Transmitted wavelength at glass/air interface using phase continuity

[vera1]

Homework Statement

Find the transmitted wavelength of a normally polarised wave incident at the critical angle at a glass/air interface as a function of n_1, and do the same for an incident angle of pi/3

Relevant Equations

Fresnel's equations and solutions to maxwell's equations in a non-conducting medium

In my electrodynamcis assignment I'm being asked to derive the wavelength of the normally polarised wave transmitted through a glass/air interface as a function of $n_1$ (the refractive index of the first medium) using the concept of phase continuity and the fact that maxima should be equal at the interface. I've tried to derive it and keep getting $\lambda_t = n_1/n_2 \lambda_i$. I've been asked to do this for the critical angle and for an angle of incidence equal to π/3, but I don't see how there can be a difference if Snell's law causes the incident angle to cancel out? I think I'm definitely missing something. We've derived equations for the transmitted, reflected and incident waves in class, as well as Fresnel's equations. To use Snell's law feels a bit below our current level. If it helps, I've calculated the critical angle for the glass/air interface to be 0.729 rad.

Any help would be appreciated, thank you!

 

[kuruman]

Hi @vera1 and welcome to PF.

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