A sky wave with a frequency 55 Mhz is incident on D-region of earth atmosphere at 45°.WHat is the angle of refraction is (electron density for D-region is 400 electron/c.c.)

To find the angle of refraction of a sky wave incident on the D-region of the Earth's atmosphere, we can use Snell's Law, which relates the angles of incidence and refraction to the indices of refraction of the two media involved. In this case, the wave is transitioning from free space into the ionized D-region of the atmosphere, which has a specific electron density that affects its refractive index.

Understanding the Refractive Index

The refractive index (n) of a medium can be calculated using the formula:

• n = 1 - (Ne * e²) / (2 * ε₀ * m * c²)

Where:

• Ne = electron density (in electrons per cubic centimeter)
• e = charge of an electron (approximately 1.6 x 10^-19 coulombs)
• ε₀ = permittivity of free space (approximately 8.85 x 10^-12 F/m)
• m = mass of an electron (approximately 9.11 x 10^-31 kg)
• c = speed of light (approximately 3 x 10⁸ m/s)

Calculating the Refractive Index for the D-region

Given that the electron density (Ne) is 400 electrons/cm³, we first convert this to electrons/m³:

• 400 electrons/cm³ = 400 x 10⁶ electrons/m³

Now, substituting the values into the refractive index formula:

• n = 1 - (400 x 10⁶ * (1.6 x 10^-19)²) / (2 * (8.85 x 10^-12) * (9.11 x 10^-31) * (3 x 10⁸)²)

This calculation will yield a refractive index slightly less than 1, indicating that the wave will slow down as it enters the D-region.

Applying Snell's Law

Snell's Law states:

• n₁ * sin(θ₁) = n₂ * sin(θ₂)

Where:

• n₁ = refractive index of free space (approximately 1)
• θ₁ = angle of incidence (45°)
• n₂ = refractive index of the D-region (calculated above)
• θ₂ = angle of refraction

Calculating the Angle of Refraction

Rearranging Snell's Law to solve for θ₂ gives us:

• sin(θ₂) = (n₁ * sin(θ₁)) / n₂

Substituting the known values:

• sin(θ₂) = (1 * sin(45°)) / n₂

Since sin(45°) is approximately 0.707, we can calculate θ₂ once we have n₂. After computing n₂ from the earlier step, plug it into this equation to find sin(θ₂), and then use the inverse sine function to find θ₂.

Final Thoughts

By following these steps, you can determine the angle of refraction for the sky wave as it enters the D-region of the atmosphere. This process illustrates how electromagnetic waves interact with ionized media, which is crucial for understanding radio wave propagation and communication technologies.