peacock dogbane beetle Thin Film Interference opal
k1 k2 y then if Maxima at:
Reflection from a dielectric slab: Reflectance: Io IR 1 .04 (near normal incidence) .0369 (n = relative index) n .0384 .96 R = 0.04 for glass To consider interference between the front and back reflection, assume they have the same amplitude: 0.04 Io
Dielectric Films n t What is d? Assume near normal incidence: Physical path difference: 2t Optical path difference:
Wait!! Reflections can cause phase shifts! First reflection: p phase shift Second reflection: no phase shift “Reflection” path difference: Total phase difference: Constructive Destructive How does this lead to color?
white n t t = 400 nm, n = 1.515, q = 0 R lo (nm)
normal and 45 degrees 45 0 For varying angle of incidence:
E k Goal: R = 0, T = 1 (Impedance Matching) no ng Can only adjust n
E Antireflection coating k no nf ng
Antireflection coating: two requirements 1. Destructive interference: no = 1.0 t nf = x ns = 1.5
Reflections from the front and back surfaces of a dielectric slab result in two plane waves with an optical path difference and therefore exhibit interference. The interference effects can be engineered to minimize reflectance or produce pretty colors.