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

*Correct Answer is  D: The index of refraction*  

### AI Response: (may contain errors)  

The speed of electromagnetic waves through a medium is determined by the **index of refraction**. Let's break down why this is the correct answer and why the other choices are incorrect.

### Correct Answer: D: The index of refraction

- **Index of Refraction ($n$):** This is a measure of how much the speed of light (or electromagnetic waves) is reduced inside a medium compared to the speed of light in a vacuum. The formula is:

  $$ v = \frac{c}{n} $$

  where:
  - $v$ is the speed of light in the medium,
  - $c$ is the speed of light in a vacuum (approximately $3 \times 10^8$ m/s),
  - $n$ is the index of refraction of the medium.

  A higher index of refraction means that the electromagnetic waves travel slower through the medium.

### Why the Other Choices are Incorrect:

- **A: Resistance and reactance:** These are properties related to electrical circuits, not directly to the propagation speed of electromagnetic waves in a medium. Resistance affects how much energy is lost as heat, and reactance affects how energy is stored in the circuit, but neither directly determines wave speed in a medium.

- **B: Evanescence:** This term refers to the phenomenon where waves decrease in amplitude as they propagate through a medium, particularly in the context of evanescent waves in waveguides or near surfaces. It does not determine the speed of electromagnetic waves.

- **C: Birefringence:** This is a property of certain materials where the index of refraction varies depending on the polarization and direction of light passing through it. While it affects how light propagates through such materials, it is not a general determinant of wave speed in all media.

In summary, the index of refraction is the key factor that determines how fast electromagnetic waves travel through a medium, making it the correct answer.