PH 103 Dr. Cecilia Vogel Lecture 11

Review Outline  Interference  Coherence  double-slit  diffraction grating  Spectral analysis  Cool stuff  diffraction  resolution

Interference  If two hoses spray water at a wall, twice as much water. 1+1=2  If two waves strike a wall, add wave functions. 1+1=… anywhere from 0 thru 4!!

Constructive Interference  Occurs when crest meets crest and trough meets trough:  waves are in phase  Overall intensity (brightness) is four times as bright as a single wave

Destructive Interference  Occurs when crest meets trough:  waves are ½-cycle (180 o ) out of phase  Overall intensity (brightness) is 0!

Interference Generally  Also, can have anything between fully constructive and fully destructive.  Waves might be out of phase, but not 180 o out of phase.  For two beams of equal amplitude,  you can have brightness that is anything from 0 to 4 times as bright as one beam.

Incoherence  Do you see interference between two light bulbs?  No!  Light from bulb is produced by many atoms  each atom doing its own thing.  So phase changes randomly and rapidly.  Waves go in and out of phase -- bright to dark -- faster than we can observe Bright Dark kinda Bright See average of brightness (0 thru 4) = 2 times as bright

Coherence  How do you get two waves that are coherent?  Take one source, split it, bring it back together  Then when one wave changes randomly,  the other does the same thing!  They stay in phase or out of phase or whatever.

Coherence  How do you get two waves that are coherent?  Take one source, split it, bring it back together Examples:  light passing through two (or more) slits  light passing around opposite sides of obstacle  light reflecting from top and bottom surface of thin film  light passing through and reflecting from a partially-silvered mirror

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 

Two-slit interference  Geometry: d=distance btwn slit centers  if slits d and << L  difference in distance traveled ≈  d sin   or dy / L

Two-slit interference  Constructive interference if difference in distance traveled = integer # of wavelengths – BACK IN PHASE  d sin  = m  or dy / L = m  Destructive interference if difference in distance traveled = (integer- 1/2 ) wavelengths – ½-CYCLE OUT OF PHASE  d sin  = (m-1/2)  or dy / L = (m-1/2)

How does interference pattern depend on  slit separation?  Larger d, smaller y &  y -- fringes closer  Wavelength?  Longer, larger y &  y -- fringes farther  longer wavelengths diffract more  Bright fringes: y = m L/d m= integer =“order” 1 st fringe from center is 1 st order, etc  Distance between fringes:  y = L/d Two-slit interference

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-1/2)  or dy / L = (m-1/2)  Fringes are in same place as for double-slit, but sharper

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

Diffraction Spectrum  Because the position of the bright fringes  depends on wavelength,  shorter wavelengths at smaller angles,  different colors show bright at different positions,  thus spreading light into its spectrum of wavelengths

Spectral Analysis  Diffraction grating’s spectrum can be used to analyze the source of the light  Is the spectrum a single wavelength?  probably a laser  Is the spectrum made up of bands of color?  could be fluorescence  Is the spectrum continuous?  probably created by a hot solid or liquid or plasma

Spectral Analysis  Diffraction grating’s spectrum can be used to analyze the source of the light  Is the spectrum continuous?  probably created by a hot solid or liquid or plasma  Is the spectrum continuous, but with some lines missing?  probably created by a hot object as above  but there is a cool gas* between you and the source & that gas absorbs some wavelengths  Is the spectrum made up of individual lines of color?  probably made by a glowing gas* *The wavelengths of the lines identifies the gas

Beyond slits  If pattern of openings is bunch of slits  light is spread perpendicular to slit axis  If pattern of openings is more interesting  light is spread into a more interesting pattern!  exs:  Laser pointer patterns  Holograms  Computer generated holograms