In the Young’s double slit experiment, one of the slits is covered by a thin film of thickness $d$ and refraction index $n$. I want to determine the phase difference of the waves coming from each slit:
But, having a thin film of refraction index n in front of the second slit, I don’t know how to determine this phase difference. I have searched about this and I found that it would be given by
Where does this formula come from?