00:01
In this problem, we're considering refraction.
00:05
So let's start by drawing a picture of the situation.
00:09
We've got light that's traveling through air into water.
00:17
We know the index of refraction of air.
00:21
I'm going to label that n1.
00:23
And for water, i'm going to label that n2, where n1 is equal to 1 and n2 is equal to 1.
00:32
Point three three.
00:35
You know that the light is going to strike at point a so let's label that and the angle of incidence is 55 degrees so let's draw in our normal here is our white and we know that this angle which i'm going to label theta one actually let me draw that in black is 51 degrees or 55 degrees sorry okay we're then told the depth of the lake is three meters so i'll add that to my diagram here and on the bottom directly below point a is a point point b if refraction didn't occur we want to know how far away from point b with the laser beam strike the lake bottom.
01:48
So if refraction didn't occur, then our light would just continue on in a straight line like this.
01:55
And we want to figure out what the distance is here between point b and where it strikes the bottom.
02:05
But we know refraction does occur.
02:07
So for part b, we want to know with refraction, where will it hit? in part a, we can go ahead and actually draw this triangle that's formed.
02:24
So i'm going to redraw that over here where we know this is point a, this is point b.
02:34
This angle here is going to be theta 1 because there's no refraction.
02:41
And we know the length of this side is d because it's equal to the depth of the lake.
02:46
And what we're trying to find here is this distance x the other side of the triangle.
02:52
So we can use tangent because tangent of that angle theta 1 is going to be opposite over adjacent.
03:00
So x over d, which means then that x should be equal to d times tangent of theta 1...