The fogbow is created by sun rays passing through small water droplets. At ice cap temperatures the water drops are unstable, they are supercooled below zero Celsius. The phase change to the stable state, ice, needs nuclei on which crystals can grow. These are lacking in the pure air over the ice sheet. Homogeneous nucleation, without nuclei, usually requires temperatures below about -40 Celsius.
Fogbows form similarly to rainbows. Light enters a near spherical water drop, is refracted, a small fraction is internally reflected from the opposite side and is refracted again as it leaves.
The key difference from rainbow formation is drop size. Fog and mist droplets (1-100 micron diameter) are fairly large compared to the wavelengths of visible light but small enough that diffraction and interference effects become more pronounced. The rainbow of well-defined sharp colours is considerably broadened and colours overlap to give almost white.
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