Describe the accepted model of rainbows. Specifically, discuss how the model accounts for the size, shape, location, and color ordering of primary rainbows.

Short Answer

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The accepted model of rainbows attributes their formation to the refraction and dispersion of sunlight interacting with water droplets. When white sunlight enters a water droplet, it is refracted, bent, and dispersed into its constituent colors. The geometry and size of rainbows are determined by the rainbow angle, with primary rainbows having an angle of approximately 42 degrees. The unique shape and location of rainbows as circular arcs in the sky centered around the anti-solar point result from the constant rainbow angle. The color ordering of primary rainbows, going from red on the outer edge to violet on the inner edge, is due to the dispersion of light and the varying bending of different wavelengths.

Step by step solution

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1. Basic principles of light refraction and dispersion

In order to understand rainbows, we first need to know the interaction of water droplets with sunlight. When light passes from one medium to another, it changes its velocity and hence bends, which is known as refraction. As different colors of light (wavelengths) have different speeds in a medium, they also bend differently. This phenomenon is called dispersion. When white sunlight enters a water droplet, it is refracted and dispersed into its constituent colors, which further interact with the droplet in two major ways: reflection and refraction.
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2. Geometry and size of rainbows

When light passes through a water droplet, it is refracted into different angles depending on its wavelength (color). Some of these rays are internally reflected once within the droplet, while others are also refracted out. The angle between the incoming rays and the refracted rays for which the light intensity is highest is called the rainbow angle. For primary rainbows, this angle is approximately 42 degrees. The size of a rainbow is determined by this angle, and it remains constant regardless of the distance of the observer from the water droplets.
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3. Unique shape and location of rainbows

Rainbows appear as circular arcs in the sky, with the center of that circle exactly opposite the sun's position. This is due to the fact that the rainbow angle remains constant and always points towards the anti-solar point. Since the ground usually obstructs the lower part of the circle, we usually see only the semicircular portion of the full circle.
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4. Color ordering of primary rainbows

When light is refracted and dispersed within a water droplet, shorter wavelengths, such as violet and blue, bend more than the longer wavelengths, like red and orange. In the case of primary rainbows, which involve one internal reflection, this results in the appearance of colors arranged from red on the outer edge to violet on the inner edge. This color ordering is a direct consequence of the dispersion of light based on the different bending of various wavelengths.

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