# The speed of light in glass and water

• B
Hi,

The speed of light is given c=1/√(ε0μ0) where ε0 is permittivity of vacuum and μ0 is vacuum permeability.

The permittivity and permeability of a material is given as ε=εrε0 and μ=μr0 respectively where ε is absolute permittivity of the material and εr is relative permittivity of the material with respect to vacuum. The same goes for permeability.

The speed of light in water is given as 2.25×108 m/s and in glass it is around 1.95×108 m/s.

I assume that speed of light in a certain material could be stated as c=1/√(εμ). It looks like one cannot write c=1/√(εμ) because as you can see and as was expected that calculated value of speed of light in glass is lager than that of water.

So, how do we really calculate the speed of light in a material using its permittivity and permeability values, or where am I going wrong with my calculation?

Thank you!

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tech99
Gold Member
I don't think you can assume Er for water is around 80 at optical frequencies. Er for water varies in a complex way with frequency.

• PainterGuy
Thank you!

Question 1:
So, what do I conclude from this? I'd say that the speed of light in a certain material could be stated as c=1/√(εμ) using material's permittivity and permeability and the formula should work. But the comparison between speed of light in two or more materials should be specified for a certain frequency because both permittivity and permeability are affected by the frequency. Do you agree?

Question 2:
εr for diamond is stated as 5.5-10 and hence one could find its absolute permittivity. μr for diamond is stated as -1. 1.

The speed of light in diamond is 1.24×108 m/s. I understand that negative permeability means a diamagnetic material but in such a case how do we find the speed of light in such a diamagnetic material using c=1/√(εμ)? One cannot find the square root of a negative number.

Thanks a lot for your help and time!

tech99
Gold Member
Thank you!

Question 1:
So, what do I conclude from this? I'd say that the speed of light in a certain material could be stated as c=1/√(εμ) using material's permittivity and permeability and the formula should work. But the comparison between speed of light in two or more materials should be specified for a certain frequency because both permittivity and permeability are affected by the frequency. Do you agree?

Question 2:
εr for diamond is stated as 5.5-10 and hence one could find its absolute permittivity. μr for diamond is stated as -1. 1.

The speed of light in diamond is 1.24×108 m/s. I understand that negative permeability means a diamagnetic material but in such a case how do we find the speed of light in such a diamagnetic material using c=1/√(εμ)? One cannot find the square root of a negative number.

Thanks a lot for your help and time!
I agree with Q1.
For Q2, my understanding is that all matter is slightly diamagnetic, but the property is overwhelmed by ferromagnetism and paramagnetism in some materials. The relative permeability of diamagnetic materials is slightly less than 1, but not negative. For example, if I place a wooden core in a solenoid, it will be slightly weakened but not reversed. have a look at the Britannica site: https://www.britannica.com/science/magnetic-permeability

• PainterGuy
Thank you!

I used the following webpage for μr of diamond, http://hyperphysics.phy-astr.gsu.edu/hbase/Tables/magprop.html .

It says, "Here the quantity Km is called the relative permeability, a quantity which measures the ratio of the internal magnetization to the applied magnetic field. If the material does not respond to the magnetic field by magnetizing, then the field in the material will be just the applied field and the relative permeability Km =1. A positive relative permeability greater than 1 implies that the material magnetizes in response to the applied magnetic field. The quantity χm is called magnetic susceptibility, and it is just the permeability minus 1."

For Carbon (diamond) χm is -2.1 which means relative permeability, Km, is -2.1+1=-1.1

But as now I see it it's a different relative permeability because it's not given in reference to vacuum's permeability.

I will look for the other relative permeability value for diamond which, as you say, is never negative and let you know. Thanks a lot.

Thank you!

For Carbon (diamond) χm is -2.1x10-5.
Yes, you are correct. I did see that "10-5" but forgot to mention it.

According to this source, the μr of diamond is "1".

I also tried to calculate it myself. Again, the speed of light in diamond is 1.24x108 m/s and in water it is 2.25x108 m/s although in view of the formula c=1/√(εμ) speed of light in diamond should be greater than in water because for diamond the product "εμ" is less than that of water. But again I think it has to do with variable values of both ε and μ with respect to EM frequency.

Please let me know if I have it correct. Thanks a lot.

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Hi,

I wanted to ask a related question, rather a silly one. An electromagnetic wave has two perpendicular components - electric and magnetic components perpendicular to each other. How a material affects magnetic component is represented by μ or μr and electric component by ε or εr. If propagation of both components is affected differently by a material then obviously it would affect their individual propagation speeds in the material. Wouldn't it be possible that electric and magnetic components get 'misaligned' with each other and electromagnetic wave ceases to exist because its two components are no longer propagating hand in hand. In other words, one component gets ahead of the other one. I have also read that it's the electric component which interacts with matter more strongly compared to the magnetic counterpart. The speed of an electromagnetic wave in a material is by v=1/√(εμ) and both ε and μ changes with frequency.

I understand that practically this never happens; an EM wave enters one side and leaves the other side as one piece.

Thank you!

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