Physics Help Forum Does Fermat principle explain refraction inside water?

 Jan 9th 2015, 02:37 PM #1 Junior Member   Join Date: Jan 2013 Posts: 24 Does Fermat principle explain refraction inside water? A light ray is the fastest route between two points P and Q,but what if Q is at the bottom of the sea so that light cannot reach it?
 Jan 9th 2015, 04:37 PM #2 Senior Member     Join Date: Apr 2008 Location: Bedford, England Posts: 668 If it is not in a vacuum, the photon arriving at Q is not the same photon that left P. The Photon from P is absorbed by an electron in the next atom along, which almost immediately emits another photon which is absorbed by an electron in the next atom along, which almost immediately emits another photon which is absorbed by an electron in the next atom along... If the material is very transparent, a photon eventually reaches Q If Q is very distant, or the material is not very transparent, the photon eventually meets an atom that does not re-emit it and it never gets to Q. topsquark likes this. __________________ You have GOT to Laugh !
 Jan 10th 2015, 06:23 AM #3 Junior Member   Join Date: Jan 2013 Posts: 24 What is the fastest route between P & Q if light cannot reach Q? Be carefull about math:it is not a trick!You cannot put Q on a "ray" because P & Q define the ray!It is exactly the Q point whitch defines the ray in Fermat's definition.
 Jan 10th 2015, 01:19 PM #4 Physics Team     Join Date: Jun 2010 Location: Morristown, NJ USA Posts: 2,339 harve - Fermat's theorem is an attempt to explain the path of a light ray that progresses from P to Q, but if the light isn't going from P to Q then it doesn't apply. Fermat's theorem doesn't attempt to explain how light is absorbed or reflected along the way, only how it is refracted at the boundary between two areas of different indexes of refraction. topsquark likes this.
Apr 24th 2017, 01:21 AM   #5
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ocean

 Originally Posted by ChipB harve - Fermat's theorem is an attempt to explain how it is refracted at the boundary between two areas of different indexes of refraction.
So how is it refracted at the ocean surface between air and seawater?

 Apr 24th 2017, 06:56 AM #6 Senior Member   Join Date: Aug 2010 Posts: 403 If $\displaystyle \theta$ is the angle at which the light ray strikes the surface of the water, $\displaystyle \phi$ is the angle at which the light ray continues into the water, $\displaystyle m_a$ is the "refractive index" in air and $\displaystyle m_w$ is the refractive index in water then $\displaystyle \frac{sin(\theta)}{sin(\phi)}= \frac{m_a}{m_w}$. If you know the angle, $\displaystyle \theta$, at which the light strikes the surface of the water, as well as the indexes of refraction, then the angle at which the light continues into the water is given by $\displaystyle sin(\phi)= \frac{m_w}{m_a}sin(\theta)$. That follows directly if you know what "Fermat's theorem" is but I don't know what else you want. topsquark likes this. Last edited by HallsofIvy; Apr 24th 2017 at 06:58 AM.
 Apr 24th 2017, 11:21 PM #7 Junior Member   Join Date: Jan 2013 Posts: 24 Snell's rule Thanks Ivy,but I have known this as the "Snell's rule" witch derives from Fermat's theorem.
Apr 26th 2017, 12:05 AM   #8
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emitted photon

 Originally Posted by MBW The Photon from P is absorbed by an electron in the next atom along, which almost immediately emits another photon which is absorbed by an electron in the next atom along, which almost immediately emits another photon which is absorbed by an electron in the next atom along...
I read that there is a slight lag from atom to atom. This delay must be appeared as a slowing of the speed of light inside the medium: But,how light speed remains constant inside a medium?

Last edited by harve; May 25th 2017 at 05:37 AM.

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