Rainbow — Core Principles

Core Principles

A rainbow is a natural optical phenomenon caused by the interaction of sunlight with atmospheric water droplets. It involves three key processes: dispersion, refraction, and total internal reflection.

White sunlight, a mixture of colors, first enters a raindrop and undergoes refraction, splitting into its constituent colors (dispersion) because each color bends at a slightly different angle. The light then travels to the back of the droplet, where it undergoes total internal reflection, bouncing back inside.

Finally, it exits the droplet, undergoing a second refraction, further separating the colors and directing them towards the observer. The primary rainbow, the brighter one, results from one internal reflection, showing red on the outside and violet on the inside, with an angular radius of about $42^circ$.

The secondary rainbow, fainter and larger, results from two internal reflections, with colors reversed (violet outside, red inside) and an angular radius of about $51^circ$. For a rainbow to be seen, the sun must be behind the observer, and water droplets must be in front.

Each observer sees a unique rainbow, as it's an optical effect, not a physical object.

Important Differences

vs Secondary Rainbow

Aspect	This Topic	Secondary Rainbow
Number of Internal Reflections	One	Two
Relative Brightness	Brighter	Fainter
Order of Colors (Top to Bottom)	Red, Orange, Yellow, Green, Blue, Indigo, Violet (ROYGBIV)	Violet, Indigo, Blue, Green, Yellow, Orange, Red (VIBGYOR - inverted)
Angular Radius (approx. from anti-solar point)	$40^circ - 42^circ$	$51^circ - 54^circ$
Position Relative to Each Other	Inner arc	Outer arc

The primary and secondary rainbows are distinct optical phenomena arising from different light paths within water droplets. The primary rainbow is formed by one total internal reflection, making it brighter with red on the outside and violet on the inside, spanning an angular range of approximately $40^circ$ to $42^circ$ from the anti-solar point. In contrast, the secondary rainbow involves two total internal reflections, leading to a fainter appearance, an inverted color order (violet outside, red inside), and a larger angular radius of about $51^circ$ to $54^circ$. These differences in reflection count, intensity, color sequence, and angular position are key distinguishing features.