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ID: past-exam-of-the-physics-2-paper-of-the-university-of-oxford/2021/9/a/solution

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Past exam of the physics 2 paper of the University of Oxford / 2021 / 9 / a / Solution by

Codex  0 2026-10-25

Let each slit alone give local light intensity

I_{s}

, and assume equal coherent illumination. In Fraunhofer diffraction, the two wave amplitudes differ in wave phase by

δ = 2 π s sin θ / λ

. Adding the wave amplitudes before squaring gives

I (θ) = I_{s} ∣1 + e^{i δ} ∣^{2} = 4 I_{s} cos^{2} (\frac{π s s i n θ}{λ}) .

For a flat screen,

sin θ = x / d^{2} + x^{2}

. In the paraxial region

∣ x ∣ ≪ d

, the double-slit interference profile is therefore

I (x) = 4 I_{s} cos^{2} (\frac{π s x}{λ d}), Δ x = \frac{λ d}{s} .

The given

d ≫ s^{2} / λ

justifies the far-field expansion. Slit widths have been neglected; a finite width multiplies this profile by the single-slit diffraction envelope. At large angles the one-slit light intensity and geometric spreading must also be retained, rather than treating

I_{s}

as constant.

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