Humans have green eyes due to a combination of genetics and the amount of melanin present in their irises. It's not actually a green pigment, but rather a result of light scattering.
Here's a breakdown:
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Melanin: The amount of melanin is the primary factor. Green eyes have less melanin than brown eyes but more than blue eyes. Melanin is a brown pigment.
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Light Scattering (Rayleigh Scattering): This is the key to the green appearance. Because there's not a lot of melanin to absorb the light, some light scatters. When light scatters, the shorter wavelengths (blues and greens) are scattered more readily.
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Lipochrome: Some research suggests that a yellowish pigment called lipochrome might be present in some green eyes, contributing to the green hue. However, this is less definitively proven than the role of melanin and light scattering.
In essence, green eyes occur because the low amount of melanin allows light to scatter, and the structure of the iris scatters light in a way that appears green. It's similar to how the sky appears blue - it's not actually blue, but the scattering of sunlight makes it look that way.