Polar bears look white, but their fur does not contain white pigment in the way you might expect.
The individual hairs are mostly translucent.
The white appearance comes from the way light interacts with the coat.
Light scatters through the fur
When light enters the dense coat, it is reflected and scattered by huge numbers of hairs.
That scattered light comes back toward your eyes.
The combined effect makes the fur look white or creamy.
This is somewhat similar to why snow looks white even though ice is clear. In both cases, lots of small transparent or translucent structures scatter light.
The skin underneath is dark
Beneath the fur, polar bear skin is much darker.
That dark skin can absorb solar energy when light reaches it.
But the bear’s main protection from Arctic cold comes from its thick coat and a substantial layer of body fat.
Does the fur always look bright white?
No.
Lighting can make the coat look creamy or yellowish.
Dirt, oils, and whatever the bear has been doing can change its appearance too.
The fur is not a perfectly white painted surface.
Why is the coat so thick?
Polar bears live in an environment where preventing heat loss is critical.
Their dense fur traps insulating air.
The underlying body fat provides another strong layer of insulation.
That is the opposite temperature problem from animals such as elephants, which use large ears to help release body heat.
Is polar bear fur hollow?
Descriptions of polar bear hair often focus on its translucent appearance and structure.
For this explanation, the important point from the recorded script is that the hairs are not simply filled with white pigment.
The white look comes mainly from light interacting with the coat.
So the bear looks white because of optics.
The skin underneath is much darker than the coat suggests.
And that’s the short explanation.
Related explanations: Why is snow white if ice is clear?, Why do penguins huddle together?, and Why do elephants have big ears?