Then film interference. I'm going to show you how to solve thin film interference problems. So thin films operate under very similar principles to other interference problems and that we start by looking at path difference. So let's say we have a source of light, maybe it's the sun, maybe it's something else, we'll just go with the sun. And it shines light down and that light encounters a thin film. So let's say a layer of ice. And so here's our layer of ice. This is obviously not to scale. And some of that light will reflect off of that surface. And then it will enter an observer's eyeball, or some machine detector. And some of the light, when it encounters this interface between the ice and the air, is going to get transmitted. And then it has another choice if you want to use that word. When it encounters the interface between the ice and the liquid water at this surface. And some of it's going to reflect, and then it's going to encounter the surface. And then some of that light will get transmitted. So these are just two possible paths. There's other paths that this light could take. But this light will be transmitted up into the observer's eyeballs as well. And so what we want to do first, like I said, is derive a formula for the path difference in this physical situation. So let's go ahead and give these distances some names. So we'll call the distance from the source of light to the surface of the thin film distance A. We'll call the distance from the thin film to the observer, distance B. And then by convention, the thickness of the thin film is given the symbol T. Not to be confused with time in this context, T means the thickness of the thin film. So the light that reflects off of the surface will go a distance, we'll call that distance A, plus distance B. And then the second distance will be A, plus a distance of T, plus another distance of T, plus a distance of B back up to the observer. Now, we're not taking into account trigonometry or anything. We're basically assuming straight lines, but we don't want everything to overlap. So I'm drawing them at a little bit of an angle. Okay, so the path difference will be one distance minus the other. So I take this minus this and I get delta D equals 2T. So the path difference for thin film problems will typically be twice the thickness of the thin film. So we can replace delta D in the usual formulas for constructive interference with 2T. So let's do that. So we would normally have delta D equals M lambda and delta D equals M plus 1 half the wavelength, but we'll instead of writing delta D will write 2T. So 2T equals M lambda and 2T equals M plus 1 half the wavelength. So lambda is the wavelength of this light. So normally we would associate this formula with constructive interference and this formula with destructive interference. However, with thin films, it's not that simple. So there is a problem in that when light reflects off of a surface, it can get inverted. What we mean by inverted is that the electric field reverses its direction. And that occurs when it is reflecting off of a higher index of a fraction than the medium that it's currently in. So we check the index of a fraction for this medium air, which is probably close to 1. Check the index of a fraction for the thin film compared to 2. And if the thin film has a higher index of a fraction than this medium, then it would be inverted. And then same thing down here, we look at what the thin film is on top of. Find the index of a fraction for it, compare it to the index of a fraction for the thin film. And if what's below the thin film is a higher index of a fraction than this gets inverted as well. So what you have to do is count the inversions. It's going to be 0, 1 or 2. And if it's 0 or 2, then your physical intuition of this is constructive and this is destructive would be correct. However, if there's only 1 inversion, then we would use these get switched. So count inversions. And if 1, then switch the formulas. You do this one for constructive and this one for destructors. So be careful, don't skip that step. So path difference of twice the thickness, counting inversions, and then switch if these formulas around if needed. And then the third twist for thin films, or sort of special case for thin films, is that we need to be careful about what we mean when we write wavelength. What is that the wavelength? Is the wavelength out here in air or vacuum or whatever? Is it the wavelength in the thin film? Is it the wavelength of whatever the thin film is on top of? Well, it is the wavelength within the thin film. So I'm just going to use MAT as the subscript. So wavelength of the material of the thin film. And because the wavelength gets compressed within the thin film by the factor of the index of refraction for that material, we can rewrite this in term these formulas in terms of the wavelength in vacuum. So M times wavelength in vacuum over N. So I'm just replacing this with this. And then twice the thickness will be M plus 1 half, where times wavelength in vacuum divided by N. Okay, so these are the two equations that you use again being careful to count inversions. So the indices of refraction come into play twice. Both once when you're counting the inversions and then the second time when you're using this formula that N is the index of refraction for the thin film. So those are the general principles. In another video, I'm going to give you an example of using these formulas that I've shown you. And I'll show you how to solve a problem. Thanks for watching.