00:01
Hi there, so for this problem we are told that a narrow beam of light containing red with a wavelength that we know for red is equal to 660 nanometers and the wavelength that we are given for blue is equal to 470 nanometers.
00:35
Travels from earth through a one centimeter thick, flat piece of crown glass.
00:41
So the separation in here is given that is one centimeter.
00:52
And back to earth again.
00:54
Now the beam strides the glass at an angle that is given, that angle in here.
01:01
Let's call, well, that's angle in here right here is 32 degrees.
01:08
So with that said, we need to answer part a.
01:12
And part b of this problem.
01:15
Now part a, we are asked about at what angles do the two colors emerge from the glass? and the answer for that is that since we are just calculating from the initial surface to the final surface, we can apply the snail slot twice, and then we will obtain that that angle of at the end in here is just going to be, equals to the angle of incidence that in this case is just simply 32 degrees for both red and blue light.
01:51
Now for part b of this problem, we are asked about by what distance in centimeters are the red and blue separated when they emerge.
02:06
So the first thing that we can consider in this case is that what we want is this angle, in here and this angle for the red light.
02:19
Because with that and with trigonometry, because we know this size is one centimeter, so what we want is this difference in here that we're going to call delta x.
02:30
So by determining the value of x for the blue light and for the red light, and then making the difference between these two values, we will obtain that difference delta x.
02:42
But the first thing, as i said, that we need to consider is that the index of refraption of red light depends on the wavelength.
02:51
So, for example, for the red light, the index of refraption, let's call this nr for red, and it is equal to 1 .512.
03:04
Meanwhile, for blue light, the index of refraption of crown glass is equal to 1 .510.
03:18
And 24.
03:22
So now with that said, what we need to do is to apply snell's law.
03:28
So in this case, we will have the following.
03:31
So we know that the angle that we want to determine, so that is going to be the index of refraption of earth, let's call that just simply as n, times the sign of the angle of incidence that we are also known, that is 32 degrees.
03:45
And then this should be equal to the index of refraption of the one that we want to determine.
03:51
For example, let's put in here the index of refraption for red light, and this sign of the angle that we want to determine, let's call this the angle theta 2.
04:00
That angle is going to be this angle in here, theta 2.
04:05
Now with that said, solving for that, remember that you need to apply the sign of minus 1 to both sides in order to obtain this, and that will be the index of retruption of earth, sign of 32 degrees and this depended by the index of refruption of the red line for this crown glass.
04:24
And now we substitute the values.
04:25
We know that the index of refraption of earth is to simply equals to 1.
04:29
This time is a sign of 32 degrees and this divided by the index of refraption for red line, which is 1 .520.
04:40
Oh, no, 512...