Interference of Xrays from a salt crystal

[user3]

Hello,

In my textbook(Serway), Constructive interference of two rays hitting the first and the second planes , respectively, of a crystal lattice is derived as 2dsin(Θ)=mλ , where Θ is the angle shown in the picture.

My question is: shouldn't the equation be 2dsin(Θ) = (m+1/2 )λ instead? because the salt crystal is a "heavier" (larger refractive index) medium than air, so the first ray exhibits a 180 degrees phase shift.

 

[TSny]

Hi user3. Welcome to PF!

Here's one way to think about it. In x-ray diffraction you are considering reflection from successive planes in a family of planes which are oriented in the same way. How would you expect the lattice planes in the family to compare with one another in their reflective properties. In particular, if there is a phase shift of ø when the radiation reflects off one of the planes, what would you expect the phase shift to be when the radiation reflects off other planes in the family?

 

[user3]

I got it! Thank you.