Understanding the Physics Behind
Rainbows
A Complete Explanation
You can watch the summary of this post as video here.
Have you seen a rainbow?
“Of course, yes”, you may say. Perhaps, what you mean is that you have looked at rainbows. But, most likely, you have seen none. Have you ever noticed and admired the various parts of an awesome rainbow?
“So many of the little wonders of the everyday world – which can be truly spectacular – go unobserved most of the time because we haven’t been trained how to see them“
Prof. Walter Lewin
Have you ever thought about..
- The physics behind the rainbow.
- The difference between a primary bow and a secondary bow and the color sequence in them.
- Why there is a dark band between the primary bow and the secondary bow?
- In what conditions can you see a rainbow?
- Why there is bright area below the primary bow and above the secondary bow?
- Why the rainbow is always an arc instead of a straight line?
- Who was the first person to give a scientific explanation of the rainbow?
Let us investigate the last question first.
First Person To Explain
It was Isaac Newton.
Since ancient times, human beings have wondered about rainbows and have tried to explain it by associating a natural phenomenon, as it was done in many cases, with mythological stories. However, Newton, in 1704, was the first scientist to provide a convincing scientific explanation for rainbows.
First, Newton demonstrated that white light (sunlight) consisted of a spectrum of colors. When he sent a narrow beam of sunlight towards one side of a glass prism, what came out, on the other side, was a spectrum of colors (Pic.3). This ‘chromatic dispersion’ is caused by a phenomenon called refraction of light. More on refraction and chromatic dispersion in a moment.
Second, Newton also understood that the refraction of sunlight could happen in other substances too, such as water. He also realized that water droplets, in the atmosphere on a rainy day, could act as tiny prisms that enabled the splitting of sunlight into its component colors.
Third, he was able to connect the necessary components – the viewer, looking in the right direction; the sun on one side, behind the viewer; the presence of millions of water droplets in the atmosphere on the other side, in front of the viewer; water droplets’ ability to refract and reflect light – to give a perfect explanation.
Before getting into the physics of rainbow, we need to understand some of the basics of refraction and reflection first.
Refraction vs Reflection
Reflection:
Pic. 2 shows a narrow beam of light (incident white light), travelling from left through air at an inclined angle, which encounters a flat glass surface. The line that is vertical to the surface is called ‘normal’. Part of the incident light is reflected by the surface forming a beam directed upward inclined to the right. Please note that the angle between the normal and the reflected beam (angle of reflection) is equal to the angle between normal and the incident beam (angle of incident). Both are θ1. This is the law of reflection.
Refraction:
What happens to the rest of the white light at the glass surface (interface between air and glass) is more interesting. It gets bent at the surface, because glass reduces the speed of light as it enters the glass. As we can see in Pic2, the amount of bending depends on the wavelength (color) of light. Bending is greatest for violet and is least for red. Other colors lie in between these two.
The splitting of white light, due to refraction, is known as chromatic dispersion. And another key point to note is that this chromatic dispersion can also occur when sunlight falls on a water droplet too.
What happens in a Raindrop
Please refer to Pic. 4, while reading this section.
Let us consider a ray of sunlight that falls on a raindrop (at point A). A part of it refracts as it enters and separates into its component colors, as in a glass prism. Red light bends the least, as we have seen in the refraction section above, while violet bends the most. Other colors bend in between these two. All these rays travel to the other side (B) of the raindrop. At B, some of the rays reflect internally and travel to C where it refracts again to exit the raindrop; almost reversing its original direction.
(At point C, part of the rays can reflect internally again. We will consider this scenario when we discuss secondary bow.)
Calculations show that red light can come out of a rain drop between 0° and 42° (the max), while violet can reverse the course between 0° and 40° (the max). This is one of the key points to note in order to understand the science of a primary bow.
Another key point is, though the red color can emerge out of the raindrop anywhere between 0° and 42°, the intensity of red color is dominant at 42°. Similarly violet is dominant at 40°, though it can come out anywhere between 0° and 40°. Other colors are dominant in between these two colors. Thereby, this droplet creates a band of colors – violet at the 40°end and red at the 42° end – while other colors fall in between.
In the next section, let us explore how the splitting of sunlight by millions of droplets in the atmosphere results in a spectacular primary bow.
Physics of Primary Bow
Let us first focus on how the primary bow forms.
Required Conditions for Rainbow:
To see a rainbow, three conditions are to be met.
- The sun should be behind the viewer
- There must be plenty of water droplets in front of the viewer in the sky.
- Sunlight should be able to reach the water droplets; there should be no obstruction between the sun and the water droplets in the sky.
If the above conditions are met, when you look at the sky at about 42° from the reference line, as shown in Pic.6, you should be able to see a primary bow. The reference line is an imaginary line that connects your head and the tip of your shadow on the ground.
Band of colors:
You can see the red band at 42° while the violet/blue band appears at 40° and in between lie the rest of the colors (orange, yellow and green). Below 40°, that is, below the primary bow, it is just white light (bright), because all the colors are equally present from 0° to 40°. When all the colors of equal intensity are combined, we see just white light.
And above 42°, meaning above the primary bow, and below 50°, there is no light coming out from the water droplets and therefore it is a dark band between 42° and 50°.
What happens above 50°? You may see a faint secondary bow. We will discuss the physics behind the secondary bow and the rest of the unanswered questions in the next post.