What is the longest wavelength λλlambda of light that will exhibit constructive interference at normal incidence? The keratin layers are thin enough that you can think of them as representing the surfaces of a 200-nmnm "film" of air.

    λ = 800 10⁻⁹ m

Explanation:

The interference of a thin film has a contribution of pi / 2 in the reflection on the first surface and a contribution by the change of the ode length within the medium, therefore the expression for constructive interference is

              2t = (m + ½) λ

              m = 0, 1,2, ...

Let's clear

             λ = 2t / (m + ½)

To have the highest value of the wavelength m = 0

              λ = 2t / (0+ ½)

              λ = 4 t

Let's calculate

              λ= 4 200 10⁻⁹

              λ = 800 10⁻⁹ m