How do I solve this Thick Film, Double Slit problem?

[jegues]

Homework Statement

See figure attached for problem statement as well as my attempt.

Homework Equations

The Attempt at a Solution

I don't know where to go from here. Can someone help me get started?

 

[ehild]

When light traverses x distance in a medium of refractive index n its phase changes by Edit: 2pi*n*x/lambda (lambda is the wavelength in vacuum).

ehild

 

[jegues]

When light traverses x distance in a medium of refractive index n its phase changes by 2pi*n/lambda (lambda is the wavelength in vacuum).

ehild

So the thickness doesn't relate to its phase change at all? How am I suppose to solve the minimum possible thickness if I can't relate it in any way to the phase change?

 

[ehild]

So the thickness doesn't relate to its phase change at all?

Sorry for the typo. The phase change is 2pi*x*n/lambda.

ehild

 

[jegues]

Sorry for the typo. The phase change is 2pi*x*n/lambda.

ehild

Wow, I actually managed to solve this one...

$$\phi_{1} = \frac{2\pi nx}{\lamda}$$

$$\phi_{2} = \frac{2\pi x}{\lamda}$$

$$\Delta \phi = \frac{2 \pi x (n-1)}{\lamda} = \pi$$

Therefore, 488nm.

Now I just got to figure my other problems out !