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

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

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

Equation vs. Experiment Coherent, monochromatic Light wavelength Slits (Turned perp.) Rectangular Screen m  dsin(  ) = m d

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

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

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

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

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

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?)

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

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

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

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

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

Pretty Picture Moon Raindrop What you see

Headlights Resolved (barely) Unresolved

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]

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

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

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

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

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

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