Raindrop Ray Fan: Descartes Rainbow, Dispersion and…

What the Raindrop Ray Fan Is

The Raindrop Ray Fan is a simulation that allows you to visualize how sunlight interacts with spherical raindrops. By tracing individual rays of light through these drops, it demonstrates the principles of refraction and dispersion, leading to the formation of primary and secondary rainbows.

This simulation also highlights the Alexander dark band, which occurs between the two bows due to destructive interference of light.

Why It Happens

When sunlight enters a raindrop, it bends or refracts at the surface. This bending is described by Snell's law, which states that the ratio of the sine of the angle of incidence to the sine of the angle of refraction is constant and equal to the ratio of the indices of refraction of the two media.

After internal reflection within the drop, light exits at a different angle due to further refractions. The varying wavelengths of light (dispersion) cause different colors to emerge at distinct angles, creating the colorful arcs we see as rainbows.

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The Role of Snell's Law and Fresnel Losses

Snell's law is crucial in understanding how light bends when it passes from one medium to another. It explains why different colors emerge at slightly different angles, leading to the separation of white light into its constituent colors.

Fresnel losses account for the energy lost due to reflection at each surface interaction. These losses are particularly significant as they contribute to the intensity and visibility of the rainbow.

The Alexander Dark Band

Between the primary and secondary rainbows, there is a dark band known as the Alexander dark band. This occurs because light that would have formed this part of the spectrum undergoes destructive interference when it exits the raindrop from different angles.

This phenomenon can be observed in nature under specific conditions, providing a fascinating insight into the complex interactions between light and water droplets.

Frequently asked questions

How does Snell's law apply to rainbows?

Snell's law explains how light bends as it enters and exits a raindrop, causing different wavelengths (colors) of light to refract at slightly different angles.

What causes the dark band between the primary and secondary bows?

The dark band is caused by destructive interference of light that would have formed this part of the spectrum as it exits the raindrop from different angles, leading to a cancellation of light intensity in that region.

Why do we see only one primary and sometimes a secondary rainbow?

The primary rainbow is more visible because it involves fewer internal reflections within the raindrop. The secondary rainbow occurs due to an additional internal reflection, which makes it fainter but still observable under certain conditions.

Can we see a tertiary or higher-order rainbow?

Yes, theoretically, higher-order rainbows can be observed with more reflections inside the raindrop. However, they are extremely faint and difficult to see in nature due to the increasing losses of light at each reflection.

Try it live

Everything above runs in your browser — open Raindrop Ray Fan: Descartes Rainbow, Dispersion and Alexander Dark Band and change the parameters while it is running. Nothing is installed, nothing is uploaded, the whole model lives in one tab.

▶ Open Raindrop Ray Fan: Descartes Rainbow, Dispersion and Alexander Dark Band simulation