Fermat's Principle & Snell's Law

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Introduction to Fermat's Principle and mathematical derivation of the Snell's Law

This video was prepared for UCL physics second-year 'Developing Effective Communication' module project.

Hasan Sayginel

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I think there is a mistake in the derivative in 3:59 it should be -2(d-x) for the OB part

Adrian-tlnc

For the ones interested, 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!

SimulatingPhysics

Hey why u stopped posting...this clip was really helpful to me... please continue posting more .

psatabdipatra

anyone coming from story of your life?

Eruapha

Best explanation ever.. really loved it👏👏

amantiwari

4:12 I think that the second triangle is wrong. It should be (d - x) in the left side.

GuilherHast

this is a very informative video with clear and easy to follow explanations

dorota

In derivation of sin theta t, how does the opposite side become x... It has to (d-x). When you differentiate (d-x)^2 it would be, -2d+2x...

samgerard

Fermat's principle is telelogical when applied to human existence. We are all photons (beings of light). A ray of light has to know where it will ultimately end up before it can choose the direction to begin moving in. Your destiny was sealed the moment you were conceived.

colonelsanders

now i got it, thanks to the beach analogy. thanks for the input

dasmaldas

There is a misstep in your differentiation & for getting sin(theta(r)) you need d-x what you'll get from the right calculation.

creativeideas

Thanks Bro for your awsome explanation.

ihatecodingso

This video is a great explanation! The only explanation I found I could understand. What decides the light's destination? It seems like point B is the point the light would have gotten to by going straight (as if there was no medium change), but then the light's that becomes the shortest to that same point when a medium is in the way... is this correct?

okebaram