Wave Optics at Interfaces – Reflection and refraction basics For electromagnetic radiation incident on a smooth interface, which relation is always true?

Introduction / Context:
When an electromagnetic wave meets a planar boundary, part of it may reflect and part refract. The geometric relationships between the incident, reflected, and refracted rays govern sensor viewing geometry and radar/lidar returns.

Given Data / Assumptions:

• Smooth, plane interface between two homogeneous media.
• Angles measured from the normal to the interface.
• Standard laws of reflection and refraction.

Concept / Approach:
The law of reflection states θ_i = θ_r (incidence equals reflection). Refraction follows Snell’s law n1 * sin θ_i = n2 * sin θ_t, which does not imply θ_i = θ_t except for equal indices.

Step-by-Step Solution:
Apply reflection law: θ_incidence = θ_reflection ⇒ true.Apply refraction law: θ_refraction generally differs from θ_incidence unless n1 = n2.Option (c) is ill-posed; angles do not add that way.

Verification / Alternative check:
Derivations from Fermat’s principle or boundary conditions on EM fields yield the same reflection law; experiments confirm mirror-like reflection symmetry.

Why Other Options Are Wrong:

• (a) Violates Snell’s law in general.
• (c) Not a recognized geometric relationship.
• (d) Cannot be correct because (a) and (c) are false.

Common Pitfalls:
Measuring angles from the surface instead of the normal or assuming equal refractive indices causes mistakes.

Final Answer:
Angle of incidence = angle of reflection