In the context of the double-slit experiment, the wave nature of light refers to the behavior of photons, which are particles of light, exhibiting wave-like characteristics. However, it is important to note that photons do not require a medium to propagate as traditional mechanical waves do (such as sound waves requiring a medium like air or water).
In classical physics, light was thought to propagate through a hypothetical medium called the luminiferous ether. However, the concept of the luminiferous ether has been largely abandoned since the late 19th century when the Michelson-Morley experiment failed to detect its presence. The development of modern physics, particularly Einstein's theory of relativity and quantum mechanics, led to the understanding that light can travel through a vacuum, devoid of any medium.
According to quantum mechanics, photons are considered to be quanta (or discrete packets) of electromagnetic energy. They can exhibit wave-like properties, such as interference and diffraction, even though they do not require a material medium to propagate. Instead, photons are associated with an electromagnetic field that permeates all of space. This field can interact with charged particles and other electromagnetic fields, giving rise to the wave-like behavior observed in phenomena like the double-slit experiment.
Therefore, in the context of the double-slit experiment, the "medium" associated with the wave nature of light is the underlying electromagnetic field itself, which exists everywhere, including empty space.