- #1

Fjolvar

- 156

- 0

I'm trying to derive/simplify Fresnel's equation for r perp from its form:

[n

to ---> - sin ([tex]\theta[/tex]

From what I've gathered you need to use Snell's law n

and also substitute the identity cos^2[tex]\theta[/tex] = [tex]\sqrt{1-sin^2\theta}[/tex]

I've been playing with the substitutions along with the trig identity Sin (a-b) = sinacosb - cosasinb... but i cannot get it to work. Any help would be greatly appreciated. I'm stuck mostly on getting rid of the square root after making the substitution to get the trig identity form. Thanks.

[n

_{i}cos [tex]\theta[/tex]_{i}- n_{t}cos[tex]\theta[/tex]_{t}] / [n_{i}cos [tex]\theta[/tex]_{i}+ n_{t}cos[tex]\theta[/tex]_{t}]to ---> - sin ([tex]\theta[/tex]

_{i}- [tex]\theta[/tex]_{t}) / sin ([tex]\theta[/tex]_{i}+ [tex]\theta[/tex]_{t})From what I've gathered you need to use Snell's law n

_{t}sin[tex]\theta[/tex]_{t}= n_{i}sin[tex]\theta[/tex]_{i}and also substitute the identity cos^2[tex]\theta[/tex] = [tex]\sqrt{1-sin^2\theta}[/tex]

I've been playing with the substitutions along with the trig identity Sin (a-b) = sinacosb - cosasinb... but i cannot get it to work. Any help would be greatly appreciated. I'm stuck mostly on getting rid of the square root after making the substitution to get the trig identity form. Thanks.

Last edited: