Why Does a Rainbow Contain a Pure Spread of Spectral Colors?

A common misconception is that a rainbow contains a pure spread of spectral colors. In reality, while a rainbow displays a range of colors, it does not represent a perfectly pure spectrum. Let’s delve into the reasons for this phenomenon.

Understanding Spectral and Non-Spectral Colors

A spectral color is defined as a color that consists of only one wavelength component of electromagnetic radiation. In contrast, non-spectral colors are mixtures of multiple wavelengths, embodying various spectral colors. For example, simple lasers can produce effectively pure spectral colors, which are distinct from the colors seen in a rainbow.

The visible electromagnetic spectrum is a continuous range that includes all spectral colors, typically ordered by wavelength: red, orange, yellow, green, blue, and violet. The entire electromagnetic spectrum is continuous and theoretically contains an infinite number of spectral colors. This means that even if we do not have a specific name for certain colors between red and orange, they still exist as spectral colors.

The Role of Natural White Light

Natural white light, such as sunlight, encompasses all spectral colors. When this white light is separated into its individual components—effectively forming a pure spectrum—this occurs without the narrow absorption lines that can sometimes complicate the spectrum’s purity.

When light passes through a glass prism, the different spectral colors bend at varying angles due to the prism’s dispersive nature. This results in a pure spectrum that becomes visible when the light reflects off a surface, such as a wall or screen. It’s important to note that a prism will only create a pure spectrum if the incoming light beam is sufficiently thin.

Raindrop Interaction and Rainbow Formation

The situation changes when light interacts with raindrops. Unlike prisms, raindrops have a spherical shape, which leads to different bending angles for various wavelengths of light. This curvature results in a slightly mixed spectrum of colors. For example, the bright red light at the outer edge of a rainbow exits the raindrop at an angle of approximately $42.1^\circ$. However, some red light is also emitted at various angles between $0^\circ$ and $42.1^\circ$. Similarly, violet light is predominantly bent to exit at $40.6^\circ$, but it also appears at angles between $0^\circ$ and $40.6^\circ$.

Blurring of Colors in a Rainbow

Due to this bending of light at varying angles, each point in a rainbow contains a mixture of spectral colors. As you move inward from the outer edge of the rainbow toward its center, the colors blend more, resulting in a faint white interior. The reason for this mixing is fundamentally tied to the round shape of raindrops, causing different parts of the light beam to encounter the raindrop’s surface at different angles. This leads to a spectrum that is not purely defined.

For instance, while pure red light is primarily bent into a $42.1^\circ$ angle, the color observed at $41.9^\circ$ is a mix of orange and a bit of red, and at $41.7^\circ$, we see yellow blended with orange and red. Consequently, the colors appear to blur together, leading to a less distinct spectrum compared to that produced by a prism.

Conclusion: Prism vs. Raindrop

In summary, both a prism and a raindrop disperse white light into a spectrum of colors through refraction. However, the key difference lies in their shapes: a prism has flat surfaces, producing a pure spectrum, while a raindrop’s round surface results in an impure spectrum. This distinction is crucial, as it explains why the terms “rainbow” and “visible spectrum” are often conflated in everyday language, despite their scientific differences.

The visual representation of a rainbow, compared to a mathematically pure spectrum, illustrates this concept clearly. A rainbow appears with colors that are more blended and washed out, emphasizing the inherent structure of the phenomenon rather than limitations of photographic equipment. Notably, the last bright color in a rainbow is purple (a mixture of red and violet), whereas the last visible color in a pure spectrum is violet.

This nuanced understanding of the behavior of light and color helps clarify why rainbows, while beautiful and vibrant, do not contain a pure spread of spectral colors.