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Old Jan 9th 2015, 03:37 PM   #1
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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?
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Old Jan 9th 2015, 05:37 PM   #2
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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.
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Old Jan 10th 2015, 07:23 AM   #3
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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.
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Old Jan 10th 2015, 02:19 PM   #4
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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.
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Old Apr 24th 2017, 02:21 AM   #5
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ocean

Originally Posted by ChipB View Post
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?
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Old Apr 24th 2017, 07:56 AM   #6
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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.
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Last edited by HallsofIvy; Apr 24th 2017 at 07:58 AM.
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Old Apr 25th 2017, 12:21 AM   #7
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Snell's rule

Thanks Ivy,but I have known this as the "Snell's rule" witch derives from Fermat's theorem.
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Old Apr 26th 2017, 01:05 AM   #8
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emitted photon

Originally Posted by MBW View Post
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 06:37 AM.
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