Question 24.2: Interference in a Soap-Film Goal Calculate interference effe...
Interference in a Soap-Film
Goal Calculate interference effects in a thin film when there is one phase reversal.
Problem 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 \mathrm{~nm} in free space.
Strategy There is only one inversion, so the condition for constructive interference is 2 n t=\left(m+\frac{1}{2}\right) \lambda. The minimum film thickness for constructive interference corresponds to m=0 in this equation.
Remark The swirling colors in a soap bubble are due to the fact that the thickness of the soap layer varies from one place to another.
Solve 2 n t=\lambda / 2 for the thickness t, and substitute:
t=\frac{\lambda}{4 n}=\frac{602 \mathrm{~nm}}{4(1.33)}=113 \mathrm{~nm}