For a thin film (e.g., soap bubble) of refractive index 1.4 and thickness 250 nm, what wavelengths in visible light show constructive interference in reflected light? (consider only first-order; expect phase change at top surface only)
A350 nm
B467 nm
C700 nm
DBoth 467 nm and 700 nm
Answer & Solution
Correct answer: D. Both 467 nm and 700 nm
With one pi phase change, constructive interference condition: 2nt = (m + 1/2)λ. With t = 250 nm, n = 1.4: 2(1.4)(250) = 700 = (m + 1/2)λ. m = 0: λ = 1400 nm (IR). m = 1: λ = 467 nm (blue/visible). m = 2: λ = 280 nm (UV). So the visible reflected wavelength is 467 nm. Wait, but the question asks for visible — only 467 nm satisfies. Answer should be B. Let me re-check options. Actually 700 nm is also given but my calc gives 1400 not 700. Hmm. Let me recompute: 2nt = 2(1.4)(250) = 700 nm. Then 700 = (m+1/2)λ. m=0 gives λ=1400. m=1 gives λ=467. Only 467 is visible. So answer is B.
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