Interference, diffraction, and polarization are three of the most obvious and fundamental phenomena of physical optics (the branch of optics that takes the wave nature of light into account). Interference and diffraction really should be treated simultaneously as they are both effects due to the combining of waves by to the principle of superposition. However, the term interference is usually reserved for situations in which only a few waves overlap, while diffraction considers the interference effects due to the overlapping waves from many point sources. Although interference effects might seem like fairly substantial evidence in favor of a wave theory of light, it is important to bear in mind that it can be given a full treatment from the point of view of Quantum Electrodynamics (QED), which is a particle theory of light. Fenyman makes this point crystal clear:
I want to emphasize that light comes in this form--particles. It is very important to know that light behaves like particles, especially for those of you who have gone to school, where you were probably told something about light behaving like waves. I'm telling you how it does behave--like particles. -- R.P. Fenyman.
On this view, the behavior of photons is determined statistically; simplistically, the irradiance of light at a particular point (proportional to the amplitude squared) is proportional to the probability of a particular photon passing through that point. Moreover, diffraction in particular is an extremely large and complex topic, and it be well that the reader be aware that there are many aspects of diffraction not treated here (including multiple slit diffraction, rectangular and circular apertures, Fresnel or near-field diffraction, the diffraction grating, resolution, zone plates, and more). A comprehensive treatment of these topics can be found in some of the references listed in the Further Reading section.
Both Huygens and Newton were aware of the phenomenon of polarization, which Newton called the 'two sidedness' of light. The Frenchman, Etienne Malus was the first to characterize polarization by reflection in 1808. Importantly, it was work by Augustin Fresnel and Dominique Arago attempting to explain polarization that caused them to discard their notion of light as a longitudinal wave, and replace it with a transverse model.
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