The starting observation is that light moves in a straight line. This can be deduced from the geometry of shadows and the objects casting them, and can be tested by making and observing rays of light (e.g., by passing sunlight through a hole in a screen, and using dust/smoke/mist to observe the ray).

We can note that most waves we observe - or at least things that we easily recognise as waves, such as water waves - don't travel as rays in straight lines like light does. Water waves can be observed to curve near the beach, and to spread out if they pass through a gap, and to spread in expanding circles when we drop a rock into a pond. From our everyday experience with waves, rays of light do not appear to behave like waves.

Do rays of light behave like particles? Not obviously. First, if we throw a particle, it doesn't travel in a straight line (rather, a parabolic path). Light will reflect from surfaces and continue largely as it was before, except in a different direction. If we bounce particles off a surface, they tend to lose a lot of energy. From our everyday experience of particles (e.g., rocks) moving through the air, rays of light do not appear to behave like particles.

One might think that perhaps it is neither. Perhaps light is just instantaneous influence between object and eye. Observation and simple experiment shows that light travels either very quickly or instantaneously. This is a more serious problem for wave theory than particle theory, but "instantaneously" suggests it is neither.

Al-Haytham in Book I of his Optics discusses what was known about light (English translation in Sabra, A. I., ed. (1989), The Optics of Ibn al-Haytham. Books I-II-III: On Direct Vision. English Translation and Commentary. 2 vols, Studies of the Warburg Institute, 40, translated by Sabra, A. I., London: The Warburg Institute, University of London). He discusses many ways by which we know that light travels in straight lines, and the current theories of light. He supports the theories that light moves from objects to the eye, rather than from the eye to objects. There is no need to discuss the question of whether light is a wave or particle - with the knowledge of the time, this kind of discussion would simply be adding a further layer of speculation. Given that there is no indication that light is either a wave or particle, why introduce hypotheses that explain nothing?

What phenomena are there to explain? Straight-line propagation of rays, reflection (Euclid's law: the angle of reflection equal the angle of incidence), Snell's law (refraction, and not known both widely and correctly until Snel and Descartes (but see ibn Sahl's much ealier work on refraction (Rashed, Roshdi. “A Pioneer in Anaclastics: Ibn Sahl on Burning Mirrors and Lenses.” Isis, vol. 81, no. 3, 1990, pp. 464–491); ibn Sahl is sometimes credited as the discover of Snell's law).

To this starting point, we can add four later observations:

1. Light travels at a fast, but not infinite, speed (Rømer's measurement of the speed of light from the timing of eclipses of the moon's of Jupiter). This is problematic for particle theories of light - why would all light particle emitted by sources, whether dim or bright, hot or cold, travel at the same speed. Having a single distinct speed makes more sense for waves (but note that we can see that water waves of different wavelengths travel at different speeds - it is a problematic observation for wave theory as well).

2. Diffraction - light doesn't travel in straight lines. At least near a small aperture, or the edge of an object, it will curve and spread out. This is something we see waves do (e.g., water waves on a pond). We could speculate about attractive and repulsive forces between the edges of the aperture and particles of light, and shoehorn these observations into a particle theory, but wave theory explains them very naturally.

3. Interference, producing effects such as the coloured fringes we see in thin films, and other effects such as Newton's rings. Pure wave theory. One can graft elements of wave theory onto a particle theory, such as Newton did with his fits of easy transmission and fits of easy reflection.

4. Polarisation. Direction, and direction other than the direction of propagation matters. Light can be converted from unpolarised to polarised. What is the difference between the two kinds of light? Easy to "explain" with particle theory (e.g., postulate disk-shaped particles of light, which are aligned when light is polarised). Difficult to explain with wave theory, unless you combine (a) transverse waves with (b) the idea of an incoherent superposition of waves.

Given such addition observations, and a climate in physics where stories about emission of particles/atmospheres by magnets and electrically charged objects were being used to "explain" phenomena such as electric and magnetic forces, particle and wave explanations of light make sense.

• Particle theories easily explain straight line propagation of rays, and reflection, and can explain refraction is one postulates a force between surface and particle of light, and can qualitatively explain diffraction with such forces. Interference is difficult, and polarisation is easy. But particles carry momentum, and should exert force! Why don't we observe radiation pressure? (But Kepler had already suggested that emanations from the sun push comet tails away from the sun, so one could say that we did observe it.)

• Huygens put a lot of the pieces together for wave theory, explaining straight line propagation of rays, reflection, refraction, and even things like total internal reflection and frustrated total internal reflection. But there was a bigger problem for wave theory: if light is a wave, what is the medium for the wave? So, postulate a luminiferous ether. Simple! All we need to do is suggest some substance that fills all of space, which we (and other matter, such as the planets) can move through with the greatest of ease. Problematic indeed is the quantification of ether theory which suggests a very high elastic modulus (stiffness) for the ether, much greater than that of steel, in order for the waves of light to travel at the observed speed. For a good review of early wave theories of light, see Shapiro, A.E. "Kinematic optics: A study of the wave theory of light in the seventeenth century", Arch. Hist. Exact Sci. (1973) 11: 134. https://doi.org/10.1007/BF00343533

The stage was set for the battle between wave and particle theories of light: the 18th century. Some arguments were simply wrong (wave-ists saying that light could be particles since there was no radiation pressure; Euler had already shown that waves in an ether would result in radiation pressure (his wave-theory explanation of why comet tails were pushed away)). The status of Newton as a great scientist helped particle theory. But Young's wave theory, and then Fresnel's wave theory were decisive. For details of this battle: Eugene Frankel, "Corpuscular Optics and the Wave Theory of Light: The Science and Politics of a Revolution in Physics", Social Studies of Science, Vol 6, Issue 2, pp. 141-184 (1976).

This led to an interesting 19th century as far as light was concerned: with light as a wave, and therefore a luminiferous ether being required, what were the properties of that ether? In the 1860s, there were two key breakthroughs: Maxwell's theory of the electromagnetic field (1865), which suggested that light was an electromagnetic wave, and Ludvig Lorenz's electromagnetic theory of light (1867), the equivalency of which to his own theory was noted by Maxwell in a footnote in his Treatise of 1873. Maxwell's theory was tied to a theory of the ether, and Lorenz's theory was not (and he suggested that an ether was not necessary).

Light was now explained: light was an electromagnetic wave. Experimental production and detection of electromagnetic waves (other than light) by Heinrich Hertz in 1888 hammered the point home, and Hertz's re-derivation of Maxwell's equations without assuming a model of the ether made it acceptable, and Hertz's (and Heaviside's) simplification of Maxwell's theory to the modern 4 "Maxwell's" equations (known for a while as the Hertz-Heaviside equations) made it understandable (as Sommerfeld wrote, "scales fell from my eyes when I read Hertz's great paper"). The wave theory was now supreme. There were only a small handful of phenomena about light that remained mysterious:

1. Light in moving media (which gave rise to the Special Theory of Relativity, with major steps by Hendrick Lorentz and Henri Poincare, and almost-complete by Einstein, capped by Minkowski). The solution to this problem erased one question for which the ether had been the answer: why does light travel at the speed of light? (While popular mythology often holds that it erased the ether, the ether remained alive and well in physics, especially English physics, until about 1920, when it was pummelled into oblivion by the ultraviolet catastrophe (see 3 below).

2. Atomic spectra. Clearly, atoms were very complicated.

3. Blackbody radiation. The ultraviolet catastrophe: Why don't objects emitting thermal radiation cool down instantly? (The ether theory version: why isn't the specific heat capacity of the ether infinite?)

(to be continued)