Using the same two-slit setup with d = 0.25 mm and λ = 600 nm, what is sin θ for the second bright fringe (m = 2)?

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Multiple Choice

Using the same two-slit setup with d = 0.25 mm and λ = 600 nm, what is sin θ for the second bright fringe (m = 2)?

Explanation:
In a two-slit setup, bright fringes occur where the path difference equals an integer multiple of the wavelength, so dsinθ = mλ. Solve for sinθ: sinθ = mλ/d. Convert the values: d = 0.25 mm = 2.5×10^-4 m, λ = 600 nm = 6×10^-7 m, and m = 2. Then sinθ = (2)(6×10^-7) / (2.5×10^-4) = 1.2×10^-6 / 2.5×10^-4 = 4.8×10^-3. So sinθ = 0.0048. This is a small angle, so θ ≈ sinθ ≈ 0.0048 rad ≈ 0.27 degrees.

In a two-slit setup, bright fringes occur where the path difference equals an integer multiple of the wavelength, so dsinθ = mλ. Solve for sinθ: sinθ = mλ/d.

Convert the values: d = 0.25 mm = 2.5×10^-4 m, λ = 600 nm = 6×10^-7 m, and m = 2. Then sinθ = (2)(6×10^-7) / (2.5×10^-4) = 1.2×10^-6 / 2.5×10^-4 = 4.8×10^-3.

So sinθ = 0.0048. This is a small angle, so θ ≈ sinθ ≈ 0.0048 rad ≈ 0.27 degrees.

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