What They (Probably) Don't Teach You About Rainbows At School

Why rainbows are curved - a simple question that leads to deep physics exploration.

• Raindrops spreading white light into colors like a prism is an oversimplification • Standard explanations don't address why you never see a rainbow when looking toward the sun • Most sources fail to explain why it's darker above a rainbow than under it

• How can sunglasses make a rainbow disappear? • Why can rainbows sometimes be much smaller than usual? • How does rainbow physics connect to a Nobel Prize discovery?

Going deep into the full explanation using novel demonstrations and animations that reveal how rainbows really work.

Using a glass sphere to represent a raindrop, a laser representing sunlight, and observing how light behaves when entering and reflecting inside the sphere.

• When light strikes a sphere, some reflects off the front surface and some transmits through • At the back surface, light again splits between reflection and transmission • The amount reflected depends on angle of incidence, polarization, and the media involved

Electromagnetic waves encounter charges in the medium, pushing them back and forth like masses on springs, creating new electromagnetic waves that phase shift the original light, decreasing its wavelength and speed.

The refractive index (speed of light in vacuum divided by speed in medium) explains how light bends - around 1.5 for glass and 1.33 for water - governed by Snell's law.

As the laser moves up the sphere, the reflected ray reaches a maximum angle before turning around - a turning point that concentrates light rays at one specific angle.

• Over a range of impact parameters, reflected beams concentrate at essentially the same angle • This concentration of light rays is called a caustic • For red light through water, this maximum scattering angle occurs at 42 degrees below horizontal

Geometry determines the behavior - as the laser moves higher, the refraction point continues moving until reaching a special point where the angle of incidence becomes so steep that the geometry reverses.

Different colors have different maximum scattering angles: blue light around 40 degrees, green at 41 degrees, and red at 42 degrees, due to how different frequencies interact with atomic oscillations.

When uniformly illuminated, a single raindrop creates a cone of light - white inside with a colored ring on the outside, with the maximum scattering angles for each color forming distinct caustics.

• For your eye to see red light, the angle from sun to raindrop to eye must be 42 degrees • Violet light forms at 40 degrees • The rainbow arch is created by all raindrops at these specific angles relative to your position

Each observer sees a unique rainbow with their shadow at the center - no two people see the exact same rainbow, and even your left and right eyes see different rainbows due to the geometry involved.

Rainbows are only visible when the sun is below 42 degrees from the horizon, which is why they appear in early morning or late afternoon, not in the middle of the day.

The reflecting light in a rainbow occurs very close to Brewster's angle, where light with electric field parallel to the reflection plane is transmitted while perpendicular light is reflected.

• Only reflected light with electric field perpendicular to the plane of reflection creates the visible rainbow • This makes rainbow light polarized - horizontal at the top and more vertical on the sides • Polarization orientation depends on the rainbow's position in the sky

Polarized sunglasses can make rainbows disappear or brighter depending on filter orientation, by blocking or allowing the polarized rainbow light through.

Below a rainbow is brighter because raindrops reflect all colors of light off their back surfaces, while above the rainbow is darker because raindrops are outside the maximum deflection angle of all colors.

The secondary rainbow comes from an additional internal reflection inside raindrops - light reflects twice instead of once off the inside sphere surfaces.

• Secondary rainbows are much fainter because light is lost with each reflection • The colors are inverted compared to the primary rainbow • This light creates a minimum deflection angle around 50 degrees for red light

Between 42 and 50 degrees lies a noticeably dark area because no light from first or second internal reflections exits the raindrop at these angles.

• Photographic evidence exists of third and fourth order rainbows from three or four internal reflections • Under laboratory conditions, up to 200th order rainbows have been detected • Higher order rainbows are extraordinarily faint and require perfect conditions

Multiple rainbow-like bands appearing under a primary rainbow, occurring only when raindrops are very small - just tenths of a millimeter in diameter.

• Light rays passing just above and below the primary rainbow ray travel slightly different distances on the order of a wavelength • This creates constructive and destructive interference patterns • Results in series of light and dark bands inside the main rainbow

Different colors in supernumerary rainbows overlap more than in the main rainbow, producing strange colors like magenta - a combination of blue and red light.

Glories or Brocken bows are small circles of color only 2-4 degrees wide, much smaller than the usual 42-degree rainbow, also created by interference in tiny water droplets found in fog and clouds.

In tiny droplets, light striking the edge can wrap around and come straight back at the source, and because droplet distance varies on the order of a wavelength, interference patterns emerge.

• Light traveling directly forward interferes constructively, creating a bright spot • Off-center light travels extra half-wavelengths, creating dark rings • Further out, light travels extra full wavelengths, creating bright rings again

Different colors have different wavelengths, so their bullseye patterns don't completely overlap - superimposing them creates rings of color visible as glories.

• In 1894, CTR Wilson observed colored rings around shadow in mist and wanted to replicate them in the laboratory • He invented the cloud chamber specifically to study glories • The cloud chamber later revealed particle tracks, leading to his Nobel Prize - an accidental breakthrough from studying rainbow-like phenomena

For millennia, rainbows have been nature's challenge to human understanding - asking 'can you figure this out?' and providing satisfying answers about how our world works.

• School teaches memorizing colors and basic light behavior without true comprehension • Real learning means mastering a subject through understanding mechanisms, not just facts • Rainbows exemplify the difference between memorization and genuine scientific understanding

Each observer sees a completely unique rainbow because the geometry is personal to their position - your left and right eyes see different rainbows, making it a truly individual optical experience.

Understanding rainbows means grasping refraction, reflection, interference, caustics, polarization, and the geometry of light - a comprehensive physics education compressed into one natural phenomenon.