Specular vs Diffuse Reflection – Which law applies to specular reflection? When a surface reflects radiation in a mirror-like manner (specular reflection), which law does that reflection obey most directly?

Introduction / Context:
Surface reflection behaviour shapes the appearance of objects in imagery. Two limiting cases are specular reflection (mirror-like) and Lambertian diffuse reflection (equal radiance in all directions relative to surface normal with cosine scaling). Identifying which physical law governs each helps in interpreting glint, water surfaces, and polished materials.

Given Data / Assumptions:

• Incident beam on a smooth surface at an angle to the normal.
• Wavelength range where geometric optics applies.
• Idealized specular or diffuse limits for clarity.

Concept / Approach:

Specular reflection obeys the geometric law that the angle of reflection equals the angle of incidence, both measured in the plane of incidence—commonly associated with Snell’s laws of refraction/reflection at interfaces. In contrast, Lambert’s cosine law describes diffuse reflectors, and Planck’s law governs thermal emission spectra of blackbodies, not reflection.

Step-by-Step Solution:

Verification / Alternative check:

BRDF models reduce to a delta-like lobe for an ideal specular surface, consistent with Snellian reflection.

Why Other Options Are Wrong:

Lambert’s law models matte surfaces; Planck’s law concerns emission, not reflection; “All of these” mixes incompatible laws.

Common Pitfalls:

Confusing specular glint with Lambertian shading; overlooking the plane-of-incidence condition; conflating emission with reflection phenomena.

Final Answer:

Snell’s law (angle of incidence equals angle of reflection in the plane of incidence)