Interference, Diffraction & Polarizationlight as wavesinterferencePowerPoint PresentationSlide 5Slide 6Slide 7double slit experimentSlide 9Young’s interference experimentSlide 11questionSlide 13other ways of causing interferencephase changes at boundariesthin film interferencethin film analysisNoteSlide 19another caseSlide 21newton’s ringsquiz (extra credit)Slide 24diffractionSlide 26interference pattern from a single slitslit widththe diffraction patternSlide 30diffraction from a single hairdouble slit interference revisiteddouble-slit experimentSlide 34diffraction gratingseparating colorsSlide 37Slide 38polarizationpolarized lightHow to polarize?polarization by absorptionpolarizers and intensitySlide 44polarization by reflectionSlide 46sunglassespolarization by scatteringInterference, Diffraction & PolarizationPHY232 – Spring 2007Jon Pumplinhttp://www.pa.msu.edu/~pumplin/PHY232(Ppt courtesy of Remco Zegers)PHY232 - Remco Zegers - interference, diffraction & polarization 2light as wavesso far, light has been treated as if it travels in straight linesray diagramsrefraction, reflectionTo describe many optical phenomena, we have to treat light as waves.Just like waves in water, or sound waves, light waves can interact and form interference patterns.Remember c = f PHY232 - Remco Zegers - interference, diffraction & polarization 3interferenceconstructive interference destructive interference at any point in time one can construct the total amplitudeby adding the individual componentsPHY232 - Remco Zegers - interference, diffraction & polarization 4Interference IIIconstructive interferencewaves in phasedemo: interference+=destructive interferencewaves ½ out of phase+=PHY232 - Remco Zegers - interference, diffraction & polarization 5Interference in spherical wavesmaximum of wave minimum of wavepositive constructive interferencenegative constructive interferencedestructive interferenceif r2-r1 = n then constructive interference occursif r2-r1 = (n+½) then destructive interference occursr1r2r1=r2PHY232 - Remco Zegers - interference, diffraction & polarization 6PHY232 - Remco Zegers - interference, diffraction & polarization 7light as wavesit works the same for light waves, sound waves, and *small* water wavesPHY232 - Remco Zegers - interference, diffraction & polarization 8double slit experiment•the light from the two sources is incoherent (fixed phase with respect to each other•in this case, there isno phase shift between the two sources •the two sources of light must have identical wave lengthsPHY232 - Remco Zegers - interference, diffraction & polarization 9Young’s interference experimentthere is a path difference: depending on its size the wavescoming from S1 or S2 are in or out of phasePHY232 - Remco Zegers - interference, diffraction & polarization 10Young’s interference experimentIf the difference in distance between the screen and each of the two slits is such that the waves are in phase, constructive interference occurs: bright spot difference in distance must be a integer multiple of the wavelength: d sin = m, m=0,1,2,3…m = 0: zeroth order, m=1: first order, etc.if the difference in distance is off by half a wavelength (or one and a half etc.), destructive interference occurs (d sin = [m+1/2], m=0,1,2,3…)path differencedemoPHY232 - Remco Zegers - interference, diffraction & polarization 11distance between bright spotsif  is small, then sin     tan so: d sin = m, m=0,1,2,3… converts to dy/L = m difference between maximum m and maximum m+1:ym+1-ym= (m+1)L/d-mL/d= L/dym=mL/dtan=y/LLdemoPHY232 - Remco Zegers - interference, diffraction & polarization 12questiontwo light sources are put at a distance d from a screen. Each source produces light of the same wavelength, but the sources are out of phase by half a wavelength. On the screen exactly midway between the two sources … will occura) constructive interferenceb) destructive interference+1/2distance is equalso 1/2 difference:destructive int.PHY232 - Remco Zegers - interference, diffraction & polarization 13questiontwo narrow slits are illuminated by a laser with a wavelength of 600 nm. the distance between the two slits is 1 cm. a) At what angle from the beam axis does the 3rd order maximum occur? b) If a screen is put 5 meter away from the slits, what is the distance between the 0th order and 3rd order maximum?a) use d sin = m with m=3 =sin-1(m/d)=sin-1(3x600x10-9/0.01)=0.01030b) Ym = mL/d m=0: y0 =0 m=3: y3 = 3x600x10-9x5/0.01 = 9x10-4 m = 0.9 mmPHY232 - Remco Zegers - interference, diffraction & polarization 14other ways of causing interferencerememberequivalent to:12n1<n2n1>n21 2PHY232 - Remco Zegers - interference, diffraction & polarization 15phase changes at boundariesIf a light ray travels from medium 1 to medium 2 with n1<n2,the phase of the light ray will change by 1/2. This will not happen if n1>n2.1 2n1<n21/2 phase changen1>n21 2no phase changeIn a medium with index of refraction n, the wavelengthchanges (relative to vacuum) to /nPHY232 - Remco Zegers - interference, diffraction & polarization 16thin film interferencen=1n=1.5n=1The two reflected rays caninterfere. To analyze this system,4 steps are needed:1. Is there phase inversion at the top surface?2. Is there phase inversion at the bottom surface3. What are the conditions for constructive/destructive interference?4. what should the thickness d be for 3) to happen?PHY232 - Remco Zegers - interference, diffraction & polarization 17n=1n=1.5n=1thin film analysis1. top surface?2. bottom surface?3. conditions?4. d?1. top surface: n1<n2 so phase inversion 1/2 2. bottom surface: n1>n2 so no phase inversion3. conditions:1. constructive: ray 1 and 2 must be in phase2. destructive: ray 1 and 2 must be out of phase by 1/24. if phase inversion would not take place at any of the surfaces: constructive: 2d=m (difference in path length=integer number of wavelengths) due to phase inversion at top surface: 2d=(m+1/2) since the ray travels through film: 2d=(m+1/2)film =(m+1/2)/nfilm destructive: 2d=mfilm =m/nfilm12PHY232 - Remco Zegers - interference, diffraction & polarization 18NoteThe interference is different for light of differentwavelengthsPHY232