima (second minimum) 36-

  41. Ex.11-6 36-1 thin air wedge

  42. Intensity in Single-Slit Diffraction, Qualitatively 1st side max. N=18 q = 0 q small 1st min. Fig. 36-7 36-

  43. Intensity and path length difference Fig. 36-9 36-

  44. Fig. 36-8 Intensity in Single-Slit Diffraction, Quantitatively Here we will show that the intensity at the screen due to a single slit is: In Eq. 36-5, minima occur when: If we put this into Eq. 36-6 we find: 36-

  45. Ex.11-7 36-2

  46. Diffraction by a Circular Aperture a a Light Light q q Distant point source, e,g., star d Image is not a point, as expected from geometrical optics! Diffraction is responsible for this image pattern q lens 36-

  47. Resolvability Fig. 36-11 Rayleigh’s Criterion: two point sources are barely resolvable if their angular separation qR results in the central maximum of the diffraction pattern of one source’s image is centered on the first minimum of the diffraction pattern of the other source’s image. 36-

  48. Ex.11-8 36-3 D = 2.0 mm d = 1.5 mm

  49. 11-4.9Diffraction – (繞射)

  50. Ex.11-9 36-4 d = 32 mm f = 24 cm λ= 550 nm

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