I. More on interference, phase, and path length a. Start with geometry determine Δr determine Δδ maybe phasors b. Interference pattern determine Δδ determine Δr geometry (find θ, d, a) c. Δδ = 2π*(Δr/λ) d. Example: Light of 510 nm falls on a barrier with 3 slits spaced 2.5μm from its adjacent slit. A pattern of dots appears on a distant screen determine θ 2 for the 2 nd side max. i. Use b in order to solve ii. Question: what is the phase difference? 1. for constructive: maxima are at even numbers of π a. second side max is at 4π 2. Δr = (Δδ/2π)* λ = (4π/2π)* λ = 2λ 3. distant: Δr = dsinθ 2λ = dsinθ θ = arcsin(2λ/d) θ = arcsin(2*510x10-9 /2.5x10-6 ) = .42 rad or 24 o e. Example: two speaker example i. Use a in order to solve 1. Δr = |r 2 = r 1 | = 5 – 4 = 1m 2. Δδ = 2π*( Δr/ λ) = 2π(1/4) = π/2 rad 3. A tot = Sqrt(A 1 2 + A 2 2 ) = sqrt(2)*A II. Applications a. Concert Halls
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