Lec 24 Thursday April 8 Chapter 12 Wave Optics Extra office hours TODAY 4 30 5 30 pm We are here Geometric optics compared to wave optics Phase Coherence Interference Huygens principle diffraction Slits and gratings Diffraction patterns spectra Thin films Exam II The average grade on exam II was 69 An A is 82 or above a B is 71 or better a C is 59 or better Review of interference patterns The pattern that two in phase speakers makes is shown below The speakers are displaced 2 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 1 Review Find the wavelength of light from a diffraction pattern Note 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 is X S D Wavelength of light S X D measure all in the same units This is a slit This a double slit This is a grating 4 Single slit diffraction Large hole width little diffraction Fresnel Very small spreading Very slight fuzzy edges Small hole width lots of diffraction Fraunhofer Distance from center to minimum p 334 D b D distance to screen b slit width 5 Diffraction is spreading of rays Double slit diffraction Wavelength of light S X D X slit separation D screen distance S spot separation S Alternating light and dark lines are called fringes 6 Multiple slit grating diffraction Wavelength of light S X D X slit separation D screen distance S spot separation S This line is called second order Alternating light and dark lines are called fringes 7 Reason for multiple lines in the pattern The additional lines higher orders correspond to 1 2 3 etc difference in the distances 8 Diffraction gives a spectrum if the incident light contains many wavelength Wavelength of light S X D X slit separation D screen distance S spot separation S Alternating light and dark lines are called fringes 9 Lec 24 Thursday April 8 Chapter 12 Wave Optics We are here Geometric optics compared to wave optics Phase Coherence Interference Huygens principle diffraction Slits and gratings Diffraction patterns spectra Thin films 10 Application Thin films A 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 11 Hard and soft reflections Hard 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 surface 12 Demo this Hard 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 material 13 Hard 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 14 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 Fold this one over to get the reflected wave Hard reflection fold over the transmitted wave and turn it upside down Demo with thick plate Soft reflection air 15 glass Enhanced reflection from a film 1 thick The two reflected rays add in phase brighter reflection if the round trip in 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 1 Film Glass Incident light First reflection air to film Second reflection film to glass 16 Consider a coating on glass 1 thick with index of refraction 1 3 How did I know how to draw the reflected wave The hard reflected wave is upside down so if the incident wave is at a crest where it hits the film then the reflected wave is at a trough where it starts on its backward path 17 Reflections cancel for a film The two reflected rays are out of phase dimmer reflection if the round trip in the coating is Both reflections are hard coating glass Incident light First reflection hard air to film Second reflection hard film to glass 18 Consider an antireflection coating on glass thick with index of refraction 1 3 Note that the two waves reflected cancel Each is turned upside down One travels further round trip than the other Thus the two reflected waves are out of phase and the reflection is cancelled 19 How the logic works for thin films film causes extra 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 film is also an antireflection coating For an oil slick the second reflection is soft and the reflected ray is inverted something else happens 20 Reflections from an oil slick wavelength reflects less reflects more Index of refraction for oil is 1 5 for water 1 3 oil water n 1 5 n 1 3 0 5 Incident light First reflection hard air to oil Second reflection soft oil to water 21 Why do anti reflection coatings look purple An anti reflection coating is made 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 22 What are Newton s rings There is a wedge of air between the two lenses placed together Where the wedge is is thick the two reflected rays have paths different by 1 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 tapes 23 Soap bubbles are thin films Air to soapy water is a hard reflection Soapy water to air is a soft reflection Demo soap film 24 Thin films in nature Thin films create iridescent colors Peacock and hummingbird feathers blue and cyan is from thin layers of cells Abalone shells and pearls layers of calcium carbonate deposited in thin layers by the abalone or oyster Butterfly wings thin layers of scales Opal a mineral contains tiny particles regularly spaced which create colors by interference 25