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Mathematical graphics rainbow
Red, orange, yellow, green, blue, indigo and purple from the outer ring to the inner ring? Seven colors.

Rainbow, in fact, as long as there are water droplets in the air and the sun shines behind the observer at a low angle, it may produce an observable rainbow phenomenon. Rainbow usually appears in the afternoon, just after the rain. At this time, the air is less dusty and full of water droplets, and one side of the sky is dark because there are still rain clouds.

However, observers can see the sunlight without being covered by clouds above or behind them, so rainbows are easier to see. Another place where rainbows are often seen is near waterfalls. When the weather is clear, you can spray water or mist into the air with your back to the sun, or you can create an artificial rainbow.

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In fact, if the conditions are right, you can see a full circle of circular rainbows. The water droplets emitted by sunlight into the air are refracted → reflected → refracted, and then emitted to our eyes, forming a rainbow. Solar beams of different colors. The deflection angle between the rainbow beam and the original beam is about 180-42 = 138 degrees.

That is to say, if the sunlight is horizontal to the ground, the elevation angle of viewing the rainbow is about 42 degrees. The following animation shows that all light beams from the same viewing angle must be on a conical surface.

Imagine you are looking at the rainbow in the east, and the sun is setting in the west behind you. White sunlight (the combination of all colors in the rainbow) passes through the atmosphere, passes eastward over your head, and meets the water drops falling in the storm.

When the light beam touches the water drop, there are two possibilities: first, the light may directly penetrate it, or more interestingly, it may touch the front edge of the water drop, bend the inside of the water drop when it enters, then reflect back from the back end of the water drop, and then leave from the front end of the water drop and refract it to us. This is the light that forms a rainbow.

The bending degree of light passing through water drops depends on the wavelength (i.e. color) of light-red light has the largest bending degree, followed by orange light and yellow light, and so on, and violet light has the smallest bending degree.

Each color has a specific bending angle. The refraction angle of red light in sunlight is 42 degrees, while that of blue light is only 40 degrees, so each color appears in a different position in the sky.

If an imaginary line is used to connect the back of the head with the sun, then the place at an angle of 42 degrees with this line is where the red color is. These different positions outline an arc. Since the angle between the blue and the imaginary line is only 40 degrees, the blue arc on the rainbow is always below the red.

The reason why the rainbow is curved is of course inseparable from its formation and the shape of the earth, because the surface of the earth is curved and covered by a thick atmosphere.

After the rain, the water content in the air is higher than usual. When sunlight shines into the air, water droplets are refracted. At the same time, because the atmosphere on the earth's surface is an arc surface, sunlight refracts on the surface, forming an arc rainbow we see!

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