Double-slit interference

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Light of one wavelength through **two close, coherent slits** overlaps on a screen to make a row of **equally spaced bright and dark fringes**.

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One of the **bright or dark bands** on the screen in a double-slit (or similar interference) pattern.

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The gap from one **bright** fringe to the **next** bright fringe — the same all the way across the screen.

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$s = \dfrac{\lambda D}{d}$ — **given** in the data booklet (s spacing, λ wavelength, D slit-to-screen distance, d slit separation).

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**s** fringe spacing, **λ** wavelength, **D** slits-to-screen distance, **d** slit separation — all in metres.

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s gets **bigger** — d is on the bottom of s = λD/d, so closer slits give wider fringes.

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s gets **bigger** — λ is on the top, so a longer wavelength widens the fringes.

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They must give light of the **same wavelength** with a **fixed phase relationship**, so the pattern is stable instead of flickering.

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About **θ ≈ λ/d** radians, from d sin θ = nλ with sin θ ≈ θ for small angles.

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The energy 'missing' at the dark fringes is **redistributed into the bright fringes**; the total energy over the whole screen is unchanged.

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**Mixing units** — convert every length to metres (mm = 10⁻³ m, nm = 10⁻⁹ m) before substituting into s = λD/d.

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s = λD/d = (6.0×10⁻⁷ × 2.0) / (0.5×10⁻³) = 2.4×10⁻³ m = 2.4 mm.