Polar bear guard hairs are not white — they are hollow, colorless, keratin tubes with no pigment. A single hair held up to light is clear. What you see as "white fur" is countless partial reflections off thousands of hair surfaces scattering light in random directions, the same reason ground glass or snow looks white.
Because the tube wall (n≈1.3–1.6) surrounds a hollow air core, a ray entering near the tip at a steep-enough angle undergoes total internal reflection off the wall every time it grazes the core or outer surface — exactly like a step-index optical fiber — and rides straight down to the black, melanin-rich skin, where it is absorbed as heat. Whether real skin actually gains meaningful warmth this way (vs. from insulation alone) is a genuine, still-debated question in the biology literature — this sim shows the light-guiding mechanism itself, not a settled verdict on how much it heats a real bear.
- Incident angle / refractive index set the refraction angle at the tip and the resulting angle at the wall — Snell's law both times.
- Guiding succeeds only while the wall angle stays above the critical angle asin(1/n); below it, light leaks straight out the side instead of reaching the skin.