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#1 2014-05-04 23:29:53

Agnishom
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From: The Complex Plane
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Refraction - Frequency is constant

Please post a genuine proof that frequency is conserved during refraction?


'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
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#2 2014-05-05 00:55:53

bob bundy
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Registered: 2010-06-20
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Re: Refraction - Frequency is constant

Frequency is determined by the distance between wave maxima (or minima).  Since you cannot get energy from nothing (nor lose it) the maxima (and minima) after passing through the boundary must be conserved, so the frequency must be constant.

Bob


You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei

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#3 2014-05-05 04:34:13

Agnishom
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From: The Complex Plane
Registered: 2011-01-29
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Re: Refraction - Frequency is constant

Frequency is determined by the distance between wave maxima (or minima).

That is wavelength


'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
'You have made another human being happy. There is no greater accomplishment.' -bobbym

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#4 2014-05-05 05:17:29

bob bundy
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Re: Refraction - Frequency is constant

It's both; as they're related by the speed of light in the medium.

Bob


You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei

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#5 2014-05-05 05:19:38

Agnishom
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From: The Complex Plane
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Re: Refraction - Frequency is constant

I'm kind of confused.


'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
'You have made another human being happy. There is no greater accomplishment.' -bobbym

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#6 2014-05-05 05:22:57

Agnishom
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From: The Complex Plane
Registered: 2011-01-29
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Re: Refraction - Frequency is constant

Since you cannot get energy from nothing (nor lose it) the maxima (and minima) after passing through the boundary must be conserved, so the frequency must be constant.

Why does wavelength change then?


'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
'You have made another human being happy. There is no greater accomplishment.' -bobbym

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#7 2014-05-05 05:54:51

bob bundy
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Registered: 2010-06-20
Posts: 6,532

Re: Refraction - Frequency is constant

I'm working on a diagram,  It will take a while.  sad

Bob


You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei

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#8 2014-05-05 06:13:46

Agnishom
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From: The Complex Plane
Registered: 2011-01-29
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Re: Refraction - Frequency is constant

Hmm, thanks for your efforts.


'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
'You have made another human being happy. There is no greater accomplishment.' -bobbym

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#9 2014-05-05 06:25:13

bob bundy
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Registered: 2010-06-20
Posts: 6,532

Re: Refraction - Frequency is constant

OK, I've got one.  Hope it helps.

The ladder on the left represents a beam of light moving from left to right towards the boundary, shown in red.

The wavelength is represented by AB.  Each cross line represents a transverse wave maximum.  They are equally spaced and connected by the formula

When the beam reaches the boundary, the speed of light is lower (let's say).  But the rate at which wave-fronts arrive at the boundary is unchanged.  Maxima must start at the boundary at the same rate and travel through this new medium at the slower rate, let's say d < c.  n is unaffected by the transmission through the boundary.  CD is the new wavelength; I'll call it mu.

Bob

View Image: refraction.gif

You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei

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#10 2014-05-05 06:31:21

bob bundy
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Registered: 2010-06-20
Posts: 6,532

Re: Refraction - Frequency is constant

Oh yes; forgot this:

The wave-fronts are perpendicular to the direction of the beam because it is a transverse wave.  As CD is shorter than AB, the beam bends towards

the normal.  You can work out the usual angle of incidence and refraction connection by doing some trig.  using the red line as the hypotenuse.

Bob


You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei

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#11 2014-05-05 06:44:58

Agnishom
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From: The Complex Plane
Registered: 2011-01-29
Posts: 18,887
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Re: Refraction - Frequency is constant

Will check tomorrow; Going to sleep smile


'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
'You have made another human being happy. There is no greater accomplishment.' -bobbym

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#12 2014-05-05 07:20:00

bob bundy
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Registered: 2010-06-20
Posts: 6,532

Re: Refraction - Frequency is constant

Sleep well.  sleep

Bob


You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei

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#13 2014-05-05 08:05:12

ShivamS
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Registered: 2011-02-07
Posts: 3,629

Re: Refraction - Frequency is constant

Light is an electromagnetic wave and as such it must obey Maxwell's equations. Two of Maxwell's equations (Gauss' law & Faraday's law) each impose a separate condition on the Electric Displacement Field & Electric Field respectively. Firstly, according to Gauss' law the boundary between two dielectric media (air & water) is uncharged then the normal component of the Electric Displacement Field must be continuous. Secondly, according to Faraday's law the normal component of the electric field must be continuous across the boundary of two dielectric media. The only way to satisfy both conditions is if the frequency of the light remains constant.

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