in this video we're looking at destructive interferences on a couple specific wavelengths
of light through two different coatings on a crown glass lens so this starts to give
you a sense for what happens when you stack thin films you can tune these thin films to kill many
wavelengths of light so on our outermost layer we have magnesium fluoride and we're told that
has an index of refraction of 1.41 under that we have a zinc sulfide layer with a very large index
of refraction of 2.20 and then the crown glass itself has an index of refraction of 1.52 by
assumption here that's air outside the magnesium fluoride thin film and that has an index of
refraction of approximately one now to keep track of things i'm going to refer to the magnesium
fluoride that's the outermost layer as material number one the zinc sulfide is material number
two and so i'm told that i want my magnesium fluoride layer to cause destructive interference
on the reflection of 600 nanometer lights and the first thing that we have to do is find the
wavelength of that 600 nanometer light inside the magnesium fluoride layer and i'm gonna call
that lambda one prime and i'll post a link back to the video with all this thin film math was first
introduced but it turns out the wavelength of the light in the material is going to be given
by the wavelength in air or vacuum that's our 600 divided by the index of refraction of the material
when i do that calculation i get 425.5 nanometers then i start thinking about the reflections
at the upper surface of this thin film and at the interface with the next thin film and
so our first reflection is phase shifted at the reflection and that's because it's a transition
from a faster medium into a slower medium for the light my second reflection that's light
that penetrated through the thin film and is now reflecting off the interface with the zinc sulfide
that's also phase shifted by the reflection and the reason why again
is because i went from a faster material into a slower material
so both of these reflected rays are phase shifted the other thing that may cause a phase shift is
the path length difference that's caused by the second reflection traveling all the way
through the thin film and back out again and i'm going to call the thickness of this first film t1
so that second reflection has an extra distance of 2 t1 to travel and because both reflections
caused a phase shift i need to get my reflections back out of phase so that this wavelength of
light is going to interfere destructively so the thinnest film that will get this done
is if 2t1 that's the travel length difference for the second reflection causes a one-half wavelength
phase shift this means my first thickness must be the wavelength of the light in the material
over four and i've got the thickness from my first thin film that's 106
nanometers next we're going to look at reflections off of that zinc sulfide layer and we want
500 nanometer light to interfere destructively off of that and to prepare ourselves we need to
compute the wavelength of our original light which was 600 nanometers so that's going to be lambda
over 2.20 i get 500 over 2.20 which comes out to 227.3 nanometers then i want to visualize both
reflections and i already have the first one it was this phase shifted reflection off the
interface between the magnesium fluoride and the zinc sulfide and then i have some light that is
transmitted through the zinc sulfide layer and reflects off the interface with the crown glass
and this is a slow to fast transition the light is actually speeding up the crown glass has a
smaller index of refraction than the zinc sulfide layer so with that reflection i get no phase shift
so just a quick note at the very end of the instructions it says assume the zinc
sulfide layer cannot be made ultra thin so there's a section at the end of my original
thin film interference video about ultra thin films and when i have this fast to slow to fast
kind of transition if i just make the thickness of the film significantly less than the wavelength
of the light that i'm using it will interfere destructively on all wavelengths and i can see why
because one reflection is phase shifted and the other is not phase shifted those will be pretty
much out of phase if i make the film extremely thin i'm talking 5 or 10 nanometers so we're
assuming that in the manufacturing process this is not possible so we want the next thickness that
causes destructive interference on 500 nanometer light so we're going to look at the thickness
of the zinc sulfide and we'll call that t2 and the extra travel distance for the second reflection is
2 times t2 and because these two reflections are already out of phase what we want is the
right travel distance to not mess with the phase at all and the smallest way to get that done the
smallest thickness that gets it done is if the extra travel distance is exactly one wavelength
so both reflections are going to emerge out of phase and we interfere destructively
so we get t2 as lambda 2 prime over 2. again what matters is the wavelength of the light
within the medium and when i run the numbers on this i get 114 nanometers for that film
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