a physics 2 question, yiikes. hard.?

Question

A mixture of red light (vacuum = 661 nm) and green light (vacuum = 551 nm) shines perpendicularly on a soap film (n = 1.35) that has air on either side. What is the minimum nonzero thickness of the film, so that destructive interference causes it to look red in reflected light?

Answer 1

The film thickness must be 1/2 wavelength for destructive interference:
2(1.35)t = 551/2
t = 10.185 nm

Answer 2

You want to absorb the green light, which means that the round trip through the film must be some multiple of a half wavelength, or a quarter wave each way. The wavelength in the film is smaller than the vacuum wavelength by a factor of 1.35, so if you do the appropriate arithmetic, you'll get the answer.