Interference ApplicationsPAL #23 InterferenceOrdersIntensity of Interference PatternsIntensityIntensity VariationThin Film InterferenceThin FilmReflection Phase ShiftsReflection Phase ChangeReflection and Thin FilmsPath Length and Thin FilmsAnti-reflective CoatingReflection and InterferenceInterference DependenciesColor of FilmInterferometerSlide 18Interference: SummaryReflectionPath Length DifferenceDifferent Index of RefractionInterference ApplicationsPhysics 202Professor Lee CarknerLecture 25PAL #23 InterferenceLight with  = 400 nm passing through n=1.6 and n=1.5 material Compare to L = 2.6X10-5 m6.5  is total destructive interference and so the above situation is brighterOrdersWhen we look at a interference pattern on a screen each bright or dark spot is represented by a value of m called an order The orders are symmetric e.g. the 5th order maxima is located both to the left and the right of the center at the same distanceIntensity of Interference PatternsHow bright are the fringes?  The phase difference is related to the path length difference and the wavelength and is given by: = (2d sin ) /  IntensityThe intensity can be found from the electric field vector E:I  E2 Where I0 is the intensity of the direct light from one slit and  is the phase difference in radiansFor any given point on the screen we can find the intensity if we know ,d, and I0 Intensity VariationThin Film Interference Camera lenses often look bluish Light that is reflected from both the front and the back of the film has a path length difference and thus may also have a phase difference and show interferenceThin FilmReflection Phase ShiftsIn addition to the path length shift there can also be a phase shift due to reflection If light is incident on a material with lower n, the phase shift is 0 wavelength If light is incident on a material with higher n, the phase shift is 0.5 wavelength The total phase shift is the sum of reflection and path length shiftsReflection Phase ChangeReflection and Thin FilmsIf the thin film covers glass, both reflection phase shifts will be zero Interference is due only to path length differenceExample: If the thin film is in air, the first shift is zero and the second is 0.5 Have to add 0.5 wavelength shift to effects of path length differenceExample:Path Length and Thin FilmsFor light incident on a thin film the light is reflected once off of the top and once off of the bottom If the light is incident nearly straight on (perpendicular to the surface) the path length difference is 2 times the thickness or 2LAnti-reflective CoatingReflection and InterferenceWhat kind of interference will we get for a particular thickness? The wavelength of light in the film is equal to:For an anti-reflective coating, the two reflected rays are in phase and they will produce destructive interference if 2L is equal to 1/2 a wavelength The two rays will produce constructive interference if 2L is equal to a wavelengthInterference DependenciesFor a film in air (soap bubble) the equations are reversed Soap film can appear bright or dark depending on the thickness Since the interference depends also on  soap films of a particular thickness can produce strong constructive interference at a particular Color of FilmWhat color does a soap film (n=1.33) appear to be if it is 500 nm thick?We need to find the wavelength of the maxima:  = (2Ln) / (m + ½) = 1330 nm / (m + ½) = 2660 nm, 887 nm, 532 nm, 380 nm … Real soap bubbles change thickness due to turbulence and gravity and so the colors shiftInterferometerTo get very accurate measurements of wavelength we use an interferometer The beam is sent through a beam splitter, bounces off mirrors and is recombined to produce fringe patterns 1/2  movement of mirror will shift pattern by one fringeInterferometerInterference: SummaryInterference occurs when light beams that are out of phase combine The type of interference can depend on the wavelength, the path length difference, or the index of refractionReflectionDepends on: Example: Equations: • •Path Length DifferenceDepends on: Example: Equations:  d sin  = (m + ½) -- minimaDifferent Index of RefractionDepends on: Example: Equations: