Why We See Rainbows: The Physics of Light Refraction

Rainbows are one of nature's most beautiful and awe-inspiring spectacles, appearing after rain showers or in misty landscapes. Although these colourful arches might seem magical, their formation is rooted in the fascinating principles of physics, specifically light refraction, reflection, and dispersion. Understanding how these processes work not only demystifies the rainbow but also reveals the complexity of light and its interactions with the environment.

This article will explore how rainbows form, focusing on the role of light refraction.

The Anatomy of Light and Colour

To understand why we see rainbows, we first need to consider the nature of light. Sunlight, though it appears white, is actually a mixture of different colours. Each colour of light corresponds to a specific wavelength, with violet having the shortest wavelength and red the longest. When sunlight passes through a prism or water droplets, it breaks into its constituent colours because each colour bends, or refracts, differently based on its wavelength.

The Science of Refraction: Light’s Journey Through a Droplet

Refraction is the bending of light as it passes from one medium to another. When light enters a medium where its speed changes—such as from air to water—it bends. In the case of rainbows, sunlight encounters millions of tiny water droplets in the atmosphere after a rain shower or within misty environments. As the light enters each droplet, it slows down and refracts.

The process begins when sunlight enters the upper surface of a water droplet, which acts as a prism. Here, the light splits into its component colours because different wavelengths of light refract at slightly different angles. This separation of colours is called dispersion and results in the spectrum of colours that make up a rainbow.

Internal Reflection: Enhancing the Colours

Once the light is inside the droplet, it doesn’t just pass through; it reflects off the inside surface of the droplet. This reflection is known as internal reflection, and it occurs because the curved surface of the droplet causes the light to bounce back rather than exiting the water immediately. As the light reflects internally, it undergoes further refraction when it eventually exits the droplet. Each time the light reflects inside the droplet, the colours separate more distinctly.

The Role of the Observer’s Angle

While the physics of light interacting with water droplets explains why the colours of a rainbow are present, the position and perspective of the observer are also essential in seeing the rainbow. For a rainbow to appear, an observer must be positioned between the sun and the water droplets, with the sun behind them. This angle—about 42 degrees between the observer’s line of sight and the reflected light—is necessary for the colours of the rainbow to converge and become visible.

The Colours of the Rainbow: Red to Violet

The colours of a rainbow always appear in a specific order: red, orange, yellow, green, blue, indigo, and violet (ROYGBIV). This order is due to each colour bending at slightly different angles. Red, which has the longest wavelength, refracts the least, so it appears on the outer edge of the rainbow, while violet, with the shortest wavelength, refracts the most and appears on the inner edge. The remaining colours fall in between, creating the familiar spectrum that we see in the sky.

Secondary Rainbows: The Double Effect

Occasionally, you may see a secondary rainbow outside the main one. This secondary rainbow is fainter and has its colours in reverse order, with red on the inner edge and violet on the outer edge. A secondary rainbow occurs when light reflects twice within the water droplet before exiting, resulting in a reversal of the colour order. This additional reflection also causes some of the light to escape, making the secondary rainbow appear dimmer.

Why Rainbows Are Circular

Many people observe only part of a rainbow and assume it’s a semicircle, but in reality, rainbows are full circles. The ground or horizon usually blocks the lower half, so only the upper portion is visible. In rare cases, such as when viewing a rainbow from an aeroplane or high vantage point, you can see the entire circular formation. This phenomenon occurs because light refraction and reflection happen uniformly across the droplet, forming a circular pattern around the anti-solar point (directly opposite the sun).

Factors Influencing Rainbow Visibility

The visibility and intensity of a rainbow depend on various factors, including the size and uniformity of the water droplets, the position of the sun, and atmospheric clarity. Larger water droplets produce more vivid colours, while smaller droplets create a more diffuse or pastel effect. Additionally, rainbows are more vibrant when the sun is lower in the sky, as the angle of sunlight entering the droplets is closer to the optimal 42 degrees.

Beyond the Spectrum: Supernumerary and Fog Bows

In some cases, you might observe an unusual variation known as a supernumerary rainbow—a series of faint, pastel-coloured bands inside the primary rainbow. This phenomenon results from interference effects as light waves overlap. Another rare rainbow phenomenon, the fog bow, forms in fog or mist with very tiny droplets. Fog bows lack vibrant colours due to the small droplet size, which scatters light more evenly and results in a pale, ghostly arc.

Rainbows in Different Cultures and Science

Rainbows have been symbols of beauty and mystery in cultures worldwide, often associated with stories, folklore, and even scientific curiosity. Sir Isaac Newton was one of the first to analyse rainbows scientifically, using prisms to study how light could split into colours. His work laid the foundation for the modern understanding of optics, ultimately leading to our grasp of rainbow formation.

Conclusion

The rainbow is a perfect example of how physics can turn ordinary natural elements into a stunning visual phenomenon. Through the interplay of refraction, reflection, and dispersion, sunlight and water droplets come together to form a spectrum of colours that captivate our imagination. Understanding the science behind rainbows not only deepens our appreciation of nature’s beauty but also demonstrates the intricate ways that light interacts with the world around us. For those interested in exploring this further, JC physics tuition can provide a deeper insight into the principles at play. Next time you see a rainbow, you’ll know that you’re witnessing a dazzling display of physics in action.