# Homework Help: ElectroMagnetic Wave In Liquid Help with Index of Refraction?

1. Nov 29, 2012

### bmb2009

ElectroMagnetic Wave In Liquid.. Help with Index of Refraction??

1. The problem statement, all variables and given/known data

Consider the propagation of an electromagnetic wave in some liquid. The y-component of its electric field is given by Ey(x,t)=4.3 x104 V/m sin(5.40E-2m-1x + 6.00E+0 x106 s-1 t). How large is the index of refraction of that liquid?

2. Relevant equations

3. The attempt at a solution

Honestly had no idea how to even start this problem? Any help would be great. Thanks!

2. Nov 29, 2012

### Ibix

Re: ElectroMagnetic Wave In Liquid.. Help with Index of Refraction??

Your equation is quite confusing. Did you mean:
Ey(x,t)=4.3x104 V/m sin(5.40x10-2m-1x + 6.00x106 s-1 t)

What you have is an equation describing the electric field of the EM wave at point x and time t.

If you freeze time at t=0, the equation simplifies somewhat. Can you read off the wavelength?

If you stand at the point x=0, the equation also simplifies somewhat. Can you read off the frequency?

That should give you enough information to derive the refractive index. Post your working if you get stuck.

3. Nov 29, 2012

### bmb2009

Re: ElectroMagnetic Wave In Liquid.. Help with Index of Refraction??

Yes sorry the equation you interpreted was what I meant... I felt like I know what I am doing but still can't get the answer. Here's what i tried. since the speed of light velocity in a material I'll call v, equals the wavelength in the material times the frequency i.e. v=wavelength*frequency and since the index of refraction, n, equals c/v...If I can find the wavelength and the frequency I should be able to find the v and in turn the index of refraction. I know from my text book that E(x,y)=E_0(sin(2*Pi(x/wavlength - frequency*t))) so I should just have to factor out a 2Pi from the terms inside the sine correct? I tried this and it did not work... Help :/

4. Nov 30, 2012

### Ibix

Re: ElectroMagnetic Wave In Liquid.. Help with Index of Refraction??

Your methodology seems right. Perhaps you made an arithmetic error? Post your wavelength, frequency, velocity and index, and I can take a look.

By the way - I presume the wave is moving in the x-direction? If not, your wavelength will be wrong.

5. Nov 30, 2012

### bmb2009

Re: ElectroMagnetic Wave In Liquid.. Help with Index of Refraction??

I assume it's in the x direction because the question is posted verbatim from the textbook.
...
My wavelength: factor 2*pi from the term (x/.054m) to get x/(.054*2pi) so my wavlength =
.33929 m.
MY frequency: factor 2*pi from the term (6x10^6) = (6x10^6)/(2*pi) so my frequency = 3.23998x10^5

v=1.099x10^5 ..... this is where im confused because to get a reasonable number for the index of refraction the velocity will have to be some number x10^7 correct?

If you could run the numbers and post what you get I'd be very grateful. Thanks

6. Nov 30, 2012

### bmb2009

Re: ElectroMagnetic Wave In Liquid.. Help with Index of Refraction??

Nevermind I just re did the problem and got the right answer... thank you for your help though i really appreciate it!