Question:

Differentiate between primary and secondary rainbows.

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A simple mnemonic for the color order: "Roy G. Biv" (Red, Orange, Yellow, Green, Blue, Indigo, Violet). For a primary rainbow, Roy is at the top of the arc. For a secondary rainbow, the order is reversed.
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Solution and Explanation

Step 1: Understanding the Concept:
Rainbows are optical phenomena caused by the dispersion and internal reflection of sunlight by water droplets (like rain or mist) in the atmosphere. The differences between primary and secondary rainbows arise from the number of internal reflections the light undergoes within each droplet. 

Step 2: Detailed Explanation of Differences:

FeaturePrimary RainbowSecondary Rainbow
FormationCaused by sunlight undergoing one total internal reflection inside a water droplet.Caused by sunlight undergoing two total internal reflections inside a water droplet.
Color SequenceThe sequence of colors is Violet on the inner edge and Red on the outer edge (VIBGYOR from bottom to top).The sequence of colors is reversed due to the extra reflection. Red is on the inner edge and Violet on the outer edge.
BrightnessIt is brighter because less light is lost. Light emerges after only one internal reflection.It is fainter because light energy is lost at each internal reflection.
Angular PositionForms at an angle of approximately 40\(^{\circ}\)-42\(^{\circ}\) with respect to the observer-sun line. It appears lower in the sky.Forms at a higher angle of approximately 50\(^{\circ}\)-53\(^{\circ}\) with respect to the observer-sun line. It appears above the primary rainbow.

Step 3: Final Answer: 
The primary rainbow is brighter, lower, and has red on top, resulting from a single internal reflection. The secondary rainbow is fainter, higher, and has violet on top, resulting from two internal reflections.

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