Soap bubbles can display impressive colors, which are the result of the enhanced reflection of light of particular wavelengths from the bubbles/' walls. for a soap solution with index of refraction of 1.06, find the minimum wall thickness that will enhance the reflection of light of wavelength 725 nm in air.

5.1297*10^-7 m

Explanation:

As mentioned before, "enhanced" means constructive interference. Since the air has a lower index of refraction than the soap, there is phase shift when light hits the film. Then there is another phase shift from the soap to air because the index of refraction is higher in the soap than air. Since you want the thinnest wall, use m = 1 This gives us the equation:

2t = λ (m + 0.5)

Calculate λ

λ = λm / n = (725*10^-9m) / (1.06)

λ = 6.8396*10^-7m

Finally calculate t:

2t = 6.8396*10^-7m * (1+0.5)

t = 5.129716981*10^-7 m = 513 nm