Anti-reflective coating confusion

[Solarmew]

My professor confused me today :(
I'm trying to figure out the thickness of an anti reflection coating and it looks like from the equation
2ndcos(Θ) = mλ
that for a given λ the thickness of the film should increase for incidence slightly away from normal.
But he said that intuitively it should decrease because the waves now have to travel a longer distance through the material... which kinda makes sense, but contradicts the equation.
Could someone please explain to me exactly what it happening and whether the thickness should be expected to increase or decrease if we increase the angle and why?
@.@

 

[Doc Al]

My professor confused me today :(
I'm trying to figure out the thickness of an anti reflection coating and it looks like from the equation
2ndcos(Θ) = mλ
that for a given λ the thickness of the film should increase for incidence slightly away from normal.
But he said that intuitively it should decrease because the waves now have to travel a longer distance through the material... which kinda makes sense, but contradicts the equation.
Could someone please explain to me exactly what it happening and whether the thickness should be expected to increase or decrease if we increase the angle and why?
@.@

The distance that the 2nd reflected wave travels through the film will increase, but that's not the full story. You also need to consider the extra distance the first reflected wave must travel (due to things being at an angle).

Follow the derivation, given here: Interference Condition for Thin Films