Question E3A10:
What determines the speed of electromagnetic waves through a medium?  

Choices:  
A: Resistance and reactance  
B: Evanescence  
C: Birefringence  
D: The index of refraction    

Correct Answer is  D: The index of refraction  

Correct answer: D — The index of refraction

1) Why it’s correct
- The speed of an electromagnetic wave in a medium is set by the medium’s index of refraction, $n$, via:
  $$v = \frac{c}{n}$$
  where $c$ is the speed of light in vacuum.
- The index of refraction is determined by the medium’s permittivity and permeability:
  $$n = \sqrt{\epsilon_r \mu_r}$$
  For most non-magnetic materials, $\mu_r \approx 1$, so $n \approx \sqrt{\epsilon_r}$ and $v \approx c/\sqrt{\epsilon_r}$.

2) Why the others are incorrect
- A: Resistance and reactance  
  These are circuit parameters. Wave speed in a medium depends on its electromagnetic properties ($\epsilon$, $\mu$), not lumped R and X. Even on transmission lines, in the low-loss case:
  $$v \approx \frac{1}{\sqrt{LC}}$$
  which corresponds to $\epsilon$ and $\mu$, not R or X.
- B: Evanescence  
  Evanescent waves are non-propagating (exponentially decaying) fields below cutoff or under total internal reflection. They don’t set propagation speed through a medium.
- C: Birefringence  
  This is a phenomenon where a material has different indices (and thus different speeds) for different polarizations/directions. The speeds are still determined by the indices of refraction; “birefringence” isn’t the determining parameter itself.

3) Useful formulas and rules of thumb
- Wave speed: $$v = \frac{1}{\sqrt{\mu \epsilon}} = \frac{c}{n}$$
- Index of refraction: $$n = \sqrt{\epsilon_r \mu_r} \approx \sqrt{\epsilon_r} \text{ (if } \mu_r \approx 1)$$
- Wavelength in medium: $$\lambda = \frac{v}{f} = \frac{c}{n f}$$
- Velocity factor (e.g., coax): $$\text{VF} = \frac{v}{c} = \frac{1}{n} \approx \frac{1}{\sqrt{\epsilon_r}}$$
  Typical VFs: ~0.66 (solid PE), ~0.80–0.85 (foam PE).