Question

A soap bubble is 103 nm thick and illuminated by white light incident perpendicular to its surface. What wavelength (in nm) and color of visible light is most constructively reflected, assuming the same index of refraction as water (nw = 1.33)?

Answer 1

Answer:

λ = 547.96 nm

Explanation:

given,

thickness of soap bubble = 103 nm

refractive index of thin film = 1.33

using formula of constructive interference

$2 n t = (m + \dfrac{1}{2})\times \lambda$

t is thickness of the medium

n is refractive index

m = 0,1,2...

now,

$2 n t = (m + 0.5)\times \lambda$

at m = 0

$2\times 1.33 \times 103 =0.5\times \lambda$

λ = 547.96 nm

at m = 1

$2 n t = (m + 0.5)\times \lambda$

$2\times 1.33 \times 103 =1.5\times \lambda$

λ = 182.65 nm

the only visible light enhanced by the thin film is of wavelength

λ = 547.96 nm