The Holographic Security Strip · AI Generator #GEN-B5FDA1C3

Physics · optics

Problem

A security strip on a credit card uses a thin film hologram to prevent counterfeiting. The hologram consists of a transparent polymer film of thickness d=2.4  μmd = 2.4\;\text{μm} and refractive index n=1.6n = 1.6, deposited on a reflective metal backing. When white light illuminates the strip at normal incidence, constructive interference occurs for reflected light at wavelength λ=600  nm\lambda = 600\;\text{nm} (orange), creating a bright orange appearance. A counterfeiter attempts to reproduce this effect but only has access to a polymer with refractive index n′=1.4n' = 1.4. To match the original orange reflection at λ=600  nm\lambda = 600\;\text{nm}, what thickness d′d' should the counterfeiter use for their film?

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