in this video we introduced the index of refraction for light traveling within a
material then we introduced the idea of refraction and we work a couple refraction examples so when
light enters a material the effective speed of the light changes and when i say effective speed
i'm trying to emphasize that the speed of light is still the same old constant 3 times 10 to the 8th
meters per second but in a material the light is constantly interacting with the molecules in the
material which then re-radiate the light and this effectively slows the propagation of the wave we
talk about the change in speed by introducing the idea of the index of refraction for the material
the index of refraction just quantifies how much the speed slows down
and that's n equals c over v so written this way i can see that when v gets smaller n gets
bigger so like if v was half the speed of light in the vacuum the index of refraction would be 2.
so let's work a quick example with index of refraction i want the speed of light in
water given that its index of refraction is 1.33 so we're just going to take our index
of refraction formula and solve it for v and i plug in c the speed of light in a vacuum
and divide by 1.33 and when i do this i get 2.26 times 10 to the 8th meters per second so one
effect of the change in speed is that light will bend when it changes from one medium to another
and this is called refraction so on the right hand side we have two pictures of different refractions
the first one has a light ray entering a slower material and the second one has the light ray
exiting the slower material moving into a faster material so the real answer for why this banding
occurs comes from applying boundary conditions to a differential equation that describes the light
wave but here we're just trying to physically motivate the qualitative behavior that we're
seeing and so what we do is we visualize these wave fronts that's little white line segments
representing crests on the light wave that's going in the direction the ray is pointing
and we can see in this first picture where i have this light ray moving from a faster material to a
slower material does this wave crest right at the boundary well the bottom edge of that is entering
the slower material before the top edge of that that means this part of the wavefront slows down
while this part keeps moving quickly at the top and effectively this causes a rotation
of the wave front so by the time all these wave fronts pass into this lower material they've all
been tilted to a more extreme angle and we see the refraction of the ray toward the normal line
in other words my refracted angle is smaller than my incident angle there's the incident
there's the refracted in the second picture we use a similar sort of physical motivation
i have wave fronts in the slower material and it's approaching this interface where
the waves switch to a faster material well at some point this wavefront that's
right next to the interface is going to have the top edge pass into the faster
medium while the bottom edge is still moving slowly and this amounts to a rotation clockwise
of that wavefront and by the time that wavefront emerges from the material
it's going to have this new direction where i can see my ray has been refracted away from the normal
so in this case the refracted angle is going to be bigger than the incident angle so this physical
reasoning is at least a good mnemonic device for remembering which way things are going to refract
and one more thing i want to put on this slide is snell's law which quantifies how much these light
rays are going to refract so snell's law when you have a transition from one medium to the next
this is how the indices of refraction and the incident and refracted angles
are related n1 sine theta 1 equals n2 sine theta 2. so let's take a look at how to apply snell's
law in this first example i have a fast to slow transition and i see the ray bending toward the
normal so this is a ray transitioning from air to water with an incident angle of 35 degrees
now the effective speed of light in air actually is a little bit slower than it
is in a vacuum it's like 1.0003 but to the degree of precision we normally work we're just gonna say
it's approximately 1. then we already saw water that's 1.33 and my incident angle i'm going to
call this theta 1 is 35 degrees and then we're trying to solve for the refracted angle so we
apply snell's law and 1 sine theta 1 is equal to n2 sine theta 2 and n1 is 1 theta 1 is 35 degrees
and 2 is 1.33 and theta 2 is unknown and i'm going to go ahead and call it theta r for refracted
angle so we divide by 1.33 and then we take the inverse sine and we'll have our angle into three
sig figs we get 25 and a half degrees so again that's going to be smaller than the incident angle
which is another way of saying the ray has bent closer to the normal so in the second example you
might notice that i just made a couple corrections that incident angle was actually too big to get a
refraction coming out of the crown glass and that ray would have undergone total internal reflection
and i'll post a link to that that's the next video i'm making today
so i changed the angle to 38 degrees so that i would get a refracted angle less than 90.
and we're going to call the crown glass material number one and n is 1.52 in crown glass
and i have a ray transitioning from inside the glass to outside so i see it bending away
from the normal that'll be material number two that's the error
where again we're going to say the index of refraction is approximately one
and we apply snell's law and all we have to do is take the inverse sine of 1.52 sine 38
we've got the refracted angle and this turns out to be 69.4 degrees
if you find the physics content on zack's lab helpful click on the zaxlab logo on the right
to browse playlists and subscribe to the channel i produce over 100 new videos per
month and subscribing is the easiest way to find new content thanks for watching