Double-slit problem with incident and refracted angles

[Taulant Sholla]

Homework Statement

For the given configuration, the path difference between the 2 rays is given as δ=dsinθ₁ - dsinθ₂

Homework Equations

Small angle approximation?

The Attempt at a Solution

I'm used to seeing a double-slit situation where only the exit angle is specified, and thus path difference is simply δ=dsinθ. Here, though, we have an incident and refracted θ₁ and θ₂. Any hints at deriving the following will be appreciated:

δ=dsinθ₁ - dsinθ₂

 

[Brian T]

Here's a question for you, why do you think one term is positive while the other is negative (i.e. what does it mean physically)?