Double rainbow

The outer rainbow, reflected twice

Sometimes a fainter rainbow appears outside the first one. It is made by light that reflects twice inside the drops, and it sits about 51° from the shadow point. The extra reflection flips the order of the colors (violet on the outside), and light leaks out one more time, so it is fainter. The sky between the two rainbows is darker than the sky around it.

Why?Light that reflects once cannot leave at more than 42°, and light that reflects twice cannot leave at less than 51°. So no light from either one arrives in between, and a dark band appears. On the other hand, the sky inside the first rainbow is brighter than the sky around it.

Learn moreThe dark band between the two rainbows is called Alexander’s band, after the Greek scholar who first described it about 1,800 years ago. The outer rainbow runs from about 50.2° for red to about 53.5° for violet, so its band is wider. Light that reflects three or four times appears very faintly in the sky toward the Sun and is almost impossible to see with the naked eye.

Angle of the outer rainbow

51°

Outer rainbow · red

50.2° (inner edge)

Outer rainbow · violet

53.5° (outer edge)

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