1. Sep 13, 2008

### bcjochim07

1. The problem statement, all variables and given/known data

A soap bubble is essentially a very thin film of water (n=1.33) surrounded by air. The colors thata you see in the soap bubbles are produced by interference.

Derive an expression for the wavelengths for which constructive interference casues a strong reflection from a soap bubble of thickness d.

2. Relevant equations

3. The attempt at a solution
2pi* m = 2pi*2d/(lambda/n) + intial phi = phase shift

In this case, when the light reflects off the bubble, the wave is shifted by pi, but when the waves go through the bubble reflect at the second water-air interface, the waves aren't shifted by pi, so the initial phase difference is equal to pi

2pi*m = 2pi*2dn/lambda + pi

pi(2m-1) = 4pi*dn/lambda

.5(m-.5) = dn/lambda

lambda= 2.66d/(m-.5) Is this right?

2. Sep 21, 2008

### bcjochim07

could someone please check my answer? I would really appreciate it. Thanks.

3. Sep 23, 2008

### bcjochim07

Please? I really would like to know.

4. Sep 23, 2008

### n0_3sc

ok firstly, are you only considering normal incidence?

secondly, I derived it and got:
$$d = (2m \pm 1)\frac{\lambda_s}{4}$$
$$\lambda_s$$ is the wavelength in the soap.
Which is the same as yours if you don't divide everything by 2 in your equation.

Also, derivation for thin films is very nicely shown on page 393-395 in "OPTICS" by "E. HECHT"