Relate Equations 4.6, 4.7, 4.8 for Refraction Angles | Physics

[kimaru08]

Trying to relate Equation 4.6, 4.7, 4.8 from here: [PLAIN]http://physics.nmt.edu/~raymond/classes/ph13xbook/node35.html[/URL][/b]

Basically trying to relate the deviation angle, incident angle, refractive index and apex angle.

2. The equations are in the link.
3. My attempts are less than fit to be posted, no clue where to begin. I've tried putting in trig identities, and it just not pretty.

If you guys can help in someway greatly appreciate it.Thnx.

 

[malawi_glenn]

what do you want? the deviation angle as a function of incident angle, refractive index and apex angle ?

 

[kimaru08]

Yep, i have no clue how derive though. In my attempts I'm always left with an equation that lacks one of either, D,n, apex angle or incident.

 

[malawi_glenn]

what have you tried, can you post it? You said that you didnt know where to begin.

 

[kimaru08]

Its a derivation, it involves pure algerba especially in this case. The only way( i know at least) to derive equations is through substituting and eliminating certain variables.

And the attempts I've made are just trying plug stuff into 1 equations try to eliminate and so forth. It takes me nowhere though.

Maybe you can point me in the right direction?

 

[malawi_glenn]

how can I point you when I don't even know what you have tried?

and can you state the original problem once again.

 

[kimaru08]

Nvm: I think i got it.

D= theta1 - apex + arcsin [n Sin(apex)Cos(theta2) -cos(apex)Sin(theta1)]

Just need to to get rid of Cos(theta2).