Interference in Thin Films, figuring out the phases

[emmy]

Homework Statement

I don't have a question on a specific problem, I am more caught up in the determination of the phases- I'll give a general problem to use as an example:

In Fig. 35-41, light is incident perpendicularly on a thin layer of material 2 that lies between (thicker) materials 1 and 3. The waves of rays r1 and r2 interfere, and here we consider the type of interference to be either maximum (max) or minimum (min). We are given:

n1=1.32
n2=1.75
n3=1.39
we want to find a max
for the 3rd least thickness of L (in nm)
λ=382nm (in air)

Figure:

rays are tilted for clarity

Homework Equations

Since we want a maximum, the general equation for a maximum would be:
2L=(m+1/2)λ/n2

The Attempt at a Solution

in the case of this problem, we add an additional λ/2 for the incidence of r1 on n2.
so my real question is this-

why is it that you multiply m by 2 to end up with 2m+1 in this case? when do you just use (m+1)λ vs (2m+1/2)λ


I've been reading and researching for hours now, so any help would truly be appreciated.

 

[Simon Bridge]

High-speed to slow speed you get a phase inversion.
http://www.kettering.edu/physics/drussell/Demos/reflect/reflect.html
... it has neat animations of the effect for string, you have to scroll down for the general.

That 2m+1 gives you an odd number - do you see why an odd number is needed?

The trick is to try drawing a wave as it propagates through the film. What happens if it's an even number?