Phase shift upon reflection

Gold Member
Its always said that a reflected light ray acquires a phase shift equal to ## \pi ## if ## n_1 < n_2 ##. But considering the Fresnel coefficients, its revealed that its only for the s-polarization reflection coefficient that ## n_1 < n_2 ## causes the coefficient become negative. The p-polarization reflection coefficient becomes negative only when ## \sin^2 \theta_1 > \frac{1}{1+(\frac{n_1}{n_2})^2} ##. So why the first sentence doesn't distinguish different polarizations?
Thanks

blue_leaf77
Homework Helper
I guess the author implicitly assumes normal incidence.

Gold Member
I just found* that the p reflection coefficient becomes negative when ## n_2 < n_1 ##, exactly the opposite condition for s reflection coefficient!

*## n_2 \cos\theta_1<n_1 \cos\theta_2 \Rightarrow \frac{n_2}{n_1} \cos\theta_1 < \cos\theta_2 \Rightarrow \sin\theta_1\cos\theta_1 < \sin\theta_2 \cos\theta_2 \Rightarrow \sin{2\theta_1} < \sin{2 \theta_2} \Rightarrow \\ \theta_1 < \theta_2 \Rightarrow n_2 < n_1##

blue_leaf77