An educational worksheet explaining the science behind rainbows with a vibrant rainbow illustration.

Problem Analysis:

The task involves understanding how a rainbow is formed and explaining the process step by step. The text provided in the image outlines the key components of this phenomenon, including sunlight, water droplets, refraction, reflection, and dispersion. The goal is to explain these concepts clearly.

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Solution Explanation:

#### Step 1: Understanding Sunlight
- Sunlight is composed of white light, which is actually a mixture of all colors of the visible spectrum (red, orange, yellow, green, blue, indigo, violet). This is why we see rainbows as colorful arcs.

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#### Step 2: Role of Water Droplets
- Raindrops act as tiny prisms. When sunlight enters a raindrop, it undergoes several optical processes:
1. Refraction: As sunlight enters the raindrop, it slows down and bends (refracts) because it moves from air into water, which has a higher refractive index.
2. Dispersion: White light splits into its component colors because different wavelengths (colors) of light bend by different amounts. Red light bends the least, while violet light bends the most.
3. Reflection: After entering the raindrop, the light reflects off the inner surface of the drop. This reflection causes the light to change direction.
4. Second Refraction: The reflected light then exits the raindrop, bending again as it moves from water back into air.

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#### Step 3: Formation of the Rainbow
- When sunlight passes through millions of raindrops in the atmosphere, each drop acts as a prism, dispersing and reflecting light. The combination of these processes creates a circular arc of colors in the sky.
- The primary rainbow appears when light reflects once inside the raindrop. The colors appear in the order: violet on the top and red on the bottom because violet light bends more than red light.
- The secondary rainbow (if visible) occurs when light reflects twice inside the raindrop. This results in the colors appearing in reverse order (red on top and violet on the bottom), and it is fainter than the primary rainbow.

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#### Step 4: Observer's Perspective
- To see a rainbow, the observer must be between the sun and the raindrops. The sun should be behind the observer, and the raindrops should be in front. The angle between the observer, the sun, and the raindrops is approximately 42 degrees for the primary rainbow and 50 degrees for the secondary rainbow.

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Final Answer:

A rainbow is formed due to the interaction of sunlight with water droplets in the atmosphere. Here’s the step-by-step process:
1. Refraction: Sunlight enters a raindrop and bends as it slows down in water.
2. Dispersion: The white light splits into its component colors because different wavelengths bend by different amounts.
3. Reflection: The light reflects off the inner surface of the raindrop, changing direction.
4. Second Refraction: The light exits the raindrop, bending again as it moves back into air.
5. Circular Arc: Millions of raindrops collectively create a circular arc of colors in the sky.
6. Primary Rainbow: Forms when light reflects once inside the raindrop, with violet on top and red on the bottom.
7. Secondary Rainbow: Forms when light reflects twice, appearing fainter and with reversed color order.

Thus, the mysterious beauty of a rainbow is explained by the interplay of refraction, reflection, and dispersion of sunlight through water droplets.

Final Answer: \boxed{\text{Rainbows are formed by the refraction, reflection, and dispersion of sunlight through water droplets in the atmosphere.}}