in this video we discuss changes in the wavelength of light when it changes from one
medium to another then we work a simple example showing how to calculate the wavelength of light
in a medium to start things out we visualize light waves in a vacuum as transverse waves on a string
light traveling on the direction of a light ray can be visualized
as a simple wave train like we see in the first animation on the upper left
note that i've marked a point on the string that's oscillating up and down the frequency
of oscillation of that point is what we mean by the frequency for the wave so we can write down
for light traveling in a vacuum the speed is equal to c the speed of light the wavelength is lambda
for frequency we use an f and remember the wave speed equation says v equals f lambda
the speed with which this wave propagates is given by multiplying frequency and wavelength
well in this case that means c is equal to f lambda or i could say the wavelength
is c over f but what happens to this light wave if it enters a medium say glass first we already
know the wave will effectively slow down by a factor of n the index of refraction and i'll
post a link real quick to the video where this was first discussed so the speed is reduced but notice
that the frequency of the wave doesn't change again we're tracking that white spot on the wave
and watching it go up and down the frequency of the light in a vacuum is exactly the same as the
frequency of the light when it propagates into the material making an analogy to waves on a string
we visualize the transition of light from the fast to slow medium by tying a light string to a heavy
string and that white dot is the knot between the two strings and of course it's wiggling up
and down at the same rate for each of these waves otherwise the string would be broken
alright so everywhere in the wave the frequency is the same but what changes here i can see in
the picture it appears to be the wavelength that changes so if you have a smaller speed
and the frequency stays the same looking at v equals f lambda it must be lambda the got smaller
to explain that decrease in the velocity so we can replace the new wave speed with
c over n and solve for lambda prime and then i realized that c over f that was our original
wavelength in a vacuum so i arrive at this really useful formula the wavelength of light in a medium
is equal to the wavelength in a vacuum divided by the index of refraction for the sake of
completeness on the bottom right hand side we have a transition from a slow medium to a fast medium
and again what's changing here is not the frequency i can see the frequency of each
wiggle is the same by watching that white dot at the interface between the two materials
and it's just the wavelength that changes when the speed changes so no matter what transitions occur
as a light wave is passing through different media the frequency is the thing that stays the same
and then the wavelength in any particular medium is just given by the simple formula
the wavelength and vacuum divided by the index of refraction let's wrap things up with a simple
example so we have red light with wavelength 650 nanometers entering a slab of crown glass
the index of refraction is given to us as 1.52 and we want the wavelength of this light
in the crown glass so there's not a lot to do here i take my original wavelength which is assumed to
either be in vacuum or in air which is a close enough approximation 650 nanometers and divide
by my index of refraction to three sig figs i get 428 nanometers for the wavelength of this light
within the glass and we're done with the example so i want to make a quick comment on this because
i've seen a lot of videos that do something wrong at this point so this red light had a wavelength
of 650 nanometers now it has a wavelength of 428 nanometers does that mean this is somehow violet
light when it's traveling inside the glass if i were able to put my eye inside the glass would
i see purple instead of red and the answer is no it's the frequency that matters because when the
light travels into your eye it's always going to end up with whatever wavelength 650 nanometer red
light ends up with when it's inside the fluid in your eye so it's still the same frequency of
wiggling for the light it's the same wavelength for the light within the fluid in your eye you're
going to detect red regardless of what medium you're in all right so now we know how light is
transmitted at an interface between two media in the next video we're going to discuss reflections
for light at an interface if you find the physics content on zack's lab helpful click on the zaxlab
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