1. The problem asks why the sky appears blue during the day, even though sunlight looks white, and why it can appear red or orange at sunrise and sunset. 2. The explanation involves the scattering of sunlight by the Earth's atmosphere, specifically Rayleigh scattering. 3. Sunlight is composed of multiple colors, each with different wavelengths. Blue light has a shorter wavelength, while red light has a longer wavelength. 4. Rayleigh scattering occurs when light interacts with particles much smaller than its wavelength, such as molecules in the atmosphere. The intensity of scattered light is inversely proportional to the fourth power of the wavelength, given by the formula: $$I \propto \frac{1}{\lambda^4}$$ where $I$ is the intensity of scattered light and $\lambda$ is the wavelength. 5. Because blue light has a shorter wavelength than red light, it is scattered much more strongly in all directions by the atmosphere. 6. During the day, when the Sun is high, the scattered blue light dominates the sky's color, making it appear blue to an observer on the ground. 7. At sunrise and sunset, sunlight passes through a thicker layer of atmosphere, scattering away most of the blue and green light out of the direct path. The longer wavelengths like red and orange are less scattered and thus become more prominent, coloring the sky red or orange. 8. This explains the observed color changes of the sky based on the interaction of sunlight with atmospheric particles and the wavelength-dependent scattering effect.