How big is a rainbow?

Episode Summary

Executive Summary: Listener Sakura asks: 'How big is a rainbow?' Through experiments and expert interviews, episode reveals rainbows have fixed angular size (42 degrees radius, 84 degrees diameter) but no linear size—size perception is illusion. Rainbow circle, secondary rainbows, and third to fifth order rainbows exist. Rainbow cone extends from eye into rain shower.

Main Topics: Listener Question and Motivation (Priority: 5/5): Listener Sakura asks how to measure a rainbow, leading to exploration of angular versus linear size. Rainbow Formation and the Rainbow Angle (Priority: 5/5): Experiment with water cylinder and then water-filled light bulb demonstrates rainbow formation via refraction and reflection, showing light concentration at specific angles. Angular vs. Linear Size: The Expert Explanation (Priority: 5/5): Raymond Lee explains that all rainbows have same angular size (about 84 degrees) but linear size varies with distance perception; they are optical illusions. Full Circles, Double and Higher-Order Rainbows (Priority: 4/5): Discussion of circular rainbows visible from aircraft and double/triple rainbows caused by multiple internal reflections. 3D Cone and Volume of Rainbow-Producing Droplets (Priority: 3/5): Rainbow is a three-dimensional cone of light from raindrops; volume of rain shower can give impression of size.

Key Arguments: Rainbows have an angular size (42 degrees radius) but no linear size; they are not objects at a specific distance. The perceived size of a rainbow is an illusion based on context with distant objects. Rainbows are actually circles, and higher-order rainbows (double, triple etc.) exist but are fainter. The volume of rain-producing droplets contributes a sense of 3D size to the rainbow.

Data Points: Rainbow angle (red): 42 degrees - Rainbow's angular size Rainbow angle (violet): 40 degrees - Rainbow's angular size Diameter of primary rainbow: 84 degrees - Rainbow angular diameter Angular size increase: 10 degrees larger than primary - Secondary rainbow angular size difference Rainbow order documented: Fifth order (photographed) - Highest order rainbow documented in nature Rainbow order discovery: Third and fourth orders discovered in same summer - Third and fourth order discovery

Pivotal Quotes: "It has a fixed size in angle, but it is not an object, so it doesn't have a linear size." — Raymond Lee: Raymond Lee explains that rainbows have no fixed linear size, only angular. "I knew all this... and yet my compelling mistake when I saw one... was to back up to try to get more of it in the frame." — Raymond Lee: Raymond Lee confesses he fell for the size illusion himself. "I was just looking at it like, huh? That's it. You know, I'm stuttering in my head." — Harold Edens: Harold Edens describes discovery of fifth order rainbow in a photo.

Implications: Listeners learn not to trust visual size perception of rainbows; they are fixed in angle but variable in volume and how much (%) of circle is visible. Encourages deeper scientific curiosity about everyday optical phenomena.