Not a homwork problem, Fresnel Equations

[Alvis]

Homework Statement

I was just curious, I know you can derive the critical angle using Snell's law..but could you use it using the Fresnel Equations of reflection, both of them?

Homework Equations

|r|=1 internal reflection of light
r(tm)=(n1cos(theta-i)-n2cos(theta-t))/(n1cos(theta-i)+n2cos(theta-t))
r(te)=(n2cos(theta-t)-n1cos(theta-t))/(n1cos(theta-t)+n2cos(theta-i))
I'm putting theta-t and theta-i to denote incident angle and transmittance angle

supposed to arrive at crit angle=arcsin(n2/n1)

The Attempt at a Solution

r(te)=
[(n2cos(theta-t)-n1cos(theta-t))/(n1cos(theta-t)+n2cos(theta-i))]^2=1r(tm)=
[(n1cos(theta-i)-n2cos(theta-t))/(n1cos(theta-i)+n2cos(theta-t))]^2=1

 

[Charles Link]

$R=1$ at the critical angle because $cos(\theta_t) =0$ since $\theta_t=90 \, degrees$. I think it is necessary to use Snell's law to compute the critical angle $\theta_i=\theta_c$. For $\theta_i$ greater than the critical angle, $\theta_t$ does not exist. $\\$ Note: In your very first equation of part 3, I think the first "theta-t" should be a "theta-i". $\\$ Additional note: To get Latex, you need to put " ## " on both sides of the expression.