Code Notes made by Vaibhav Rathod

PathTracer Learning - Concept - Fresnel Effect

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Written by Vaibhav Rathod

Concept: Fresnel Effect

What Is the Fresnel Effect?

  • At any interface between two media, light is partially reflected and partially transmitted
  • The ratio depends on the angle of incidence
  • At grazing angles (θ → 90°): almost all light is reflected
  • At normal incidence (θ = 0°): only a small fraction is reflected
  • This is why water looks like a mirror when viewed at a shallow angle

Exact Fresnel Equations (Schlick’s Approximation)

  • Full Fresnel equations (from Maxwell’s equations) are expensive
  • Schlick (1994) approximation — used in virtually all real-time renderers
  • F(θ) = F0 + (1 - F0) * (1 - cos(θ))^5
  • cos(θ) = dot(V, H) — angle between view direction and half-vector
  • F0 — reflectance at normal incidence (0° angle)

F0 Values

  • Dielectrics (non-metals: plastic, glass, skin, wood)
    • F0 ≈ 0.04 (4%) for most dielectrics
    • Range: 0.02 (water) to 0.08 (gemstones)
    • Formula from IOR: F0 = ((n - 1) / (n + 1))²
    • Glass (n=1.5): F0 = ((1.5-1)/(1.5+1))² = 0.04
  • Metals (conductors: gold, silver, copper, iron)
    • F0 = base color of the metal (RGB values)
    • Gold: F0 ≈ (1.0, 0.71, 0.29)
    • Silver: F0 ≈ (0.95, 0.93, 0.88)
    • Copper: F0 ≈ (0.95, 0.64, 0.54)
    • Metals absorb transmitted light — no diffuse component

Metallic Workflow (PBR)

  • metallic parameter in [0, 1]
  • F0 = lerp(vec3(0.04), baseColor, metallic)
  • diffuse_color = baseColor * (1 - metallic) — metals have no diffuse
  • This is the Disney/Unreal/Godot PBR convention
  • Why: real materials are either dielectric (F0=0.04) or metal (F0=baseColor)
  • Values between 0 and 1 are for blending (e.g., dirty metal, oxidized surface)

Energy Conservation with Fresnel

  • Fresnel tells us how much light is reflected vs transmitted
  • For opaque surfaces: transmitted = 1 - F(θ) → absorbed or diffusely scattered
  • Specular contribution: F(θ) * f_specular
  • Diffuse contribution: (1 - F(θ)) * f_diffuse
  • This ensures total reflectance ≤ 1
  • In code: 
    vec3 F = schlick(F0, dot(V, H));
vec3 kS = F;                    // specular fraction
vec3 kD = (1.0 - kS) * (1.0 - metallic);  // diffuse fraction (metals have no diffuse)
vec3 brdf = kD * diffuse + kS * specular;

Exact Fresnel (for Reference)

  • For dielectrics (real IOR):
    • rs = (n1*cos(θi) - n2*cos(θt)) / (n1*cos(θi) + n2*cos(θt))
    • rp = (n2*cos(θi) - n1*cos(θt)) / (n2*cos(θi) + n1*cos(θt))
    • F = (rs² + rp²) / 2
    • cos(θt) from Snell’s law: cos(θt) = sqrt(1 - (n1/n2)² * (1 - cos²(θi)))
  • For conductors (complex IOR n + ik):
    • More complex formula involving absorption coefficient k
    • Schlick with measured F0 is a good approximation

Total Internal Reflection

  • When light travels from dense to less dense medium (e.g., glass to air)
  • At angles beyond the critical angle: all light is reflected, none transmitted
  • Critical angle: θ_c = arcsin(n2/n1) where n1 > n2
  • In GLSL refract: returns vec3(0) when TIR occurs
  • Check: 1 - eta² * (1 - NdotI²) < 0 → TIR

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