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I’m working through Griffiths E&M and on page 408 he gives the boundary conditions for oblique incidence. I’ve spent an hour trying to understand how he goes from the boundary condition $$\epsilon_1(\textbf{E}_{0I} + \textbf{E}_{0R})_z = \epsilon_2(\textbf{E}_{0T})_z$$ to $$\epsilon_1(-E_{0I}\sin{\theta_I}+E_{0R}\sin{\theta_R})=\epsilon_2(-E_{0T}\sin{\theta_T})$$

And I must say I’m miffed. Any help greatly appreciated...enter image description here

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    $\begingroup$ Please let us know what's got you miffed. Perhaps fill in the steps that you would take, and show how you get a different answer. It's hard to help when we don't know what the sticking point is. $\endgroup$ – garyp Jul 29 at 2:00
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I'm guessing that your confusion has to do with not noticing or misinterpreting the subscript "z" in the first equation. It means take the z component of the vector, hence the $\sin(\theta)$ on both sides (the opposite signs on the left side have to do with directions).

If that was not your confusion you will have to be more specific about what it is that confuses you.

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