While light can exhibit both particle-like and wave-like properties, the phenomenon you're describing—light appearing to "spread" or diverge as it travels further from its source—is primarily due to its wave nature. This behavior is known as diffraction.
Diffraction occurs when light encounters an obstacle or passes through an aperture (an opening). When light waves encounter an obstruction or aperture, they can bend or spread out. This spreading is a characteristic of wave behavior and is not exclusive to light waves but can occur with other types of waves as well, such as water waves or sound waves.
The amount of diffraction that occurs depends on the size of the aperture or obstacle relative to the wavelength of the light. If the aperture or obstacle is small compared to the wavelength, the diffraction effects are more pronounced. As light waves pass through a small aperture or encounter a small obstacle, they tend to spread out and interfere with one another, causing the light to diverge or scatter.
This spreading of light is why, for example, you can observe the pattern of light and dark fringes when light passes through a narrow slit or when it interacts with the edges of an object. These phenomena are known as diffraction patterns.
It's worth noting that while light does exhibit particle-like behavior, particularly in certain experiments or interactions, the spreading of light as it travels further from its source is primarily explained by its wave nature and the phenomenon of diffraction.