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!
Thank you! For thse who didnt know what he did in the derivative: He uses the expression as a function in which z is the main unknown. He derivates z because times depends on z and if you could see the graphic function the lowest point would be whose derivative is equal to zero. I hope you enjoy the video :)
Hmmm...you'll need to know calculus first. The best online resource for learning calculus (where I also happen to work) is the School Yourself website (mentioned in the video's description).
6:05 why can we use the alternate interior angle, if it's value differs from the actual angle we want? Why does it still give us a valid equation? That's the only part I don't seem to understand
how did you deferential time with respect to z? I understood how you did differentiation. my question is why? how did we get to know that we have to differentiate time wrt z?
Omkar Chavan It's easier to work from where the yellow and blue meet because they share the same horizontal distance, z. When you differentiate you'll only be working with one variable making everyone's life easier lol
Because time, t, is a function of distance, z. As z increases, the time taken to travel that distance also increases. Remember that the goal here is to find the horizontal distance that will minimise time.
to understant imagine total time to be a function of z this means z is changing and is a variable whereas the length x, length y and d are constant value which don't change with respect to time
@@Parth_Wasnikyeah but couldn’t you just say the total time is a function of x and that z, d and y are set constants and then by that logic set the derivative with respect to x to 0?
illogical conclusion at 1:17. v1 > v2 doesn't mean most of the path should be in the blue region. Here is a counterexample. Assume v1 = v2 + 0.0000000000000001, points A and B are 0.00000001 and 1 unit away from interface plane, respectively, and points A and B lie on a line that makes a 45 degree angle with the interface plane. Then giving A a longer path than B in its medium would result in a longer time than a straight line path between both points.
longer path doesn't mean longer than what it took in 2nd medium, it means relatively longer than the straight-line path taken by light in first medium itself, try calculating the times in both cases, your logical conclusion will fail
@@devd_rx Duh My counterexample gives a situation where allowing the path to be longer in the region where light is faster gives a longer time than a straight line path. Just draw diagram Let A and B lie on a line that makes a 45 degree angle with interface. Let A be 1 unit above interface and B 10 units below. Let v1 be marginally greater than v2 (v1 = v2 + 0.0000000000001). Now if v1=v2 then the straight line path would give shortest time. Buy since v1 is sufficiently close to v2 then the kink wouldn't be noticeable and would appear to be a straight line path. Also the fact that A is extremely close to the interface where B is significantly distant gives the contradiction in his statement. Snell's law still holds of course. His rational at 1.:17 is wrong though
The speed of light changes as it goes through different forms of matter. It goes fastest in vacuum. v=c/n or n=c/v is the ratio of the speed light as it travels through a specified medium compared to how it travels in vacuum.
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!
briilient thought process bros
How do you know the frequency, f, of the light doesn't change as the light move from the first medium to the second medium?
@@davidbrisbane7206 frequency would not change even though penetrating through mediums
awesome derivation
holy fucking shit.....
This derivation is simple and straightforward. Thanks.
Nope
This is one of the best educational videos i've seen. Clear and straight to the point.
just like the path of the light ray
Thank you!
For thse who didnt know what he did in the derivative:
He uses the expression as a function in which z is the main unknown. He derivates z because times depends on z and if you could see the graphic function the lowest point would be whose derivative is equal to zero.
I hope you enjoy the video :)
It’s been 4 years, but I’d still like to thank you for writing this explanation.
I think it is the best explanation about Fermat principle! Think you !
Nice. Simple. Straightforward. Out falls the laws of reflection and refraction.
Thanks bro you save my time and literally my life
Hmmm...you'll need to know calculus first. The best online resource for learning calculus (where I also happen to work) is the School Yourself website (mentioned in the video's description).
Sir please give this link ...I'm not able to find it .
This was so nicely explained! Thanks!
Wow! This was explained so well, thankyou!
Beautifully done
Jazakallah sir
fantastic. quick and exact! thanks
This is a very nice derivation. A similar derivation was used recently by S.H. on youtube.
This is exactly what I needed !! Thank you !!!!!!!!!!!!!!!!!!!!!!!
Easy and straightforward, thank you.
Great ❤🧡💛💚💙💜
Thanks man it helped me too much
This video is very good, it helped me a lot
this helped a lot....it was useful that i knew calculus :)
Beautiful! Thank you!
Thanks dear Sir, I am from Pakistan
thank you
Fantastic video 👍 Thanks a lot :)
6:05 why can we use the alternate interior angle, if it's value differs from the actual angle we want? Why does it still give us a valid equation? That's the only part I don't seem to understand
Wow this is a beautiful explanation.
Excellent
Thank you!
how did you deferential time with respect to z? I understood how you did differentiation. my question is why? how did we get to know that we have to differentiate time wrt z?
Omkar Chavan It's easier to work from where the yellow and blue meet because they share the same horizontal distance, z. When you differentiate you'll only be working with one variable making everyone's life easier lol
Because time, t, is a function of distance, z. As z increases, the time taken to travel that distance also increases. Remember that the goal here is to find the horizontal distance that will minimise time.
The Time light takes to reach point B is a function of Z. and everything else is pretty much a constant
if you ever so slightly increase or decrease z then the time increases so the question reduces to what z makes the time stationary or least
Wonderful !!!!!
sooooo amazing!!! THANKS!!!!
how can ı understand this derivation
thank you this helped
super video
Awesome! Thanks for this proof!
Here is the video deriving snell's law using simple calculus!
Thank you so much
Well done!
I don’t understand, why do we differentiate with respect to z and not x, d or y? What’s so special about z?
Excellent presention
Thanks man
Very very nice!
Perfect😍💫
thank you!
thx a lot
Wow this makes a lot of sense
All i dont get is why is z a variable and d is a constant. Why
to understant imagine total time to be a function of z this means z is changing and is a variable whereas the length x, length y and d are constant value which don't change with respect to time
@@Parth_Wasnikyeah but couldn’t you just say the total time is a function of x and that z, d and y are set constants and then by that logic set the derivative with respect to x to 0?
Thank you sirr
Very good!
Why is dt/dz =0?
illogical conclusion at 1:17. v1 > v2 doesn't mean most of the path should be in the blue region. Here is a counterexample.
Assume v1 = v2 + 0.0000000000000001, points A and B are 0.00000001 and 1 unit away from interface plane, respectively, and points A and B lie on a line that makes a 45 degree angle with the interface plane. Then giving A a longer path than B in its medium would result in a longer time than a straight line path between both points.
longer path doesn't mean longer than what it took in 2nd medium, it means relatively longer than the straight-line path taken by light in first medium itself, try calculating the times in both cases, your logical conclusion will fail
@@devd_rx
Duh
My counterexample gives a situation where allowing the path to be longer in the region where light is faster gives a longer time than a straight line path. Just draw diagram
Let A and B lie on a line that makes a 45 degree angle with interface.
Let A be 1 unit above interface and B 10 units below. Let v1 be marginally greater than v2 (v1 = v2 + 0.0000000000001).
Now if v1=v2 then the straight line path would give shortest time. Buy since v1 is sufficiently close to v2 then the kink wouldn't be noticeable and would appear to be a straight line path. Also the fact that A is extremely close to the interface where B is significantly distant gives the contradiction in his statement. Snell's law still holds of course. His rational at 1.:17 is wrong though
Why do you subtract the equestion, you add it first so taking the derivative shouldn’t make you subtract right?
i Am Also Confused About That
ha ha ha!!! Goood work!!!
how did you differentiate with respect to z with x and y in the equations? are x and y constants?
yes x and y are constant values
Brilliant
there is any other method for deriving snell's law
Use the conservation of momentum in photons
All good, except it doesn't explain why Fermat's principle is correct.
4:30 why d over dz
the derivative of time with respect to the distance along z.
good
could you also explain why V = C/n please?
Index of refraction is by definition n = c/v, where c is the speed of light in vacuum and v is the speed of light in the medium.
The speed of light changes as it goes through different forms of matter.
It goes fastest in vacuum.
v=c/n or n=c/v is the ratio of the speed light as it travels through a specified medium compared to
how it travels in vacuum.
yezz ...
You have to improve somethings.
Like: you have written d( t1+t2)/dz from where you had bring this
oh and d
itü optik eef227e tayfaya selam
If u r meant to derive shell's law derive it with proper explanation or dont derive it
If you're trying to spell Snell, spell it properly or don't spell it.
.