With increases of ionic density, the R.I, of ionosphere

Options

A. decreases
B. increases
C. does not change
D. may increase (or) decrease

Answer

To address the question regarding the relationship between ionic density and the refractive index (R.I.) of the ionosphere, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding the Ionosphere**:
The ionosphere is a region of the Earth's upper atmosphere, from about 30 miles (48 km) to 600 miles (965 km) above the surface, where ionization occurs due to solar radiation. This ionization creates free electrons and ions, which are crucial for radio wave propagation.

**Hint**: Remember that the ionosphere is characterized by the presence of free electrons and ions due to solar radiation.

2. **Defining Refractive Index**:
The refractive index (R.I.) of a medium is defined as the ratio of the speed of light in a vacuum to the speed of light in that medium. It can be mathematically expressed as:
\[ n = \frac{c}{v} \]
where \( n \) is the refractive index, \( c \) is the speed of light in a vacuum, and \( v \) is the speed of light in the medium.

**Hint**: Recall that the refractive index indicates how much light slows down in a medium compared to a vacuum.

3. **Effect of Ionic Density on R.I.**:
As the ionic density increases in the ionosphere, there are more free electrons available. The presence of these free electrons affects the propagation of electromagnetic waves (like radio waves). The refractive index of a medium with free electrons can be approximated by:
\[ n \approx 1 - \frac{N e^2}{\epsilon_0 m \omega^2} \]
where:
- \( N \) is the electron density (ionic density),
- \( e \) is the charge of an electron,
- \( \epsilon_0 \) is the permittivity of free space,
- \( m \) is the mass of an electron,
- \( \omega \) is the angular frequency of the wave.

**Hint**: Consider how the increase in electron density (ionic density) influences the speed of light in the ionosphere.

4. **Conclusion**:
From the above relationship, we can conclude that as the ionic density \( N \) increases, the term \( \frac{N e^2}{\epsilon_0 m \omega^2} \) increases, leading to a decrease in the refractive index \( n \). Therefore, with an increase in ionic density, the refractive index of the ionosphere decreases.

**Hint**: Think about how the increase in ionic density impacts the electromagnetic wave's interaction with the medium.

### Final Answer:
With an increase in ionic density, the refractive index of the ionosphere decreases.