한국어로 읽기 The 42° Rainbow

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Bending again on the way out

Each color leaves the drop in its own direction

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Light leaving the drop

The reflected light travels to the lower front of the drop and passes back into the air. It bends once more on the way out, and the colors spread even further. Yellow light leaves about 42° below the direction of the Sun. Red leaves at about 42.4° and violet at about 40.6°, so each color has its own exit angle.

Why?Light bends twice, once going into the water and once coming out, and both times violet bends more. So the light from a single drop fans out, each color in a slightly different direction.

Learn moreRed and violet leave about 1.8° apart. A rainbow’s band in the sky is about that wide too, roughly the width of one or two fingers held at arm’s length. On the protractor, 0° points toward the Sun (the incoming light turned around).

Exit angle (yellow light)
42°
Red leaves at
42.4°
Violet leaves at
40.6°

calculated from the refractive index of water (IAPWS, 20 °C) and the laws of refraction and reflection

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Wikipedia: Rainbow

More in the series

The numbers come from the refractive index formula for water (IAPWS 1997) and the laws of refraction (Snell) and reflection (Fresnel). In the 3D view, the raindrop and the spreading of colors inside it are drawn larger so you can see them.