1. (Assessed, both parts)
A. In class, using Snell’s Law we discussed the dependence of the maximum frequency of reflection on the zenith angle of transmission. Using some simple geometry, determine a relationship between the MUF, plasma frequency, the height of the ionosphere, and the distance to the target. For simplicity, assume that an ionosphere is a thin plane.
B. How does allowing for the curvature of the Earth (and ionosphere) affect the relationship you derived in B)? To demonstrate this, derive an expression that relates the ground distance and peak height of the ionosphere to the Maximum Usable Frequency. Examine test cases or plots to elucidate the dependency of MUF on the distance to the target and ionosphere height. You may again assume that the ionosphere is represented by a thin layer, this time a concentric sphere around the earth at a fixed height.