한국어로 읽기 The 42° Rainbow

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The shadow point

The sky shines 42° from your head’s shadow

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Through my eyes, Sun at my back

Now we are back on the ground. With the Sun at your back, the shadow of your head points to the spot exactly opposite the Sun. Let’s call that direction the shadow point. Raindrops 42° away from the shadow point send their bunched-up light straight toward your eyes. That is why that part of the sky looks bright.

Why?Sunlight comes from very far away, so its rays arrive almost parallel, and the direction toward the Sun is the same from every raindrop. For light leaving a drop 42° away from the Sun’s direction to reach your eye, that drop has to sit 42° away from the shadow point as seen from your eye.

Learn moreWhen the Sun is 15° above the horizon, the shadow point is 15° below it. So the top of the rainbow sits about 27° above the horizon (42 − 15). The raindrops on screen are drawn much larger so you can see them.

Angle from the shadow point
42°
Shadow point
15° below the horizon
Top of the rainbow
about 27° above the horizon

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.