Making double rainbows with relative refractive indices

Rainbows are all in the retinas of the observer. As bright sunlight shines on a nearly spherical water droplet, it reflects in a cone-shaped beam. Because of refraction, the angle of that cone varies for each color. When multiple droplets in the sky experience the same phenomenon, they create the image of a curved rainbow — or two.

Zheng et al. described how to replicate rainbows in the lab as an interesting problem for undergraduate students in optics and as a demonstration for middle or high schoolers.

“In our paper, we are making efforts to demonstrate rainbows with different refractive indices for students,” said author Yuan Zheng. “It is not only because we wanted to illustrate how rainbows are formed, but also because we were wondering why secondary rainbows can occasionally be seen together with the primary ones.”

The team tried multiple ways to simulate the natural environment of rainbow formation using a transparent spherical lens as a water droplet substitute. But changing the refractive index was difficult because solid materials rarely reach values as low as water.

“Finally, we realized that the most effective way to adjust the refractive index was by changing the surroundings of the transparent spheres in a relative way,” said Zheng. “We do this by replacing the air with sugar solution.”

A higher relative refractive index caused the viewing angle of the primary rainbow to decrease and that of the secondary rainbow to increase. After a critical value, the secondary rainbow was no longer observable.

The authors believe this will make a valuable educational tool because rainbows are universally impressive and fascinating.

Source: “Rainbows in different refractive indices,” by Yuan Zheng, Kexun Shen, Xianghe Wang, and Xing-Xing Yao, The Physics Teacher (2023). The article can be accessed at https://doi.org/10.1119/5.0086915 .