# Cause for refraction of light

Yeah sure, change in speed of light as it travels from one medium to another. But why does it affect the path? I mean, shouldn't the light ray just go in the same direction with a different speed? Why does it have to change its path?

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Gold Member
If we think light as a wave

Cause for refraction of light.

I have heard those examples before, but do they actually explain the phenomenon? Or do they just give a similar situation where the direction changes with speed? Bottomline, does light change direction for the same reason as the above phenomena?

UltrafastPED
Gold Member
The example given in #2 is a very general property of wave behavior - it works for light, sound, ripples in water, etc. It can be shown by an application of the Hughens' wavelet principle, ~1678 by Christiaan Huyghens:
http://en.wikipedia.org/wiki/Christiaan_Huygens#Optics

If you know differential equations you can derive this behavior from the wave equation:
http://hyperphysics.phy-astr.gsu.edu/hbase/waves/waveq.html

This is usually done in an upper level physics course such as electromagnetic field theory or optics.

Drakkith
Staff Emeritus
I have heard those examples before, but do they actually explain the phenomenon? Or do they just give a similar situation where the direction changes with speed? Bottomline, does light change direction for the same reason as the above phenomena?
Yes, light is an EM wave and the examples given are the reason refraction occurs.

Thank you.

Another way to understand that is the principle of minimum optical path (which basically means the light ray takes the path that minimizes the total amount of time taken to go from point A to point B).

jtbell
Mentor
principle of minimum optical path
Which is commonly known as Fermat's principle, and is perhaps more easily Googlable under that name.

morrobay
Gold Member
Is this correct : The refractive index of a material at a particular frequency , n =c/v is caused by the EM wave being slowed in the material because the electric field creates a disturbance in the charges of each atom , primarily the electrons proportional to the permittivity.
This oscillation of charges itself causes the radiation of an electromagnetic wave of the same frequency that is slightly out of phase with the incident wave. The sum of these two waves creates a wave of the same frequency but shorter wavelength than the original leading to a slowing in the waves travel.

It is my understanding that the superposition of two waves of same frequency and out of phase
produces a resultant wave with amplitude change only : (2ymcos(ø/2)

Last edited:
Is this correct : The refractive index of a material at a particular frequency , n =c/v is caused by the EM wave being slowed in the material because the electric field creates a disturbance in the charges of each atom , primarily the electrons proportional to the permittivity.
This oscillation of charges itself causes the radiation of an electromagnetic wave of the same frequency that is slightly out of phase with the incident wave. The sum of these two waves creates a wave of the same frequency but shorter wavelength than the original leading to a slowing in the waves travel.

It is my understanding that the superposition of two waves of same frequency and out of phase
produces a resultant wave with amplitude change only : (2ymcos(ø/2)
The statement is correct. Note that this is not just a superposition of two waves which would indeed affect the phase only. More electrons are being stimulated all the time along the wave path and continuously add their effects to the wave.

jtbell
Mentor
It is my understanding that the superposition of two waves of same frequency and out of phase produces a resultant wave with amplitude change only : (2ymcos(ø/2)
The phase of the resultant wave is generally different from both of the two original waves:
$$A_1 \cos (\omega t + \phi_1) + A_2 \cos (\omega t + \phi_2) = A \cos (\omega t + \phi)$$
where
$$A^2 = A_1^2 + A_2^2 + 2A_1 A_2 \cos (\phi_2 - \phi_1)\\ \tan \phi = \frac {A_1 \sin \phi_1 + A_2 \sin \phi_2}{A_1 \cos \phi_1 + A_2 \cos \phi_2}$$

You will understand it better if you read Principle of least action. Moreover, refraction of light also depends upon the geometry and internal atomic structure of that particular element.

Here's Fermat's Principle or Principle of Least Action

http://en.wikipedia.org/wiki/Fermat's_principle

Regards.

Thank you.

I do we have a doubt in the principle of least action. Why do we want the kinetic energy to be large and the potential energy less if we want a small difference? Why cant both be large or both small? Wouldn't the difference be less then?

I do we have a doubt in the principle of least action. Why do we want the kinetic energy to be large and the potential energy less if we want a small difference? Why cant both be large or both small? Wouldn't the difference be less then?
What difference? The least action principle states that the action is stationary for the true paths taken by particles where the action S is given by S = K - U - that is kinetic energy minus potential energy.When you say you want a small difference we must state what is being measured that happens to have a small difference. You can't just say small difference and leave it at that. Makes no sense.

morrobay
Gold Member
The Poynting vector S = rate of energy flow per unit area = dU/dtA = 1/μ0ExB
When the EM wave is oblique at the boundary of medium then the value of S is less than incident wave ( greater area).
Then is it correct to say that refraction is a way that this decrease in S is opposed at the boundary ?

What difference? The least action principle states that the action is stationary for the true paths taken by particles where the action S is given by S = K - U - that is kinetic energy minus potential energy.When you say you want a small difference we must state what is being measured that happens to have a small difference. You can't just say small difference and leave it at that. Makes no sense.