1. Wave nature of light: Young’s experiment
Physics 123, Spring 2006
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Lecture V

2. EM wave equations
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3. Description of waves using complex numbers
w=2pf – cyclic frequency, k=2p/l –wave vector
E=E0sin(kx+wt+d), d-phase at t=0, x=0 Calculations are greatly simplified by using complex numbers:
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4. Light
Ray model describes light well, when obstacles are large compared to wavelength nm (red-violet)
If this is not the case light should be treated as a wave – EM wave.
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5. Huygens principle
Christiaan Huygens ( ) – wave theory of light
NB. Newton was in favor of corpuscular (particle) nature of light: ironically both are right
Huygens principle – true for any wave
Every point on a wave front can be considered as a source of tiny wavelets that spread out in the forward direction at the speed of the wave. The new front is a superposition of the wavelets
That is why waves can go around obstacles
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6. Longitudinal wave Transverse wave
Matter
Transverse wave
Wave
Matter
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7. Light is a transverse wave
Light = EM wave
Light is a transverse wave
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8. Polarization Since light is a transverse wave it can be polarized.
Y polarization – E oscillates along Y
X polarization – E oscillates along X
Polaroids pick one polarization
Polaroids crossed at 90o block all light
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9. Waves Wave velocity: Wavelength – l, m v=lf Frequency f, Hz
In vacuum v=c
In medium v=c/n
Wavelength – l, m
Frequency f, Hz
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10. Constructive and destructive interference
in phase out of phase not in phase
Constructive Destructive Partially destructive A 2A
<A
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11. Young’s experiment Monochromatic light (same l)
Double slits distance d
Interference pattern
Maxima (bright): d sinq = m l m=0,1,2,3,….
Minima (dark): d sinq = (m+½ ) l
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12. Adding waves
Two waves observed at a certain location, can set it to be x=0: E1=E10sin(wt+kx), E2=E20sin(wt+kx+d)
Suppose for simplicity E10=E20 Add electric fields (principle of superposition):
Amplitude of oscillation 2E0cos(d/2) is determined by the relative phase shift d
Intensity of the sum is proportional to cos2(d/2)
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13. Intensity in Young’s experiment
k=2p/l
E1=E0sin(wt+kl)
E2=E0sin(wt+k(l+Dl))
Phase shift comes from extra travel d=kDl
d=p, if Dl=l/2cos2(d/2)=0
d=2p, if Dl=l cos2(d/2)=1 y Dl
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14. Intensity in Young’s experiment
E=E1 +E2
E=E0 (sin(wt)+sin(wt+d))
q=0 d=0: amplitude E(q=0)=2E0
I(q=0)=4E02
Amplitude E(q)=2E0cos(d/2)
I(q)=4E02 cos2(d/2)
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15. Intensity in Young’s experiment
I(q=0)=4E02
I(q)=4E02 cos2(d/2)
Bright when cos=1, or -1
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16. Young’s experiment lr=700 nm lb=400 nm d=2000nm L=20cm
First fringes (bright spots) yr, yb-?
m=1:
y=L l/d
yr=7cm
yb=4cm
Blue is closer to the center than red
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17. Young’s experiment Interference pattern depends on l
Two different - l1, l2
Distance between slits – d
Multiple slits (diffractive grating)
same pattern, sharper lines
Interference pattern depends on l
Maxima:
d sinq1 = m l1
d sinq2 = m l2
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Lecture V