I love your videos so much!!!

I like ur talking way it is fantastic and pay my attention 😊 thankx

finally got it! thank you!

This tutorial is incredible.

Thx to you i dont have to learn the really complicated one in my textbook :D

Sir, You are a real boss =D Thanks a lot ^_^

Can anyone tell me how angle r is equal to the angle in the triangle as shown in figure

It make sense than ever ….. thank you

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!

oh my god, geometry is so beautiful indeed!

Best explanation!

beautiful .....

it's a very good proof. thank you

Great video just watched it to make sure that Snell's law had a proper proof or not and it does!!!!

HAAA! I love your style!

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

Thank you !

Your voice reminds me of Sean Astin's friend in Encino Man.

just WOW! i want that paper please. Haha

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

so clear

You gotta appreciate his enthusiam in my mind optics is the least ineteresting part of physics but i definitely ennjoyed this videos

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?

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)

love how the way you explain..haha

wow ! mind's just blown :D

Thank you 😊

You sound like sheldon. :-P

Keep going forword

why angle to normal ?

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

i understood everything except the part where u say the the two lengths take the same time

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

BOSE-EINSTEIN CONDENSATES!!!! WHAT ARE THEY?!?!?!?!?!?!?!

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.

Light slows down?! And light can speed up?!

You didnt prove why the leftmost ray travelled a distance which makes belowtriangle as right angled triangle..

9 minute video > $160 textbook.

you sound like Neil Patrick harris

,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....

Decent video but unnecessarily cringeworthy