The Oscillating Soap Bubble Interferometer · AI Generator #GEN-20EC1238

Physics · optics

Problem

A soap bubble of radius R=2.5  cmR = 2.5\;\text{cm} oscillates radially with small amplitude due to thermal fluctuations. The bubble wall has refractive index n=1.33n = 1.33 and thickness d=180  nmd = 180\;\text{nm}. When illuminated with coherent light of wavelength λ=550  nm\lambda = 550\;\text{nm} in air, the reflected light shows constructive interference. During oscillation, the bubble radius changes by ΔR=0.8  mm\Delta R = 0.8\;\text{mm} from its equilibrium value. Assuming the bubble wall thickness changes proportionally with the radius (constant volume density), and that the refractive index remains constant: (a) Find the phase change in the reflected light when the bubble expands by ΔR\Delta R. (b) If the bubble oscillates sinusoidally at frequency f=25  Hzf = 25\;\text{Hz}, determine the time-averaged intensity of the reflected light as a fraction of the maximum possible intensity, assuming the light detector integrates over many oscillation cycles.

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