The Butterfly Wing Mirror · AI Generator #GEN-314CB438
Physics · optics
Problem
The brilliant blue color of a Morpho butterfly wing arises from microscopic structures that act as natural thin-film interferometers. Scientists studying these wings discover that each scale contains regularly spaced ridges with a transparent chitin layer of thickness d=220nm and refractive index n=1.56. Air gaps of the same thickness separate these layers.
When white light strikes the wing at normal incidence, constructive interference produces the characteristic blue color at wavelength λ=480nm in air. However, researchers notice something peculiar: when they immerse a wing sample in water (nwater=1.33), the wing appears to change color.
(a) For the original wing in air, verify that the given parameters produce constructive interference for blue light at λ=480nm.
(b) When the wing is submerged in water, what wavelength in air corresponds to the new color that appears brightest due to constructive interference? Assume the chitin layers remain unchanged but water replaces the air gaps.
(c) The researchers then tilt the submerged wing so that light hits it at an angle θ=30° from the normal (measured in water). At what wavelength does constructive interference now occur?