From what we said, yor conclusion seems logical. But the double slits experiment is more complicated that what I am able to tell you.
Reading from here:
you can find sentences like:
a result that would not be expected if light consisted of classical particles
I don’t have a good enough understanding of mathematics, physics and the experiment itself to tell you why exactly.
The only thing I remember well is that when the width of the two slits and their distance is comparable with the wave length, you start seeing (and I saw it in laboratory many years ago) the interference pattern.
In the Interference of individual particles paragraph it is explained what happen when you send one particle at time. In summary, the interference pattern starts to emerge hit (with the screen) after hit. The also say that “hidden variables” explanations is confuted by “More complicated systems that involve two or more particles in superposition“. They also say knowing the position of the previous hits doesn’t give you any information regarding where the next photon will hit. So, when the photon hits the screen, there is an interaction and the photon leave a trace in a position on the screen. The probability of hitting the screen in that (or any other) position is a function that can be calculated considering the wave function of the photons and considering each slit as the source of a new light wave.
The above considerations explains the “wave–particle duality”. When a photon hits the screen the photon behaves like a particle. When you send photons, one after another, the photons hit the screen creating an interference pattern. So they behave as if the two slits are the source of a new wave each.
Note that the same happens in a water wave: put a barrier with two slits, send a wave against the barrier, and you’ll see 2 new waves from the slits.
That’s not everything there is to say. Some physicists tried to describe this phenomenon with particles moving in a wave manner, but, as far as I know, only the “wave” mathematical model explain and predicts what happens. But here we are really far out of my area of knowledge. Let’s just say that I accept the quantum superposition concept for the little part that I can understand.
