Soap films

QUESTION: A portion of a soap bubble appears green (wavelength = 500 nm) or 500 x 10^-9 in a vacuum when viewed at normal Incidence in white light. Find the TWO smallest non-zero thicknesses for the soap film if the refractive index is 1.40?

Answer

The formula that gives the maximum for interference in a soap bubble film is:

2 x refractive index x film thickness = (m + ½ ) x wavelength

where m is an integer (0, 1, 2 …etc)

Therefore:
2 x 1.4 x film thickness = (m + ½ ) x 500 x 10^-9

For the first possible thickness m = 0

So: Film thickness = [500 x 10^-9]/5.6 = 8.93x10^-8 m

For the second possible thickness m = 1

So: Film thickness = 3x[500 x 10^-9]/5.6 = 2.68x10^-7 m



For further details of soap film interference see: Thin films