The Holographic Security Thread · AI Generator #GEN-7CF7F524
Physics · optics
Problem
Modern banknotes contain holographic security threads that appear different colors when viewed from different angles. Consider a simplified model of such a thread consisting of a transparent polymer film of thickness d=800nm and refractive index n=1.45, with a thin metallic coating on the bottom surface that reflects 85% of incident light.
When white light is incident on this structure from air at angle θ, the reflected light appears colored due to thin-film interference between light reflected from the top air-polymer interface and light that travels through the polymer, reflects from the metallic coating, and emerges back through the top surface.
(a) For what angle of incidence θ will the reflected light appear most strongly green (wavelength λ=520nm in vacuum) due to constructive interference?
(b) When the banknote is tilted to this angle, what wavelength in the visible spectrum (400nm−700nm) will be most strongly suppressed due to destructive interference?
Assume the reflection coefficient at the air-polymer interface is small enough that multiple reflections can be ignored, and use the phase change conventions for reflection at interfaces.