Interference and Diffraction. Conditions for Interference Coherent Sources - The phase between waves...
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Interference and Diffraction
Conditions for Interference
• Coherent Sources - The phase between waves from the multiple sources must be constant.
• Monochromatic - Wavelength from the sources must be of the same wavelength.
Interference• Remember the Superposition Principle
Constructive
Destructive),2,1,0( 12 nnrr
),2,1,0( 21
12 nnrr
#1
#2
r1
r2Source
Effect
Double Slit Interference
• Young’s Double-Slit Experiment• Two slits act like coherent sources• Assumption: d >> • Difference in path traveled is
• Constructive Interference sind
,...)2,1,0( sin mmd
d
Small Angle Approximation
• When << 1, then
and d L
ym = 1
m = 2
m = 0
m = -1
m = -2
tansin
mdLybright
21 m
dLydark
Intensity• Phase between waves from slits is
• Use a phasor diagram to predict the intensity
Ldy
22
E1
E2
tEE sin01
tEE sin02
2sin
2cos2 0
tEEsum
LdySSsum
20 cos4c
ES0
20
0 2
12
0-1
-2
Multiple Slits• 2 Slits
E1
E2
12
0-1
-2
12
0-1
-2
12
0-1
-2
• 4 Slits
• 3 Slits • Diffraction Grating
E1
E2
E3
E1
E2
E3
E4
mN
Resolving Power
Thin Films• Constructive interference between waves reflecting
off the top and bottom surfaces.
212 mtn
180° Phase Shift
0° Phase Shiftt
m - whole number
Single-Slit Diffraction
• Huygen’s Principle - Each point along the wave re-emits spherical waves.
m = -1
m = -2
d L
ym = 1
m = 2Destructive Interference
md sinIntensity
2
0 2/2/sin
SS
sin2 d
Resolution• Rayleigh Criterion - Can resolve two images if
the maximum of one image falls on the first minimum of another image.
a min
Slit resolution
Circular Aperture
D 22.1min
m
Resolving Detail• Detail at a distance can be
calculated by
• What detail can you see at 1 km (103m) with green light (500 nm)? (Let D=0.30cm)
rs minr
m s
Circular Aperture
D 22.1min
Interferometer• Comparing light from two separate
telescopes to increase the resolving power.• Very Large Array – Radio TelescopeVery Large Array – Radio Telescope
– 27 radio antennas in a Y-shaped 27 radio antennas in a Y-shaped – Fifty miles west of Socorro, New MexicoFifty miles west of Socorro, New Mexico– Each antenna is 25 meters in diameterEach antenna is 25 meters in diameter– Resolution of an antenna 36km acrossResolution of an antenna 36km across– Sensitivity of a dish 130 meters in diameter.Sensitivity of a dish 130 meters in diameter.
Diffraction and Interference
• Small regularly spaced openings result in bright spots.– Diffraction Grating
• Spacing of spots depend on distance between openings.– Crystallography