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I believe in lecture, we learned that light generally shows diffraction patterns, which is something that particles will not do. However, light also behaves like a particle because a unit of light is a photon, and high-energy photons will act like particles. This was explained through the photoelectric effect -- experimentally, UV light hit a metal surface and emit electrons (which have particle properties).
I found Dr. Lavelle's watering can analogy helpful for understanding this concept. In large quantities, water moves as a wave (continuously). However, we can also think of water jumping out of the (now shrunken to microscopic proportions) mouth of the water can in single molecules, or particles.
At the larger scale, light appears to be continuous like a wave, but when light is observed as the microscopic scale, it is actually made up of a stream of discrete photons. Certain behaviors of light are characteristic of waves (diffraction patterns) and other behaviors are characteristic of particles (the photoelectric effect).
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