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### Transcript of 6.2 Two slit interference Coherence Two-Slit Interference Thin film Interference

• 6.2 Two slit interferenceCoherenceTwo-Slit InterferenceThin film Interference

• Interference EffectsInterference is a general property of waves.A condition for interference is that the wave source is coherent.Interference between two waves gives characteristic interference patterns due to constructive and destructive interference.

• CoherenceFor two waves to show interference they must have coherence. Two waves are coherent if one wave has a constant phase relation to the other coherent incoherentphaseshift

• CoherenceLight fromtwo separatelight bulbs isIncoherentLight from a singlelight bulb passingthrough two slits iscoherent

• Interference=0SumConstructive Interference

• Interference=Destructive Interference

• Interference=Constructive Interference

• path differencepath difference = =r2 r1In phaseCondition for constructive interferenceCondition for destructive interferencem = 0 + 1, + 2,.r1r2Superposition of wavesat A shows interferencedue to path differencesAOrder number m

• Interference pattern of water wavesConstructiveDestructive

• Interference pattern due totwo spherical wavesAmplitude on screen=0==-m=0m=1m=-1

• Youngs two slit experimentThomas YoungDoes light show wave properties?

• Path difference from the two slitspath differenceIn the limit L>>d, the rays are nearly parallel

• Interference patternBright constructive interferenceDarkdestructive interferencem = 0, + 1, + 2, ............Central maximum

• QuestionLight from a laser is passed through two slits a distance of 0.10 mm apart and is hits a screen 5 m away. The separation between the central maximum and the first bright interference fringe is 2.6 cm. Find the wavelength lf the light. for m= 1dsin=msin ~ for smallanglessolve for

• Clicker Question 1In a two slit interference experiment, how does the separation between peaks in the interference pattern change if the distance between slits is increased?IncreaseDecreaseStays the sameIndeterminate

• Clicker Question 2In a two slit interference experiment how does the distance between the peaks on the screen change if the wavelength of the light is increased?increasesdecreases stays the sameindeterminate

• Thin film interferenceIn thin film interference the phase difference is due to reflection at either side of a thin film of transparent material.The phase difference is due to two factors:Path difference through the film (corrected for the change in speed of light in the material)Phase shift due to reflection at the interface

• Phase shift due to reflectionn1 < n2phase shift=180oReflection with inversionphase shift = 180o

• Phase shift due to reflectionReflection without inversionPhase shift = zeron1 > n2Phase shift = zero

• Thin film InterferenceFor a thin film in air the phase difference due toreflection is 180oCondition for constructiveinterference=2t=The wavelength in the film is longer than in air.

• Thin film InterferenceFor film in air the phase difference due toreflection is 180oCondition for destructiveinterference=2t=The wavelength in the film is longer than in air.

• Soap film interference pattern

• Soap film

• QuestionA vertical soap film displays a series of colored band due to reflected light. Find the thickness of the film at the position of the 5th green band (=550 nm, n =1.33)

Constructive Interference The 5th band has m=4 (the first is m=0)

• Anti-reflective CoatingAnti-reflective coatings are usedto reduce reflections at the air-glassinterface.anti-reflectivecoatingno coating

• Anti-reflective CoatingAnti-reflective coatings consists of a thin-layer of material with a refractive index in between that of air and glass. Destructive interference between light reflected at the two surfaces reduces the intensity of reflected light. n1=1.00 < n2 < n3Condition for destructive interference.tn1n2n3phase shift of 180o atboth interfaces.Total phase difference due to reflection is zero

• QuestionAn anti-reflective coating of MgF2 (n=1.38) is used on a glass surface to reduce reflections. Find the minimum thickness of the coating that can be used for green light (=550 nm).For destructive interference Quarter wavelength (in coating) thickness minimumat m=0Solve for t

• Optical compact discCd store information in a seriesof pits and bumps in the plastic.The information is read by a reflectedlaser beam. The intensity of the beam is changed byconstructive or destructive interferencedestructive interference