Here there is an alternative derivation of Snell Law (very simple), using the conservation of momentum of photons: If in medium 1 the index of refraction is n1 and in medium 2 the index of refraction is n2 and for the definition of index of refractions and wavelength we have: n1 = c / v1 , v1 = λ1 * f n2 = c / v2 , v2 = λ2 * f Dividing the above equations we obtain: n2 / n1 = λ1 /λ2 So if n2 is higher than n1, the wavelength in medium 2 is smaller than in medium 1. Now because the photon momentum is: p = h / λ Applying the conservation of momentum of the incident and transmitted photon along the parallel line of medium separation: p1 = p2 → h/λ1 *sin(θ1) = h/λ2 *sin(θ2) → n1 *sin(θ1) = n2 *sin(θ2) This is the Snell Law!! So the refraction is just a consequence of the conservation of momentum of photons!
You should make a video for light hitting a medium that has a changing index of refraction defined by n=n_o*sqrt(1+z/a) when the light hits the medium at z=0 where x is vertical and z is horizontal. its essentially light hitting a cube of sugar water with increasing intensity and the path ends up being parabolic
I tried an alternative version of this derivation, and I'd like to discuss it in this comment because considerations such as this are important for people in the sciences to consider if they want to better understand the world around them. This also goes for myself as I wish to study to become a scientist one day. At the moment, I am an amateur mathematician who has limited knowledge of physics. Stick around to see where I end up. Active discussion of this comment is encouraged for those who wish to expand on these ideas! First, assume the wave is a typical sinusoidal surface (with a finite width). Unlike Doc Schuster, in this thought experiment, I consider the possibility that the wave can move in a way such that its direction of propagation (motion) is not the same as the direction determined by the shortest distant from two crests (the direction one would expect it to travel and the direction Doc Schuster assumes it must travel in this derivation of Snell's law). Next, I assume that the direction of travel remains constant throughout its entire journey. (Contrast this with Doc Schuster's assumption.) Then what happens, as a result, is that the width of the wave (or length of the line) changes. It changes in such a way so that if one were to draw perpendiculars from each end of the span of the width of the wave before it crosses over to the other medium, then the new slanted wave would fall precisely between these two perpendiculars throughout its entire journey. (Notice that in Doc Schuster's derivation (Idek who came up with this derivation by the way), the width of the wave remains constant.) Furthermore, the direction the wave faces after it has passed to the new medium is also now at a slant (note that this is no longer the same as the direction of travel). Now, of course... this conclusion must be false because one can perform this experiment with a laser to clearly determine that the direction of travel has changed. Therefore, a question should be brewing in the mind of the scientist who read this post and thought about this post carefully. Why in God's name should the direction of travel of the wave change? For, if the wave parts were independent of each other, then they would move on happily as if they were not connected in any way, and one would experience the exact effect I just described (the wave slants and stretches but remains traveling in the same direction). However, we know this is not what happens. Therefore, we are led to the conclusion that a light beam must display some sort of resistance against changing shape. This leads me to my next exploratory question for future consideration. What if one were to make the comparison of a light beam to a sheet of plywood undergoing projectile motion in 0g that changes between two different media of air? Can the physics of the imbalance of air pressures account for this directional change? Certainly, the piece of plywood will rotate, and this rotation will cease at some point due to the force of air opposing its motion. But how closely will it match the trajectory of light? Notes: For those who are curious, I have decided to derive the equations governing the motion of the 1-D line representation of the light wave on the 2-D plane according to my first thought experiment (which, don't be mistaken, is not the way it actually works). I modeled the situation assuming that the origin lies on the line separating the two media, the positive direction of the y-axis points downwards instead of upwards, the angle given by theta_1 in the video is given simply by theta, and at time t = 0 the lower left corner of the line begins at the origin. These assumptions lead to the following set of piecewise functions (note the function is different for each vertical strip depending on the x-value): y = { (v_1*t - x*sin(theta))/cos(theta) for 0
Hi Doc! I have a question.... How do you know that in the second medium, the wave travel exactly the distance between the wavefront and the boundary in that time? Thanks
yes I also have the same doubt in fact this is a wrong proof he cant take that assumptions like that. And the correct proof can be either by conserving momentum of photons or doing some math by assuming that light takes shortest path between any two points
If you'll consider every ray of light or every (infinitely narrow) marcher in the marching band, they each turn (i.e. refract) in the same way as their neighbors. It just happens that they are each subject to nearly the exact same conditions. Good question.
Hi Doctor, I have a question for you: If the index of refraction of a material depends on the speed of light within that material, then the index of refraction is not the same for all light waves, but it depends on the wavelength. I mean: if we shoot a violet ray from vacuum to a prism, it will bend more towards the normal than a red ray, because the index of refraction decreases with bigger wavelengths (increases with the frequency). This is the explanation of light dispersion in rainbow, right? The problem is that in my physics book, indexes of refraction seem to be related only to the material (and not to the wavelength). Thank you very much, and forgive my mistakes (i'm not native)
+Miguel Gallego Just leaving this here in case somebody has the same question. Speed of light is the same for *all* lights, all frequencies. The speed of an infrared ray is no less than that of violet ray. The different energy they carry does not translate to kinetic energy! Hope this helps.
Hi, I´m here in 2021 with a question eheh We consider that it takes the same amount of time to cover the different distances you pointed above. But how can you assume that? For me it's impossible to consider something like that if we don't look at the mathematic explanation and to the fermat's principle first of all. So this Geometric Derivation is incomplete unless we consider the mathematic proof and fermat's principle, right
Doesn't light turn and slow down because the denser medium has many more atoms that the photons have to interact with, which would slow down the photons? The photon energises the electron into a higher energy shell, then the photon is released and the electron returns to a lower shell. You would have to add time, which would slow down C.
Jack Kade and Nonconcensusical, check out Prof. Phil Moriarty's explanation on the Sixty Symbols channel. The title is some like "why is light slower in glass". He'll clear it right up (no pun intended)
I was thinking like this before I've learned the truth. The answer is no. Light goes slower because speed of light in a medium is 1/sqrt(mu0Epsilon0), where mu0 is the magnetic permeattivity and Epsilon 0 is electric permeattivity of the medium
You have to understand that you are comparing the difference in the path lengths based on Fermat's principle. If the distance travelled in the first medium is v(1)delta(t) it will travel the same distance as v(2)delta(t) in the second medium. you determine the distances geometrically with respect to the angles and equate them.
![Дон ДОН, Алаудинов и СБЕЖАВШИЕ из под Курска ахматовцы 😁 [Пародия]](http://i.ytimg.com/vi/dEfCf5IK26Q/mqdefault.jpg)
Here there is an alternative derivation of Snell Law (very simple), using the conservation of momentum of photons:
If in medium 1 the index of refraction is n1 and in medium 2 the index of refraction is n2 and for the definition of index of refractions and wavelength we have:
n1 = c / v1 , v1 = λ1 * f
n2 = c / v2 , v2 = λ2 * f
Dividing the above equations we obtain: n2 / n1 = λ1 /λ2
So if n2 is higher than n1, the wavelength in medium 2 is smaller than in medium 1.
Now because the photon momentum is: p = h / λ
Applying the conservation of momentum of the incident and transmitted photon along the parallel line of medium separation:
p1 = p2 → h/λ1 *sin(θ1) = h/λ2 *sin(θ2) → n1 *sin(θ1) = n2 *sin(θ2)
This is the Snell Law!!
So the refraction is just a consequence of the conservation of momentum of photons!
But is it conservation of momentum in horizontal direction?
It make sense than ever ….. thank you
Thx to you i dont have to learn the really complicated one in my textbook :D
Great video just watched it to make sure that Snell's law had a proper proof or not and it does!!!!
I like ur talking way it is fantastic and pay my attention 😊 thankx
oh my god, geometry is so beautiful indeed!
This tutorial is incredible.
You gotta appreciate his enthusiam in my mind optics is the least ineteresting part of physics but i definitely ennjoyed this videos
Can anyone tell me how angle r is equal to the angle in the triangle as shown in figure
You should make a video for light hitting a medium that has a changing index of refraction defined by n=n_o*sqrt(1+z/a) when the light hits the medium at z=0 where x is vertical and z is horizontal. its essentially light hitting a cube of sugar water with increasing intensity and the path ends up being parabolic
I tried an alternative version of this derivation, and I'd like to discuss it in this comment because considerations such as this are important for people in the sciences to consider if they want to better understand the world around them. This also goes for myself as I wish to study to become a scientist one day. At the moment, I am an amateur mathematician who has limited knowledge of physics. Stick around to see where I end up. Active discussion of this comment is encouraged for those who wish to expand on these ideas!
First, assume the wave is a typical sinusoidal surface (with a finite width). Unlike Doc Schuster, in this thought experiment, I consider the possibility that the wave can move in a way such that its direction of propagation (motion) is not the same as the direction determined by the shortest distant from two crests (the direction one would expect it to travel and the direction Doc Schuster assumes it must travel in this derivation of Snell's law). Next, I assume that the direction of travel remains constant throughout its entire journey. (Contrast this with Doc Schuster's assumption.) Then what happens, as a result, is that the width of the wave (or length of the line) changes. It changes in such a way so that if one were to draw perpendiculars from each end of the span of the width of the wave before it crosses over to the other medium, then the new slanted wave would fall precisely between these two perpendiculars throughout its entire journey. (Notice that in Doc Schuster's derivation (Idek who came up with this derivation by the way), the width of the wave remains constant.) Furthermore, the direction the wave faces after it has passed to the new medium is also now at a slant (note that this is no longer the same as the direction of travel). Now, of course... this conclusion must be false because one can perform this experiment with a laser to clearly determine that the direction of travel has changed. Therefore, a question should be brewing in the mind of the scientist who read this post and thought about this post carefully. Why in God's name should the direction of travel of the wave change? For, if the wave parts were independent of each other, then they would move on happily as if they were not connected in any way, and one would experience the exact effect I just described (the wave slants and stretches but remains traveling in the same direction). However, we know this is not what happens. Therefore, we are led to the conclusion that a light beam must display some sort of resistance against changing shape. This leads me to my next exploratory question for future consideration. What if one were to make the comparison of a light beam to a sheet of plywood undergoing projectile motion in 0g that changes between two different media of air? Can the physics of the imbalance of air pressures account for this directional change? Certainly, the piece of plywood will rotate, and this rotation will cease at some point due to the force of air opposing its motion. But how closely will it match the trajectory of light?
Notes:
For those who are curious, I have decided to derive the equations governing the motion of the 1-D line representation of the light wave on the 2-D plane according to my first thought experiment (which, don't be mistaken, is not the way it actually works). I modeled the situation assuming that the origin lies on the line separating the two media, the positive direction of the y-axis points downwards instead of upwards, the angle given by theta_1 in the video is given simply by theta, and at time t = 0 the lower left corner of the line begins at the origin. These assumptions lead to the following set of piecewise functions (note the function is different for each vertical strip depending on the x-value):
y = { (v_1*t - x*sin(theta))/cos(theta) for 0
Would the plywood actually undergo an opposite sort of effect?
I just realized that Doc Schuster already made a video where he used lasers. So, go check out all his videos.
finally got it! thank you!
Sir, You are a real boss =D
Thanks a lot ^_^
You didnt prove why the leftmost ray travelled a distance which makes belowtriangle as right angled triangle..
it's a very good proof. thank you
Hi Doc! I have a question.... How do you know that in the second medium, the wave travel exactly the distance between the wavefront and the boundary in that time? Thanks
yes I also have the same doubt in fact this is a wrong proof he cant take that assumptions like that. And the correct proof can be either by conserving momentum of photons or doing some math by assuming that light takes shortest path between any two points
I love your videos so much!!!
Your voice reminds me of Sean Astin's friend in Encino Man.
Thank you !
Why do the pink lines from both sides of the first and the second region have to be connected? Why can't they "break" and travel on their own?
If you'll consider every ray of light or every (infinitely narrow) marcher in the marching band, they each turn (i.e. refract) in the same way as their neighbors. It just happens that they are each subject to nearly the exact same conditions. Good question.
Hi Doctor, I have a question for you:
If the index of refraction of a material depends on the speed of light within that material, then the index of refraction is not the same for all light waves, but it depends on the wavelength. I mean: if we shoot a violet ray from vacuum to a prism, it will bend more towards the normal than a red ray, because the index of refraction decreases with bigger wavelengths (increases with the frequency). This is the explanation of light dispersion in rainbow, right?
The problem is that in my physics book, indexes of refraction seem to be related only to the material (and not to the wavelength). Thank you very much, and forgive my mistakes (i'm not native)
+Miguel Gallego Just leaving this here in case somebody has the same question. Speed of light is the same for *all* lights, all frequencies. The speed of an infrared ray is no less than that of violet ray. The different energy they carry does not translate to kinetic energy!
Hope this helps.
Best explanation!
just WOW! i want that paper please. Haha
HAAA! I love your style!
wow ! mind's just blown :D
same, I always used the fermat method and the vector thing
beautiful .....
Hi, I´m here in 2021 with a question eheh
We consider that it takes the same amount of time to cover the different distances you pointed above. But how can you assume that? For me it's impossible to consider something like that if we don't look at the mathematic explanation and to the fermat's principle first of all. So this Geometric Derivation is incomplete unless we consider the mathematic proof and fermat's principle, right
so clear
love how the way you explain..haha
why angle to normal ?
i understood everything except the part where u say the the two lengths take the same time
yup cuz in slower medium the ray takes shortest possible distance to reach the other point.
Same kinda confusing to me as well
Doesn't light turn and slow down because the denser medium has many more atoms that the photons have to interact with, which would slow down the photons? The photon energises the electron into a higher energy shell, then the photon is released and the electron returns to a lower shell. You would have to add time, which would slow down C.
+Nonconcensusical no
+PieterPel; OK, thanks.
+PieterPel How else would you explain the propagation of photons through a transparent medium?
Jack Kade and Nonconcensusical, check out Prof. Phil Moriarty's explanation on the Sixty Symbols channel. The title is some like "why is light slower in glass". He'll clear it right up (no pun intended)
I was thinking like this before I've learned the truth. The answer is no. Light goes slower because speed of light in a medium is 1/sqrt(mu0Epsilon0), where mu0 is the magnetic permeattivity and Epsilon 0 is electric permeattivity of the medium
You sound like sheldon. :-P
Thank you 😊
Light slows down?! And light can speed up?!
Keep going forword
9 minute video > $160 textbook.
BOSE-EINSTEIN CONDENSATES!!!! WHAT ARE THEY?!?!?!?!?!?!?!
,omg I really do not understand geometry. The calc based proof is a million times better. Your math makes sense, but diagram wise I'm lost....
You have to understand that you are comparing the difference in the path lengths based on Fermat's principle. If the distance travelled in the first medium is v(1)delta(t) it will travel the same distance as v(2)delta(t) in the second medium. you determine the distances geometrically with respect to the angles and equate them.
you sound like Neil Patrick harris
Decent video but unnecessarily cringeworthy