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**Homework Statement**

A homework problem asks me to find the Fresnel coefficient for a linearly polarised plane wave, which is incident under an angle theta, whose electric field vector can be given as:

*E*=

*E*cos[itex]\hat{s}[/itex]+

*E*sin[itex]\hat{p}[/itex]

[itex]\hat{s}[/itex] and [itex]\hat{p}[/itex] are the unit vectors for s-polarised and p-polarised waves.

**The attempt at a solution**

The previous question on my homework sheet asked me to derive the Fresnel equations for s and p-polarised waves, which I did starting with the bondary conditions. Here, I beleive I have an unpolarised wave. My initial assumption was to take the average of both s and p-polarised light that I worked out previously.

For example,

*r([itex]\theta[/itex]i*)=(

*r*

_{s}+

*r*

_{p})/2

and

*t([itex]\theta[/itex]i*)=1-

*r([itex]\theta[/itex]i*)

However, I'm concerned this is an oversimplification and a more robust approach is in order. I'd love a nudge in the right direction or a thumbs up if my initial approach looks fine.

Thanks.