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Agenda Monday –Diffraction – Problems –How small? –How many? Tuesday –Diffraction – Laboratory, Quiz on Interference Wed –Review Fri –Bonus Quiz

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Basic Diffraction Formula x = m (constructive) x = (m+1/2) (constructive) –m integer Open question –What is x?

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Multiple Slits x = m (constructive) x = (m+1/2) (constructive) –m integer Open question – x = dsin

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Equation vs. Experiment Coherent, monochromatic Light wavelength Slits (Turned perp.) Rectangular Screen m 3 2 1 0 -2 -3 dsin( ) = m d

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Examine Situation for Given Laser Means: fixed Coherent, monochromatic Light wavelength Slits (Turned perp.) Screen m 3 2 1 0 -2 -3 dsin( ) = m d

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Range of possible d values? Given: fixed Coherent, monochromatic Light wavelength Slits (Turned perp.) Screen m 3 2 1 0 -2 -3 dsin( ) = m d

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Range of possible d values? Given: fixed dsin( ) = m d = m / sin( ) Anything related to range of d? Try big & small….

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Range of possible d values? Given: fixed dsin( ) = m d = m / sin( ) How big can d be? Pretty big, m can range to infinity…. If d is big, what happens to angle? sin( ) = m /d…. Large slit spacing, all diffraction squeezed together Interference exists – just all overlaps – beam behavior

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Large Distance (Assume large width…) Coherent, monochromatic Light wavelength Slits (Turned perp.) Screen d dsin( ) = m Slit one Slit Two

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Range of possible d values? Given: fixed dsin( ) = m d = m / sin( ) How small can d be? Pretty small, m can be zero How about for anything but m = 0 Smallest m =1 d = /sin( ) d small when sin( ) big, sin( ) <= 1 smallest d for m=1 diffraction: d = Replace: sin( )=m sin( ) = m implies if d =, three diffraction spots if d <, no diffraction (m=0?)

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Range of possible d values? Given: fixed Coherent, monochromatic Light wavelength Slits (Turned perp.) Screen m 1 0 dsin( ) = m d ~

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What Happens? Diffraction from spacing & width –Overlaying patterns, superposition 3 slits, all same spacing –Very similar to two slits Tons of slits, all same spacing –Refined interference. Focused maxima Move screen farther away from slits –Bigger angle/distance on screen Move light source, leave rest same –Nothing

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Resolution When can you identify 2 objects? Coherent, monochromatic Light wavelength Slits (Turned perp.) Screen m 1 0 dsin( ) = m d ~ w ~ Not Here…

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Resolution When can you identify 2 objects? Begin with diffraction Diffraction of light through a circular aperture 1 st ring (spot) sin( ) = 1.22 /D Same setup idea as before

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Resolution When can you identify 2 objects? Begin with diffraction Diffraction of light around a circular block 1 st ring (spot) sin( ) = 1.22 /D Same setup idea as before Things that might cause diffraction rings… Pits/dust on glasses Iris of your eye Telescope Lens Raindrops

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Pretty Picture Moon Raindrop What you see

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Headlights Resolved (barely) Unresolved

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Issue How close must a car be before you can tell it is NOT a motorcycle. (assume both headlights work) sin( ) = 1.22 /D 1.5 m Small Angle sin( ) ~ tan( ) ~ [radians]

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Issue How close must a car be before you can tell it is NOT a motorcycle. (assume both headlights work) = 1.22 /D = y/L What is D? 1.5 m = y Small Angle sin( ) ~ tan( ) ~ [radians] L

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Issue How close must a car be before you can tell it is NOT a motorcycle. (assume both headlights work) = 1.22 /D = y/L pupil: D ~ 5 mm What is ? 1.5 m = y Small Angle sin( ) ~ tan( ) ~ [radians] L

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Issue How close must a car be before you can tell it is NOT a motorcycle. (assume both headlights work) = 1.22 /D = y/L pupil: D ~ 5 mm GREEN ~ 500 nm Calculation Time 1.5 m = y Small Angle sin( ) ~ tan( ) ~ [radians] L

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Issue How close must a car be before you can tell it is NOT a motorcycle. (assume both headlights work) = 1.22 /D = y/L y/L = 1.22 /D L/y = D/(1.22 ) 1.5 m = y Small Angle sin( ) ~ tan( ) ~ [radians] L = 500 nm D = 5 mm

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Issue How close must a car be before you can tell it is NOT a motorcycle. (assume both headlights work) = 1.22 /D L/y = D/(1.22 ) L = Dy/(1.22 ) = 12km ~ 7 miles Little far, but not crazy far aberrations blur image more here 1.5 m = y Small Angle sin( ) ~ tan( ) ~ [radians] L = 500 nm D = 5 mm

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Agenda Monday –Diffraction – Problems Tuesday –Diffraction – Laboratory, Quiz on Interference Wed –Review Fri –Bonus Quiz

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