14Interference Equations, 3 The positions of the fringes can be measured vertically from the zeroth order maximumy =AssumptionsL>>dd>>λApproximationθ is small and therefore the approximation tan θ sin θ can be used
20Interference in Thin Films Interference effects are commonly observed in thin filmsExamples are soap bubbles and oil on waterThe interference is due to the interaction of the waves reflected from both surfaces of the film
23Interference in Thin Films, 4 Ray 2For constructive interferenceThis takes into account both the difference in optical path length for the two rays and the 180° phase changeFor destruction interference
24Interference in Thin Films, 5 Two factors influence interference and should be considered always for medium above and below the surface.Possible phase reversals on reflectionDifferences in travel distanceIf the thin film is between two different media, one of lower index than the film and one of higher index, the conditions for constructive and destructive interference are reversed
25Interference ExampleWhat is the least thickness of a soap film which will appear black when viewed with sodium light (λ=589.3 nm) reflected perpendicular to the film? The refractive index of soap solution is n=1.38
26CD’s and DVD’s Data is stored digitally A series of ones and zeros read by laser light reflected from the diskStrong reflections correspond to constructive interferenceThese reflections are chosen to represent zerosWeak reflections correspond to destructive interferenceThese reflections are chosen to represent ones
27CD’s and Thin Film Interference A CD has multiple tracksThe tracks consist of a sequence of pits of varying length formed in a reflecting information layerThe pits appear as bumps to the laser beamThe laser beam shines on the metallic layer through a clear plastic coating
28Reading a CDAs the disk rotates, the laser reflects off the sequence of bumps and lower areas into a photodectorThe photodector converts the fluctuating reflected light intensity into an electrical string of zeros and onesThe pit depth is made equal to one-quarter of the wavelength of the light
29DVD’s DVD’s use shorter wavelength lasers The track separation, pit depth and minimum pit length are all smallerTherefore, the DVD can store about 30 times more information than a CD
33Selective Absorption, cont E. H. Land discovered a material that polarizes light through selective absorptionHe called the material ________Axis
34Selective Absorption, final The intensity of the polarized beam transmitted through the second polarizing sheet (the analyzer) varies as_____________________________Io is the intensity of the polarized wave incident on the analyzerThis is known as Malus’ Law and applies to any two polarizing materials whose transmission axes are at an angle of θ to each other
35ExampleUnpolarized light passes through two polaroid sheets. The axis of the first is vertical, and that of the second is at 30.0 degrees to the vertical. What fraction of the initial light is transmitted?
40Optical ActivityCertain materials display the property of optical activityA substance is optically active if it rotates the plane of polarization of transmitted lightOptical activity occurs in a material because of an asymmetry in the shape of its constituent materials
41Liquid CrystalsA liquid crystal is a substance with properties intermediate between those of a crystalline solid and those of a liquidThe molecules of the substance are more orderly than those of a liquid but less than those in a pure crystalline solidTo create a display, the liquid crystal is placed between two glass plates and electrical contacts are made to the liquid crystalA voltage is applied across any segment in the display and that segment turns on
42Liquid Crystals, 2Rotation of a polarized light beam by a liquid crystal when the applied voltage is zeroLight passes through the polarizer on the right and is reflected back to the observer, who sees the segment as being bright
43Liquid Crystals, 3When a voltage is applied, the liquid crystal does not rotate the plane of polarizationThe light is absorbed by the polarizer on the right and none is reflected back to the observerThe segment is dark
44Liquid Crystals, finalChanging the applied voltage in a precise pattern canTick off the seconds on a watchDisplay a letter on a computer display
52ExampleRed light falls normally on a diffraction grating ruled 4000 lines/cm , and the second-order image is diffracted 34 degrees from the normal. Compute the wavelength of light.
53ExampleA single slit of width 0.1 mm is illuminated by parallel light of wavelength 6000 Angstrom, and diffraction bands are observed on a screen 40 cm from the slit. How far is the third dark band from the central bright band?
55ExampleAt what distance could one theoretically distinguish two automobile headlights separated by 1.4m ? Assume a pupil diameter of 6.0 mm and yellow headlights (580 nm). The index of refraction in the eye is approximately 1.33.
56Example: Human eye versus Eagles eye A hang glider is flying at an altitude of H=120m. Green light (555nm)enters the pilot’s eye through a pupil that has a diameter D=2.5 mm. The average index of refraction of the eye is Determine how far apart two point objects must be on the ground if the pilot is to have any hope of distinguishing between them. Do the same calculation for the Eagle’s flying at the same altitude as the glider and with the same refractive index for the eye.