Welcome,
Guest
. Please
login
or
register
.
1 Hour
1 Day
1 Week
1 Month
Forever
Enter your search terms
Submit search form
Web
Beg For Mercy
News:
BFM 15 Years Racing***Founded May 2005***
BFMracing
»
General Category
»
General Board
»
Homework Haven
»
Snell's Law Variation
« previous
next »
Pages: [
1
]
Author
Topic: Snell's Law Variation (Read 3835 times)
BFM_Edison
Captain
Posts: 3074
Snell's Law Variation
«
on:
September 25, 2008, 02:25:18 PM »
You probably know what Snell's Law is if you're looking at this thread. As a refresher, here is the wikipedia page on it:
http://en.wikipedia.org/wiki/Snell's_Law
I'd rather you not give me a direct answer to this question (assuming there is one). We'll use this general form for Snell's Law: n
1
sin(theta
1
) = n
2
sin(theta
2
) where the two thetas are the angles with respect to the normal. What I'm trying to know is if there is a way to define cos(theta
2
) in terms of n
1
, n
2
, and cos(theta
1
). If not, give me a hint as to how to show why this is the case. Then I can decide whether to go into reflection off of surfaces in 3-space and possibly n-space.
Logged
52.87
60.07
46.40
72.73
68.23
55.10
98.27
84.73
Goalie
Posts Too Much
Posts: 2462
Congrats Jordan Lynch, 3rd place in Heisman!!!
Re: Snell's Law Variation
«
Reply #1 on:
September 25, 2008, 03:32:14 PM »
Let's say that x
2
=y
2
. Couldn't you square both sides and then use Pythagorean identities to solve for cos(theta
1
)? That's what I'd do, anyway, even if it is a bit messy.
Logged
You blame me? Remember it had to get past 10 other players before I saw the ball.
Thanks to Spidey for this sig!
.
BFM_Edison
Captain
Posts: 3074
Re: Snell's Law Variation
«
Reply #2 on:
September 25, 2008, 03:54:52 PM »
Not sure what x and y are referring to. Anyways, I've done some proof similar to the normal derivation, but there's definitely something wrong with it and for some reason I'm not seeing it. Hay, I has idea. Nvm. But it can't involve using the normal equation and squaring it. The final solution can't have any absolute values, squares, or square roots. Need to keep the sign correct. Or will it work. Hmmmm. Will have to test it out vector-wise. No, doesn't look like it will work.
Now tell me what's wrong with this proof here please. Line number only is fine.
http://img516.imageshack.us/img516/238/failproofri1.jpg
Logged
52.87
60.07
46.40
72.73
68.23
55.10
98.27
84.73
Goalie
Posts Too Much
Posts: 2462
Congrats Jordan Lynch, 3rd place in Heisman!!!
Re: Snell's Law Variation
«
Reply #3 on:
September 25, 2008, 09:37:35 PM »
The only thing that I see is that you made a comment next to line 5 about what looks like the derivitive of (l-x)
2
. But I could not find this applied to the equation anywhere.
That's the only thing I see. I could bring it into my Calc III class tommorrow and see what my professor says.
Logged
You blame me? Remember it had to get past 10 other players before I saw the ball.
Thanks to Spidey for this sig!
.
BFM_Edison
Captain
Posts: 3074
Re: Snell's Law Variation
«
Reply #4 on:
September 26, 2008, 05:58:21 AM »
That was just a little test to make sure that it went negative and had a two since I couldn't figure the error out.
And I'll be bringing it to my Physics teacher today.
Logged
52.87
60.07
46.40
72.73
68.23
55.10
98.27
84.73
Pages: [
1
]
« previous
next »
BFMracing
»
General Category
»
General Board
»
Homework Haven
»
Snell's Law Variation