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The moon reflects the sun's light through a process called diffuse reflection. Here’s a step-by-step explanation:

1. **Surface Characteristics**: The moon's surface is covered with regolith, which is a layer of loose, fragmented material. This includes dust, soil, broken rock, and other materials. These particles have irregular shapes and rough surfaces.

2. **Sunlight Hits the Moon**: When sunlight reaches the moon, it strikes the surface. The light is composed of photons, which are particles of light energy.

3. **Diffuse Reflection**: Unlike a smooth, shiny surface that would reflect light in a single direction (specular reflection), the moon's rough surface scatters light in many directions. This scattering occurs because the irregularities on the moon’s surface cause the photons to bounce off in various directions.

4. **Visibility from Earth**: The scattered light from the moon’s surface travels in many directions, including toward Earth. This is why we can see the moon illuminated in the night sky.

5. **Brightness Variation**: The amount of sunlight the moon reflects back to Earth can vary based on the angle of the sunlight and the moon’s position relative to Earth. This is why the moon appears to have phases (new moon, crescent, quarter, gibbous, and full moon).

Although the moon reflects sunlight, it is not a perfect reflector. The moon’s albedo (the measure of how much light it reflects) is about 0.12, meaning it reflects only 12% of the sunlight that hits it. The rest is absorbed by the moon’s surface. This relatively low reflectivity is why the moon appears bright against the dark night sky, but it is not nearly as bright as the sun itself.

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