Download Interference: Phase Differences and Coherence in Wave Systems and more Slides Electrical Engineering in PDF only on Docsity!
LECTURE 26: Interference
http://content.answers.com/main/content/img/CDE/_CDVSDVD.GIF http://www.sonic.net/~ideas/graphics/mma_cd.gif 4/18/12 2
Interference
When two waves with the same frequency f and wavelength combine, the resultant is a wave whose amplitude depends on the phase different, . 4/18/12 3
Interference: Phase Differences
-1.
-0. 0
1
2 0 20 40 60 80 100 Amplitude (arbitrary units) Position (arbitrary units)
0 1 2 3 4 0 20 40 60 80 100 Amplitude (arbitrary units) Position (arbitrary units)
0 1 2 3 0 20 40 60 80 100 Amplitude (arbitrary units) Position (arbitrary units) = 0 or 1 # = 0.5 # = 0.3 # Constructive Interference Destructive Interference 4/18/12 4
Coherence
Infinite coherence length Finite coherence length
Single Photon
4/18/12 5
Intensity of Two Interfering Waves
*Two light waves not in phase:
E 1 = Eo sin ω t
E 2 = Eo sin( ω t + δ )
4/18/12 6
Intensity of Two Interfering Waves
*Maxima occur for: δ = 2 m π
*Minima occur for: δ = ( 2 m + 1 ) π
for m = 0, 1, 2, 3…. 4/18/12 7
Interference
*Three ways in which the phase difference between two waves can change:
- By traveling though media of different indexes of refraction
- By traveling along paths of different lengths
- By reflection from a boundary 4/18/12 8
Interference: Different Indexes of Refraction
*The phase difference between two waves can change if the waves travel through different material having different indexes of refraction. n 1 n 2
N 2 − N 1 =
L
( n 2 − n 1 ) L
4/18/12 13
Interference: Reflection from a Boundary
*The phase difference between two waves can change if one or both are reflected. Reflection Reflection Phase Shift Off lower index zero Off higher index 0.5# 4/18/12 14
Interference: Reflection from a Boundary
*The phase difference between two waves can change if one or both are reflected. DEMO: Soap Bubble Colored interference fringes will be seen on the screen. light beam projector mirror screen soap film 4/18/12 15 QUESTION: Which ray experiences a shift due to reflection? a) Ray 1 b) Ray 2 c) none d) both
Interference: Reflection from a Boundary
*The phase difference between two waves can change if one or both are reflected. Reflection Reflection Phase Shift Off lower index zero Off higher index 0.5# 4/18/12 16
Interference: Soap Bubble
The phase difference between the two waves is caused by:
- Phase shift on reflection for for ray 1 of 0.5 . Ray 2 does not phase shift on reflection.
- Path length difference between ray 1 & ray 2 is 2t. Ray 2 crosses the film twice. For in-phase waves (maxima - bright fringes): For out of-phase waves (minima - dark fringes): Valid for n 2 > n 1 and n 2 > n 3
2 t = ( m +
n 2
2 t = m
λ
n 2
The total difference between ray 1 and ray 2 is the extra difference traveled plus the shift due to reflection.
4/18/12 17
Interference of Reflections from a film of water
4/18/12 18
Interference of Reflections from a film of water
δ from path length difference =
2 t
⎝⎜^
⎠⎟^
2 π, where λ ' =
n
Ray 1: 1800 phase shift from reflection off water surface Ray 2: no phase change going into the water, 180^0 phase change upon reflection from glass. Since both rays are shifted upon reflection the overall difference between the two rays is just the extra path traveled:
∴ constructive interference for 2 t = m λ ', m = 0 , 1 , 2 , 3 ,...
destructive interference for 2 t = m +
⎝⎜^
λ ', m = 0 , 1 , 2 , 3...
4/18/12 19
Newton’s Rings
no phase change 1800 phase ~ zero path change optical flat length difference 4/18/12 20
Newton’s Rings:
Poor quality Excellent quality
Fringes from a wedge-shape film of air indicating how optically flat are the glass plates.
