PH 103

Dr. Cecilia VogelLecture 11

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

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