Transition from one dielectric medium to another medium

[phoenix95]

Homework Statement

A plane electromagnetic wave of frequency 5×10¹⁴ Hz and amplitude 10³ V/m, traveling in a
homogeneous dielectric medium of dielectric constant 1.69, is incident normally at the interface
with a second dielectric medium of dielectric constant 2.25. The ratio of the amplitude of the
transmitted wave to that of the incident wave is ___________.

Homework Equations

The Attempt at a Solution

It should be 1 right? I mean passing from one dielectric medium to another would result in the change of phase velocity but not the amplitude??

 

[DrDu]

You should also consider reflection.

 

[phoenix95]

You should also consider reflection.

Would you please explain a little bit? I don't know how to apply that concept...

 

[DrDu]

If the media are transparent, then the sum of the reflected and transmitted intensity must equal the incident intensity. The relative intensity of the transmitted and reflected intensity is dictated by the continuity of electric and magnetic fields at the boundary. Probably you were talking about this in class?

 

[phoenix95]

If the media are transparent, then the sum of the reflected and transmitted intensity must equal the incident intensity. The relative intensity of the transmitted and reflected intensity is dictated by the continuity of electric and magnetic fields at the boundary. Probably you were talking about this in class?

No, this question is from one of the entrance examinations... I tried searching in the internet but I couldn't find any reasonable explanations...

 

[TSny]

http://farside.ph.utexas.edu/teaching/em/lectures/node104.html

You'll also need to know how to relate the dielectric constant to the index of refraction.

 

[DrDu]

http://farside.ph.utexas.edu/teaching/em/lectures/node104.html

 

[phoenix95]

so the answer would be 0.857... Thanks a lot... The information was very useful...

 

[TSny]

so the answer would be 0.857...

I don't believe this is the correct answer.

Equation (1227) of the link gives E_t (but there is a misprint on the right of the equation where E_t should be E_i).

Note that this equation is in terms of the indices of refraction of the materials, not the dielectric constants.

I guess you have to assume that the question is concerned with the electric field amplitudes and not the magnetic field amplitudes.

 

[DrDu]

The index of refraction and the relative dielectric constant are related as $n=\sqrt{\epsilon_r}$. So n1=1.3 and n2=1.5 giving for the ratio of the transmitted to the incident electric field amplitude: 2n1/(n1+n2)=2.6/(1.3+1.5)=0.93.