Snell's law demonstration?

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1. Dec 29, 2015

Cozma Alex

I can't figure out why my demonstration of snell's law fails, that's the demonstration: (I used a photo)
I think it fails because the function t (HO) represents a line and so the concept of minimum is not defined, when I take the derivative and equal it to 0 I'm considering the case when the line is parallel to the x axis (the first derivative gives me the angular coefficient and when I equal it to 0 the line is parallel) (considering as y the time and as x HO)

Is that the problem? ( I know the real demonstration but i want to understand why this variant doesn't work)

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2. Dec 30, 2015

theodoros.mihos

$AO\sin\theta_1=AH$

3. Dec 30, 2015

Cozma Alex

But... θ1 is the angle whit the vertical

4. Dec 30, 2015

theodoros.mihos

You are right. May be better a simpler geometry.
Let $A(x_1,y_1)$ and $B(x_2,y_2)$ the end points and $O(x,0)$ the point than we need. Write the total time and take derivation $d/dx(t)=0$.

Last edited: Dec 30, 2015
5. Jan 8, 2016

toumaza

yep it is preferable to use simple geometry to demonstrate