1Lec. 24, Thursday, Nov.11 Chapter 12: Wave Optics• Geometric optics compared to wave optics• Phase• Coherence• Interference• Huygens’ principle & diffraction• Slits and gratings• Diffraction patterns & spectra• Thin films1We are here1Exam II: The average grade on exam II was 72. The median grade was 74. Exam 2 curve Histogram0510152025300102030405060708090100FrequencyMedian = 74, A > 82, B > 75, C = 56-74, D= 50-55, F below 50 BCDFAReview of interference patternsThe pattern that two in phase speakers makes is shown below:The speakers are displaced 2 ½ wavelengths vertically, so there is cancellation along a line in the vertical direction and there is addition in the horizontal direction. In the spaces between the loud areas the sound is softer.Review: Find the wavelength of light from a diffraction patternNote that the lemon and lime triangles are similar. The ratio of the shortest side to the longest side is the same for both. So, the formula relating D, X, and λ is λ / X = S / D. Wavelength of light: λ = S X / D. [measure all in the same units]5This is a slitThis is a gratingThis a double slit6Single slit diffractionLarge hole, width >> λ, little diffraction (Fresnel diffraction)Small hole, width < λ, “lots” of diffraction (Fraunhofer diffraction)Diffraction is spreading of rays. Half-width of spreading (p. 334) z = λ D / bD = distance to screenb = slit widthVery slight fuzzy edgesVery small spreadingz7Double slit diffractionWavelength of light: λ = S X / D.X = slit separation D = screen distanceS = spot separation SAlternating light and dark lines are called fringes.8Multiple slit (grating) diffractionWavelength of light: λ = S X / D.X = slit separation D = screen distanceS = spot separation SAlternating light and dark lines are called fringes.This line is called “second order”XD9Reason for multiple lines in the patternThe additional lines (higher orders) correspond to 1 λ, 2 λ, 3 λ, etc. difference in the distances. 10Diffraction gives a spectrumif the incident light contains many wavelengthWavelength of light: λ = S X / D.X = slit separation D = screen distanceS = spot separation SAlternating light and dark lines are called fringes.11• Geometric optics compared to wave optics• Phase• Coherence• Interference• Huygens’ principle & diffraction• Slits and gratings• Diffraction patterns & spectra• Thin films11We are here11Lec. 24, Thursday, Nov.11 Chapter 12: Wave Optics12Application: Thin filmsA thin film of material can be an antireflection coating. About 4% of light is reflected at the glass surface. Reflections from surfaces of lenses create “ghost”images of the sun.Hard and soft reflectionsHard reflections return upside down (180 degree phase change)Examples– wave on a rope tied to a wall – light going into higher index of refraction material– light reflecting from metal surface13Demo thisHard and soft reflections (2)Soft reflections return right side up (No phase change)Examples– wave on a rope tied to a string– light going into lower index of refraction material1415Hard versus soft reflections• Hard reflection: light goes from low index of refraction to high index, as air to glass. The phase of the reflected wave is not changed. • Soft reflection: light goes from high index to low (glass or water to air). The reflected wave is upside down (a 180 degree phase shift). Reflections from glass• Each glass surface reflects about 4% of the incident light. • Where the light enters, the reflection is hard. • Where the light exits, the reflection is soft. 16Hard reflection“fold over” the transmitted wave and turn it upside downSoft reflectionair glassFold this one over to get the reflected waveEnhanced reflection from a film 1 λ thickThe two reflected rays add in phase (brighter reflection) if the round tripin the film is two wavelengths, Also for 1 wavelength round trip, etc. Wavelengths are measured in the film, not in the air. Indices of refraction are 1.0 for air, 1.3 for film, 1.5 for glass. 17First reflection(air to film)Second reflection(film to glass)Incident light1λ Film Glass18Consider a coating on glass 1 λ thickwith index of refraction 1.3How did I know how to draw the reflected wave? The “hard” reflected wave is upside down, so if the incident wave is at a crestwhere it hits the film, then the reflected wave is at a trough where it starts on its backward path.Reflections cancel for a ¼ λ filmThe two reflected rays are out of phase (dimmer reflection) if the round trip in the coating is ½ λ. Both reflections are hard. 19First reflection(hard, air to film)Second reflection(hard, film to glass)Incident lightcoating glass20Consider an antireflection coating on glass ¼ λ thick with index of refraction 1.3Note that the two waves reflected cancel!Each is turned upside down. One travels ½ λ further (round trip) than the other. Thus the two reflected waves are out of phase and the reflection is “cancelled.”How the logic works for thin films•¼λ film causes extra ½ λ round trip for light inside the film• The wave reflected at the second surface is out of phase with wave reflected from the front if nothing else happens• The front surface reflection is inverted (hard). • The back surface reflection is inverted (hard)• The front and back reflections are still out of phase. •At ¾λ film is also an antireflection coating. • For an oil slick, the second reflection is soft and the reflected ray is inverted (something else happens). 21Reflections from an oil slick½ wavelength reflects less, ¼ λ reflects more.Index of refraction for oil is 1.5, for water 1.322First reflection(hard, air to oil)Second reflection(soft, oil to water)Incident lightoil watern=1.5 n = 1.30.5 λ23Why do anti-reflection coatings look purple? An anti-reflection coating is made ¼ wave thick for green light which is the middle of the spectrum. That means that blue and red are reflected a little bit because the film is optimized for green. The red and blue reflections together look purple. 24What are Newton’s rings?There is a “wedge” of air between the two lenses placed together. Where the wedge is is ½ λ thick, the two reflected rays have paths different by 1 λ, but one reflection is hard and one is soft, making the reflection darker since one reflected wave is inverted. Demo: Newton’s rings, cash register