# 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
Homework Helper
What does it have to do with the original problem?

Gold Member
It seems we have two conditions that result in ## r_p < 0## but only one for ## r_s<0 ##. So we have the following situations:
1) ## n_1 < n_2 ## and ## \sin^2{\theta_1}<\frac{1}{1+(\frac{n_1}{n_2})^2} ##: Only the s polarization shifts phase upon reflection.
2) ## n_1 < n_2 ## and ## \sin^2{\theta_1}>\frac{1}{1+(\frac{n_1}{n_2})^2} ##: Both polarizations shift phase upon reflection.
3) ## n_1 > n_2 ##: Only p polarization shifts phase upon reflection.
Well, at least now I have a clearer view. I'm beginning to think that the optics textbooks implicitly assume the light ray to have s polarization. Am I overestimating the number of textbooks that claim ## n_1 < n_2 ## means there is a phase shift upon reflection? Actually someone asked me this question and I remember in my own optics course that the professor kept repeating that there is phase shift when ## n_1 < n_2 ##. This is also abundant on the internet(this, this, this and this). But I don't remember whether textbooks claim as such or not. It seems to me that textbooks get it right but it became a misunderstanding among people.

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