Final answer:
The Huygens-Fresnel principle, along with solutions to Maxwell's equations, is used in calculating the x-directed backscattered field in the far-field region rather than Snell's Law, which is more applicable to initial boundary conditions in refraction scenarios.
So option (B) is the correct answer.
Step-by-step explanation:
To calculate the x-directed backscattered field in the far-field region, the principle that is most relevant is the Huygens-Fresnel principle. Snell's Law is typically used to describe the relationship between angles and indices of refraction when a wavefront passes from one medium into another. It is given by the equation n1 sin θ₁ = n2 sin θ₂. In the context of scattering problems, especially in the far-field region, one would apply Snell's Law for initial boundary conditions but would rely on solutions to Maxwell's equations and principles such as the Huygens-Fresnel for detailed field calculations.
Snell's Law can be simplified under the small-angle approximation, where sin θ ≈ θ, which makes the law take the form n1θ₁ ≈ n2θ₂. This can serve as a starting point for determining the initial conditions of the scattered wave. However, the complex wave interactions and propagation in the far-field region require a more sophisticated approach than what Snell's Law can provide.