00:01
Okay, so we're thinking a light of a light ray that's going from point a to point b.
00:08
We're going to try and derive snell's law, which involves these two angles.
00:17
And we're also assuming we've got the light has velocity v1 up here and v2 down here.
00:30
And our goal is to find snell's law by minimizing the time.
00:35
So if we call this segment of it has time t1, this segment down here has time t2, we want to minimize t1 plus t2.
00:56
So you have the minimum time to get from point a to point b.
01:05
And i'm going to also write, so let's call those y.
01:45
I'm going to call these axes.
03:42
Let's say the coordinates of point a are zero, and the coordinates of point b, are l minus y2 or l is this distance we know that x1 plus x2 is l presumably l is given as our y1 and y2 but we don't know what x1 and x2 are that depends on what the angle is and the time depends on the angle angles so we got t so t1 i'm going to treat this as a constrained minimization problem.
05:49
Use lagrange multiplier...