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Suppose TEM wave in +z normal to a boundary on xy plane at z=0. We know

1) How do I know why the reflected

2)From boundary condition, tangential

3) Books always use ##\vec E_i,\;\vec E_r,\hbox{ and }\;\vec E_t## to derive

4) The transmitted ##\vec H_t=\hat z \times \hat x H_t## because the transmitted EM wave in medium 2 is in +z direction and the ##\vec E_t## in +x direction?

5) Is this kind of boundary condition holds even in Oblique incident where the tangential ##E_r## always the same direction as tangential ##E_i##? And tangential ##H_r## is always opposite direction to tangential ##H_i##?

Thanks

**E**&**H**are tangential to the boundary. Let ##\vec E_i=\hat x E##, be the incident wave towards the boundary therefore incident**H**is ##\vec H_i =\hat z\times \hat x \frac {E_i}{η}=\hat y H##. I have a few questions:1) How do I know why the reflected

**E**is ##\hat x E_r##? How do I determine the direction of ##\hat E_r=\hat x##? Why it's not ##-\hat x##?2)From boundary condition, tangential

**E**is continuous cross boundary. Is this the reason the transmitted**E**is ##\hat x E_t## where it follows the direction of ##\vec E_i##?3) Books always use ##\vec E_i,\;\vec E_r,\hbox{ and }\;\vec E_t## to derive

**H**for incident ##\vec H_i##, reflected ##\vec H_r##, and transmitted ##\vec H_t## respectively. Is that the reason why ##\vec H_r=(-\hat z \times \hat x) H_r##? where ##-\hat z## from the direction of the reflected wave(-z) and ##\hat x## is the direction of the ##\vec E_r##?4) The transmitted ##\vec H_t=\hat z \times \hat x H_t## because the transmitted EM wave in medium 2 is in +z direction and the ##\vec E_t## in +x direction?

5) Is this kind of boundary condition holds even in Oblique incident where the tangential ##E_r## always the same direction as tangential ##E_i##? And tangential ##H_r## is always opposite direction to tangential ##H_i##?

Thanks

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