Rays Through a Large Raindrop

Last updated on September 16, 2023

Rays Through a Large Raindrop: Exploring the Phenomenon in Detail

Have you ever wondered about the fascinating optical phenomenon that occurs when sunlight interacts with raindrops? In this article, we will delve into the topic of "Rays Through a Large Raindrop" and explore the intricate details of how light behaves within these water droplets.

Understanding the Formation of Rainbows

When sunlight enters a raindrop, it undergoes a series of reflections and refractions. The primary rainbow is formed when the light is reflected once inside the raindrop. The colors we observe in the rainbow are a result of the two refractions that occur as the light enters and exits the droplet.

The Deviation of Rays and the Formation of Bows

As the rays of light travel through the raindrop, they are deviated back towards the direction of the incoming sunlight, resulting in the formation of a bow that appears opposite to the sun. The rays closer to the center of the drop experience a deviation of almost 180 degrees, while those further from the center are deviated less and less until they reach a minimum deviation angle known as the "rainbow angle."

Exploring the Rainbow Angle

The rainbow angle refers to the angle of minimum deviation at which rays of light are deviated within a raindrop. This angle is approximately 137.5 degrees for deep red light. Rays that approach the rim of the raindrop experience an increase in deviation once again.

The Brightness and Color Distribution in Rainbows

Rays of light cluster strongly around the rainbow angle, giving rise to the brightest part of the bow. The outer edge of the primary bow is formed by rays near the rainbow angle. Interestingly, different colors of light are refracted to varying degrees, with red light being refracted less than blue light. Consequently, red light occupies the outermost part of the primary bow.

Understanding Color Separation and Brightness Variation

When rays of light are deviated through larger angles, they contribute to the brightness of the sky inside the primary bow. However, due to the overlapping of colors at these angles, the sky appears colorless. Conversely, no light is deviated through angles smaller than the minimum deviation angle, resulting in a darker region beyond the outer edge of the primary bow.

Raindrop Shape and its Influence on Rainbows

Contrary to popular belief, raindrops are not tear-shaped but rather strongly spherical. This spherical shape is maintained by surface tension forces in smaller raindrops. However, larger raindrops may become flattened due to air resistance as they fall. Even slight departures from perfect sphericity can affect the formation of rainbows or lead to peculiar optical effects.

The Limitations of Geometric Optics

While we often visualize the paths of rays of light within raindrops, it is important to note that these paths are more of a conceptual representation. Geometric optics, which describes light behavior using straight-line rays, can only provide a reasonable approximation for raindrops with diameters around a millimeter. Many aspects of rainbows cannot be fully explained by geometric optics alone.

Calculation and Measurement of Deviation Angles

Deviation angles within raindrops are traditionally measured relative to the direction of incoming sunlight. For red rays forming the edge of the primary bow, the deviation angle is approximately 137.5 degrees. The center of a rainbow is directly opposite the sun, resulting in a deflection angle of 180 degrees. By subtracting the deviation angle for red light from 180 degrees, we can determine that the radius of the red edge of the primary bow is approximately 42.5 degrees.

Exploring Rays Through a Large Raindrop

In conclusion, understanding the behavior of light within raindrops offers a captivating insight into the formation of rainbows. From the intricate paths of rays to the variation in color distribution and brightness, the phenomenon of "Rays Through a Large Raindrop" showcases the beauty and complexity of atmospheric optics. While geometric optics provides a useful framework for conceptualizing these phenomena, there are still aspects that remain beyond its reach. So, the next time you witness a rainbow, take a moment to appreciate the fascinating interplay between sunlight and raindrops that brings this enchanting display to life.

Rays.. reflected once inside raindrops make the primary. Its colours are produced by the two refractions as the rays enter and leave. Rays are deviated back towards the incoming sunlight to form a bow appearing opposite the sun. The rays drawn in lighter tones form the "zero order glow", the secondary and higher order bows.

One internal reflection produces the primary bow.

Mouse over the slider to see the ray paths. Rays close to the drop centre are deviated almost 180º back on themselves. Rays further from the centre are deviated less and less until the deviation reaches a minimum (about 137.5º for deep red light). This is the "angle of minimum deviation" or "rainbow angle". The deviation increases once more as the entrance ray approaches the drop rim .

Light is deviated into a whole range of angles

Rays cluster strongly around the rainbow angle, test it with the mouse, and so the bow is at its brightest at that angle. Rays near the rainbow angle form the bow's bright outer edge.

Minimum deviation angle

Red light is refracted less than blue and its minimum deviation angle is less. Red is therefore on the outside of the primary bow.

Colour separation

Rays deviated through larger angles make the sky brighter inside the primary. The brighter sky is colourless because at those angles the colours strongly overlap.

Bright sky inside the bow

No light is deviated through angles smaller than the minimum deviation angle and the sky is therefore darker beyond the outer edge of the primary bow.

Outside the bow is dark

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Raindrops are never the tear shaped objects beloved of illustrators. Small raindrops are kept strongly spherical by surface tension forces. Larger drops are sometimes flattened by air resistance as they fall and they may even oscillate or wobble. Even small departures from sphericity destroy a rainbow or possibly cause some odd effects.

Spheres not teardrops

Ray paths are something of a fiction and geometric optics is incapable of explaining many aspects of rainbows. However, when raindrops are a millimetre or so in diameter the straight line rays are a reasonable approximation to some aspects of how light behaves.

Don't take ray paths too seriously

Deviations are traditionally measured from the direction of the incoming sunlight. The deviation angle for red rays forming the edge of the primary bow is about 137.5º. The centre of a rainbow is directly opposite the sun (a deflection angle of 180º). The radius of the red edge of the primary is therefore 180-137.5 = 42.5º

Deviation angles

The ray paths are accurately computed for wavelengths of 400 and 750 nm passing through a water drop at 0 Celsius.

Calculation

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Reference Atmospheric Optics

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