Ambartsumian's principle of invariance and the reflection of radio waves from plane inhomogeneous slabs

Using Ambartsumian's principle of invariance we investigate for radio waves the reflection coefficient of a plane inhomogeneous slab. We find that the reflection coefficient, as a function of slab thickness, satisfies the Riccati equation. From this equation we deduce a geometric theorem on the upper and lower bounds of the reflection coefficient. We illustrate the theorem by applying it to several special cases.