A manufacturer produces a transparent polymer film of thickness that is intended to…
PHYSICS · Multi-part · AP · Physics 2: Algebra-based · Waves Sound and Physical Optics · Waves Sound and Physical Optics
Problem
A manufacturer produces a transparent polymer film of thickness t=400nm that is intended to serve as a decorative color-shifting surface. The index of refraction of the polymer is not constant but varies with wavelength according to the empirical relation
n(λ)=1.30+λ21.0×104
where λ is expressed in nanometers. White light is incident normally from air onto the film, which is backed by a mirror so that only the first two reflected rays (from the top surface and from the mirror-backed bottom surface) need be considered.
(a) Derive an expression that relates the constructive-interference order m (an integer), the wavelength in air λ, the film thickness t, and the wavelength-dependent index n(λ) for normally incident light in this configuration.
(b) Using m=1, estimate the wavelength (in air) that will appear brightest in reflection. Show how you incorporate the dispersion of the index in your calculation.
(c) Repeat the calculation in part (b) for m=2 and give the corresponding wavelength.
(d) Compare the spacing between the two wavelengths you obtained with the spacing that would result if the index were wavelength-independent, and discuss qualitatively how dispersion influences the range of colors seen from the film.