Question 24.2: Interference in a Soap Film GOAL Study constructive interfer...
Interference in a Soap Film
GOAL Study constructive interference effects in a thin film.
PROBLEM (a) Calculate the minimum thickness of a soap-bubble film (n = 1.33) that will result in constructive interference in the reflected light if the film is illuminated by light with wavelength 602 nm in free space. (b) Recalculate the minimum thickness for constructive interference when the soap-bubble film is on top of a glass slide with n = 1.50.
STRATEGY In part (a) there is only one inversion, so the condition for constructive interference is 2n t=(m+{\textstyle{\frac{1}{2}}})\lambda. The minimum film thickness for constructive interference corresponds to m = 0 in this equation. Part (b) involves two inversions, so 2nt = mλ is required.
(a) Calculate the minimum thickness of the soap-bubble film that will result in constructive interference.
Solve 2nt = λ/2 for the thickness t and substitute:
t={\frac{\lambda}{4n}}={\frac{602\,{\mathrm{nm}}}{4(1.33)}}= 113 nm
(b) Find the minimum soap-film thickness when the film is on top of a glass slide with n = 1.50.
Write the condition for constructive interference, when two inversions take place:
2nt = mλ
Solve for t and substitute:
t={\frac{m\lambda}{2n}}={\frac{1~\cdot~(602\,\mathrm{nm})}{2(1.33)}}= 226 nm
REMARKS The swirling colors in a soap bubble result from the thickness of the soap layer varying from one place to another.