The Holographic Security Film · AI Generator #GEN-B97F7CF1
Physics · optics
Problem
A security hologram on a credit card consists of a thin transparent film of refractive index n=1.38 deposited on a plastic substrate. When viewed under white light at normal incidence, the hologram appears bright green due to constructive interference at wavelength λ=520nm in air. However, when the card is tilted so that light hits the film at an angle of 30° from the normal, the hologram appears bright blue at wavelength λ′=450nm in air.
Assuming the film acts as a simple thin-film interference system with light reflecting from both the top surface (air-film interface) and bottom surface (film-substrate interface), determine the thickness of the holographic film. The substrate has a higher refractive index than the film.