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Unformatted text preview: 29. We take the electric ﬁeld of one wave, at the screen, to be
E1 = E0 sin(ωt)
and the electric ﬁeld of the other to be
E2 = 2E0 sin(ωt + φ) ,
where the phase diﬀerence is given by
φ= 2πd
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. 2E E φ αE
ωt Here d is the centertocenter slit separation and λ is the wavelength. The resultant wave can be written
E = E1 + E2 = E sin(ωt + α), where α is a phase constant. The phasor diagram is shown above. The
resultant amplitude E is given by the trigonometric law of cosines:
2
2
2
E 2 = E0 + (2E0 )2 − 4E0 cos(180◦ − φ) = E0 (5 + 4 cos φ) . The intensity is given by I = I0 (5 + 4 cos φ), where I0 is the intensity that would be produced by
the ﬁrst wave if the second were not present. Since cos φ = 2 cos2 (φ/2) − 1, this may also be written
I = I0 1 + 8 cos2 (φ/2) . ...
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 Fall '08
 SPRUNGER
 Physics

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