*Question E3C06:
How does the VHF/UHF radio horizon compare to the geographic horizon?*  

*Correct Answer is  A: It is approximately 15 percent farther*  

### AI Response: (may contain errors)  

The VHF/UHF radio horizon is the distance over which radio waves can travel directly from a transmitter to a receiver without significant obstruction. This distance is typically greater than the geographic horizon due to the refraction of radio waves in the Earth's atmosphere.

### Explanation:

1. **Correct Answer: A (It is approximately 15 percent farther)**
   - The radio horizon is extended beyond the geographic horizon because radio waves are bent slightly downwards by the Earth's atmosphere. This bending effect, known as atmospheric refraction, allows radio waves to travel further than the line-of-sight distance.
   - A common rule of thumb is that the radio horizon is about 15% farther than the geographic horizon.

2. **Why the Other Choices are Incorrect:**
   - **B: It is approximately 20 percent nearer**
     - This is incorrect because the radio horizon is not nearer; it is farther due to atmospheric refraction.
   - **C: It is approximately 50 percent farther**
     - This overestimates the effect of atmospheric refraction. The radio horizon is not typically 50% farther; it is closer to 15%.
   - **D: They are approximately the same**
     - This is incorrect because the radio horizon is extended beyond the geographic horizon due to the bending of radio waves.

### Useful Formula:

The distance to the radio horizon can be estimated using the formula:  
$$
d = 1.23 \times \sqrt{h}
$$  
where:
- $d$ is the distance to the radio horizon in miles,
- $h$ is the height of the antenna in feet.

This formula accounts for the typical atmospheric refraction effect, which extends the radio horizon beyond the geographic horizon.