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PH 103 Dr. Cecilia Vogel Lecture 8

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Review Outline diffraction interference coherence Diffraction/interference examples double - slit and diffraction grating single slit thin films holograms

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Two-slit interference AKA Young’s experiment Two waves start out in phase, but one travels farther one wave gets behind (analogy: cars) Geometry: slits Observation screen

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Two-slit interference Geometry if slits d and << L difference in distance traveled = d sin or dy / L

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Two-slit interference Constructive interference if difference in distance traveled = integer # of wavelengths d sin = m or dy / L = m Destructive interference if difference in distance traveled = (integer- 1/2 )wavelengths d sin = (m - ½) or dy / L = (m - ½)

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How does interference pattern depend on slit separation? Larger d, smaller y -- fringes closer wavelength? Longer, larger y -- fringes farther longer wavelengths diffract more interference can tell yellow from red +green material? = o /n, shorter Bright fringes: dy/L = m distance between fringes: d y/L = Two-slit interference

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Many-slits = diffraction grating Each pair of slits behaves like double-slit Constructive interference if d sin = m or dy / L = m Destructive interference if d sin = (m - ½) or dy / L = (m - ½) Fringes are in same place as double-slit, but sharper

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Many-slits = diffraction grating How far apart are the slits? Suppose the are 10 lines/cm, then there is one line in 1/10 cm = 0.1 cm the lines are 0.1 cm apart generally d = 1/(number of lines per unit length)

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Single Slit diffraction pattern Dark Fringes occur at (m =integer again) So, width of center bright spot, center How does pattern depend on slit width narrower slit causes more diffraction & wider pattern wavelength longer wavelengths diffract more

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One-slit/Two-slit Confusion Note: W =slit width, but d=slit separation Is the spot bright or dark? Single-slit eqn is for dark (destructive interference) Double-slit eqn is for bright (constructive interference) What values of m are possible? M = all integers for double slit m = integers except zero for single slit Single-slitDouble-slit

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Circular opening diffraction pattern Circular diffraction pattern depends on Aperture radius, a smaller - more diffraction & wider pattern wavelength longer wavelengths diffract more So two objects separated by ½ that can be resolved as separate bright spots = “Rayleigh Criterion”

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Hologram Light wave split in two by half-silvered mirror One part shines on object, then reflects to film = “ object beam“ one part goes directly to film = “reference beam“ Interference of these two waves depends on how much further one travels than the other 3-D shape of the object recorded as Developed film is like a complicated grating When light falls on film, reproduces light from original object

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One more thing about Reflection Wave will change phase by 180 o (i.e. ½ ) if it reflects from material where the wave goes slower (higher n) Wave will not change phase if it reflects from material where the wave goes faster (lower n) Demo

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VERY Thin film When light strikes a thin film at small incident angle, some reflects from top surface, some from bottom surface. If the film is very thin, the only difference between the two reflected waves is if one has a phase change when it reflects. Does each wave experience a phase change?

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VERY Thin Films Constructive interference if both or neither change phase light comes from the smallest n, film is intermediate or light comes from largest n, film is intermediate Destructive interference if film is largest n or film is the smallest n

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Thin Films The two waves also differ in distance traveled by twice the thickness = 2t If difference in distance traveled is integer number of cycles, then same result as very thin film beware: wavelength within film (use n of film) 2t = m /n If difference in distance traveled = integer number of cycles + ½ cycle, then opposite result from very thin film again beware: wavelength within film 2t = (m+½) /n Must know what happens to very thin film 1 st !

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EXAMPLE Antireflective coating: Thin coating of material with n=1.25 on glass (n=1.55) makes 525-nm green light not reflect. How thick should the coating be? 1st: What happens when light from air hits a very thin film like this? n of film is intermediate, so it would be bright. 2nd: To make it dark instead (opposite), it must travel through a thickness given by: 2t = (m-½) /n t = (m-½) /2n=(½)(525nm)/(2(1.25)) = 105 nm =1050 Å

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