A soap bubble (n = 1.28) having a wall thickness of 116 nm is floating in air. (a) What is the wavelength of the visible light that is most strongly reflected? nm (b) Explain how a bubble of different thickness could also strongly reflect light of this same wavelength. This answer has not been graded yet. (c) Find the two smallest film thicknesses larger than the one given that can produce strongly reflected light of this same wavelength. nm (smaller thickness) nm (larger thickness)

a, b)

The problem is based on interference in thin films

formula for constructive interference

2μ t = (2n + 1) λ / 2, μ is refractive index of layer, t is thickness and λ is wavelength of light.

n is called the order of fringe. If we place n = 0, 1, 2 etc, the thickness also changes. So constructive interference is possible at more than one thickness.

Put the value of λ = 116 nm. μ = 1.28, t = 116 nm in the given equation

2 x 1.28 x 116 x 2 = (2n + 1) λ

593.92 = (2n + 1) λ

when n = 0

λ = 593.92 nm.

This falls in visible range.

c)

2μ t = (2n + 1) λ / 2

Put λ = 593.92 nm, n = 1

2 x 1.28 t₁ = 3 x 593.92 / 2

t₁ = 348 nm.

Put n = 2

2 x 1.28 t₂ = 5 x 593.92 / 2

t₂ = 580 nm.