Compare the primary and secondary rainbows as regards their angular size, color ordering, and number of internal reflections that occur in the rain droplets.

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Question: Compare primary and secondary rainbows in terms of their angular size, color ordering, and number of internal reflections in rain droplets. Answer: Primary rainbows have a smaller angular size of 42°, colors ordered from red (outer) to violet (inner), and one internal reflection in rain droplets. Secondary rainbows have a larger angular size of 51°, colors ordered from violet (outer) to red (inner), and two internal reflections in rain droplets.

Step by step solution

01

Understanding the formation of rainbows

Rainbows are optical phenomena that occur when sunlight is refracted, reflected, and dispersed by water droplets in the atmosphere. Depending on the number of internal reflections inside the rain droplets, we can classify rainbows as primary or secondary rainbows. Primary rainbows form from a single internal reflection, while secondary rainbows form from two internal reflections.
02

Comparing the angular size

Angular size is the apparent size of an object as seen by an observer, measured in angular units like degrees. To compare the angular size of primary and secondary rainbows, we need to calculate the angular size of each type. For a primary rainbow, the sunlight is refracted into the rain droplet, undergoes a single internal reflection, and then is refracted out of the droplet, forming an angle of approximately 42° between the incident light and the emergent light. This means that the angular size of the primary rainbow is approximately 42°. For a secondary rainbow, the sunlight undergoes two internal reflections inside the rain droplet. As a result, the angle between the incident light and the emergent light becomes approximately 51°. Therefore, the angular size of the secondary rainbow is approximately 51°. In summary, the primary rainbow has a smaller angular size (42°) compared to the secondary rainbow (51°).
03

Comparing the color ordering

Colors in a rainbow are results of dispersion, where wavelengths of different colors are refracted by different amounts. In a primary rainbow, the colors are arranged with the red color on the outer edge and the violet color on the inner edge. The order of colors is as follows: red, orange, yellow, green, blue, indigo, and violet (outer to inner). In a secondary rainbow, due to the additional internal reflection, the order of colors is reversed compared to the primary rainbow. The red color is now on the inner edge and the violet color on the outer edge. The order of colors in a secondary rainbow is violet, indigo, blue, green, yellow, orange, and red (outer to inner). So, the color ordering in the primary rainbow is the reverse of the color ordering in the secondary rainbow.
04

Comparing the number of internal reflections

As mentioned earlier, the primary difference between primary and secondary rainbows is the number of internal reflections occurring inside the rain droplets. In a primary rainbow, there is only one internal reflection before the sunlight is refracted out of the droplet. In contrast, a secondary rainbow forms when the sunlight undergoes two internal reflections before being refracted out of the droplet. In conclusion, comparing primary and secondary rainbows: 1. Angular size: The primary rainbow has a smaller angular size of 42°, while the secondary rainbow is larger with an angular size of 51°. 2. Color ordering: The primary rainbow has colors ordered from red (outer) to violet (inner), while the secondary rainbow has colors ordered from violet (outer) to red (inner). 3. Number of internal reflections: A primary rainbow has one internal reflection in the rain droplet, while a secondary rainbow has two internal reflections.

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