Solving Fresnel Coefficient Equations

[Dassinia]

Hello,
1. Homework Statement [/b]

http://imageshack.com/a/img17/2531/gu44.png Uploaded with ImageShack.com
I'm trying to prove this but i didn't succeed

Homework Equations

The Attempt at a Solution

For the t I multiplied by sin(θt) in the numerator and denominator and used
sin(a) * cos(b) = 1/2 × (sin(a+b) + sin(a-b))
I ended with a 4cos(θt)sin(θi)/[sin(θi+θt)+sin(θt-θi)] but then ?
For r I don't even know how to start

Thanks

 

[ehild]

Hello,
1. Homework Statement [/b]

http://imageshack.com/a/img17/2531/gu44.png Uploaded with ImageShack.com
I'm trying to prove this but i didn't succeed

Homework Equations

The Attempt at a Solution

For the t I multiplied by sin(θt) in the numerator and denominator

ehild


That is all right, but use Snell's Law n_isin(θi)=n_tsin(θt) after, and see if you can simplify...

ehild

 

[Dassinia]

and for r, how can I start

 

[ehild]

The same way.

ehild

 

[Nickie]

for sharing your attempt at solving the Fresnel coefficient equations. It seems like you are on the right track by using the trigonometric identity for sin(a) * cos(b). However, in order to solve these equations, you will need to use the boundary conditions at the interface between two media. This means taking into account the refractive indices of the two media and the angle of incidence. You can also use the Fresnel equations, which relate the incident, reflected, and transmitted amplitudes of light at a boundary between two media. I suggest reviewing these equations and the boundary conditions to help you continue with your solution. Keep up the good work!