Date post: | 21-Dec-2015 |
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Review
Outline Interference Coherence double-slit diffraction grating
Spectral analysis Cool stuff
diffraction resolution
InterferenceIf 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 (180o) 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 180o 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 atomseach 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
BrightBrightDark
kindaBright
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
togetherExamples: 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
Observationscreen
Two-slit interference Geometry: d=distance btwn slit centers if slits d and << L difference in distance
traveled ≈ dsin or dy/L
Two-slit interference Constructive interference if difference in
distance traveled = integer # of wavelengths – BACK IN PHASE
dsin = m or dy/L = m
Destructive interference if difference in distance traveled = (integer-1/2) wavelengths – ½-CYCLE OUT OF PHASE
dsin = (m-1/2) or dy/L = (m-1/2)
Ld
& ifonly
Ld
& ifonly
How does interference pattern depend onslit separation?
Larger d, smaller y & y -- fringes closerWavelength?
Longer , larger y & y -- fringes fartherlonger wavelengths diffract more
Bright fringes: y = mL/dm= integer =“order” 1st fringe from center is 1st 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 dsin = m or dy/L = m
Destructive interference if dsin = (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