# lecture32 - I nter fer ence of Li ght I ntensi ty of doubl...

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Questions: - what is the intensity of the double-slit pattern at an arbitrary position? - What about three slits? I nterference of Light I nterference of Light Intensity of double-slit pattern Three slits

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Young’s Double Slit Experiment Young’s Double Slit Experiment Screen at infinity Path difference Minimum intensity at d θ d sinθ = ( m + ½ ) λ , m = 0, 1, 2, … Δx = d sin θ Maximum intensity at d sinθ = m λ , m = 0, 1, 2, … Δx
Find the intensity of the double-slit interference pattern as a function of position on the screen. where: Two waves: E 1 = E 0 sin( ϖ t ) E 2 = E 0 sin( ϖ t + φ ) 2 2 sin x d π π ϕ θ λ λ = =

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2 2 1 2 0 4 cos ( ) 2 2 with sin R R I E I x d φ π π φ θ λ λ = = = ∆ = Trigonometry: sin a + sin b = 2 cos [(a-b)/ 2] sin [(a+b)/ 2] E 1 + E 2 = E 0 [sin( ϖ t ) + sin( ϖ t + φ )] = 2 E 0 cos ( φ / 229 sin( ϖ t + φ / 2 )] Resultant amplitude E R Resultant intensity, (a function of angle θ to the screen) 2 0 0 with I E =
- fringes are wide, with fuzzy edges - equally spaced (in sin or small ) θ θ - equal intensity position I

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