00:01
Hi there, so for this problem, we are told that if the lenses are medium flamed glass of reprupted in this, that is 1 .62.
00:14
So what in this of repruption is given? that's the value.
00:23
We're going to call it simply an.
00:26
And that is 1 .432.
00:34
And the coating is fluoride of an irrefractive index of refruption, another value.
00:41
One of them is 1 .62 and the other is 1 .432.
00:46
So the question for part a of this problem is what minimum thickness of film is needed of the lenses to cancel light of a wavelength that is given and that wavelength is 550 nanometers.
01:05
Okay, so first of all, we need to consider the interferes of the rates reflected from each side of the film.
01:13
At the front of the film, light, an error reflects off the film that is 1 .432, and there is an 180 -degree phase shift.
01:24
At the back of the film, light in the film, and equals to 1 .432 reflects off the glass, which is an indeclurephyser of of 1 .62 and there is a 180 degrees phase shift.
01:40
Therefore, the reflections introduce no net phase shift.
01:45
The path difference is just 2 times the thickness and the wavelength in the film is one of the expression that we're going to use in here, which is the wavelength in air, which is the value that we are given.
02:02
And this divided by the index of refruption.
02:05
Now, for this part of this problem, since there is no net phase difference by reduced by their reflections, the condition for destructive interframes is that 2 times the thickness is equal to the order m plus 1 divided by 2 times the wavelength.
02:25
So we can solve in here for the thickness, so that will be just simply the wavelength divided by 2, and this times the order m plus 1 divided by 2.
02:40
Okay, so now in this case the thickness is then when we set m equals to zero, that will be the wavelength divided by four.
02:55
But we use the fact that the wavelength is just the wavelength in earth divided by the index of repruption.
03:03
In this case, it's four times the index of repruption.
03:06
So that will be then in here 550 nanometers, this divided a few...