Question

A film of soapy water on top of a plastic cutting board has a thickness of 255 nm. What wavelength and color is most strongly reflected if it is illuminated perpendicular to its surface?

Answer 1

the reflected wavelength is lano = 4.55 10⁻⁷ m which corresponds to the blue color

Step-by-step explanation:

This is a case of reflection interference, we must be careful

* There is a 180º phase change when light passes from the air to the soap film (n = 1,339), but there is no phase change when passing from the pomp to the plastic (n = 1.3)

* the wavelength within the film is modulated by the refractive index

λₙ = λ₀ / n

if we consider these relationships the condition for constructive interference is

2 t = (m + ½) λₙ

2t = (m + ½) λ₀ / n

λ₀ = 2t n / (m + ½)

we substitute the values

λ₀= 2 255 10⁻⁹ 1,339 / (m + ½)

λ₀ = 6.829 10⁻⁷ (m + ½)

let's calculate the wavelength for various interference orders

m = 0

λ₀ = 6.829 10⁻⁷/ ( 0 + ½ )

λ₀ = 13.6 10⁻⁷

it is not visible

m = 1

λ₀ = 6,829 10⁻⁷/ (1 + ½)

λ₀ = 4.55 10⁻⁷

color blue

m = 2

λ₀ = 6.829 10⁻⁷ / (2 + ½)

λ₀ = 2,7 10⁻⁷

it is not visible

therefore the reflected wavelength is lano = 4.55 10⁻⁷ m which corresponds to the blue color