Why is the inside of the rainbow brighter?

Recently we showed this photo of a double-rainbow over Ireland (http://bit.ly/29dIuai) and one of our comments asked why, in a picture like this, the inner part of the rainbow appears clearly brighter than the outer part?

The rainbow is forming from light bouncing through water droplets. In a view like this, the sun is behind the viewer, so its light is coming past you. The sunlight enters a droplet of water at the edge and refracts; light waves bend when they move between substances with different indices of refraction. The bent sunlight then reflects off the far side of a water droplet and then is bent again upon leaving the water droplet. This process of reflection and refraction takes sunlight and sends it back in the direction it came from. A viewer will then see an arc of separated color because different wavelengths or colors of light refract at slightly different angles as they move from one material to another, so the colors are spread out across an area.

This process also controls the brightness change. Only light entering the water droplet at a perfect angle is reflected and refracted properly to give a rainbow; that’s why rainbows always cover the same size on the horizon.

Light traveling across the sky can also enter raindrops and be bent even if it isn’t at the perfect angle to create a rainbow. Light entering at angles that don’t perfectly produce a rainbow is bent and concentrated in the inner part of the rainbow, causing it to be noticeably brighter particularly in camera shots.

Thus, the inner part of the rainbow is brighter because light is being focused by the raindrops at the center of the rainbow, while at angles outside the rainbow the geometry is wrong so little extra light comes back.

The sky is actually darkest between the primary and the secondary rainbow as much of the light between these two bows is the light that concentrates in the inner band to brighten it. This darkened region is nicknamed “Alexander’s dark band” after Alexander of Aphrodisias who first noted it 1800 years ago.

-JBB

Image credit: Grand Canyon National Park. https://flic.kr/p/k2pYSD

References: http://hyperphysics.phy-astr.gsu.edu/hbase/atmos/ligsky.htmlhttps://eo.ucar.edu/rainbows/http://bit.ly/29dIlnn