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Double Slit Diffraction Physics 202 Professor Lee Carkner Lecture 27
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PAL #26 Diffraction Single slit diffraction, how bright is spot 5 cm from center? = 680 nm, a = 0.25 mm, D = 5.5 m Convert y =5 cm to tan = y/D, = arctan (y/D) = 0.52 deg Need to find to find I = ( a/ )sin = 10.5 rad I = I m (sin / ) 2 = 0.007 I m Nearest minima What is m for our ? a sin = m m = (a sin / = 3.33 Between 3 and 4, closer to 3
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Double Slit Diffraction In double slit interference we assumed a vanishingly narrow slit and got a pattern of equal sized (and equally bright) maxima and minima In single slit diffraction we produced a wide, bright central maximum and weaker side maxima The interference maxima are modulated in intensity by a broad diffraction envelope
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Diffraction and Interference
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Double Slit Pattern The outer diffraction envelope is defined by: a sin =m Between two minima, instead of a broad diffraction maxima will be a pattern of interference fringes d sin = m a,d and are properties of the set-up, indicates a position on the screen and there are two separate m’s (one for the diffraction and one for the interference)
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Patterns e.g. You would expect the m = 5 interference maxima would be bright, but if it happens to fall on the m = 3 diffraction minima it will be dark What you see at a certain angle , depends on both of the m’s We can use the location of two adjacent diffraction minima (sequential diffraction m’s) to define a region in which may be several interference maxima i.e. first define the diffraction envelope, then find what interference orders are inside
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Diffraction Envelope
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Diffraction Dependencies For large (d) the interference fringes are narrower and closer together For longer wavelengths the peaks are further apart For solving diffraction/interference problems: Can find the interference maxima with d sin =m There are two different m’s
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Intensity = ( a/ ) sin = ( d/ ) sin The combined intensity is: I = I m (cos 2 ) [(sin / ] 2
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Diffraction Gratings What happens when white light passes through a double slit? But each maxima is very broad and they overlap a lot If we increase the number of slits (N) to very large numbers (1000’s) the individual maxima (called lines) become narrow A system with large N is called a diffraction grating Used for spectroscopy, the determination of a materials properties through analysis of the light it emits at different wavelengths
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Maxima From Grating
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Location of Lines The angular position of each line is given by: d sin = m The m=0 maxima is in the center, and is flanked by a broad minima and then the m=1 maxima etc. Called an order
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Using Gratings Rather than a continuous spectrum of all colors, the gas only produces light at certain wavelength called spectral lines By passing the light through a grating we can see these spectral lines and identify the element Each element has a unique pattern of lines
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Emission Lines of Hydrogen
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Resolving Power and Dispersion What do we want from our grating? Gratings with a high resolving power (R) produce narrow lines R = Nm D = m / (d cos )
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Next Time Final Exam, Monday 9-11am Study, PAL, notes, old tests Bring pencil and calculator
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