You are basically asking whether the photon goes through one of the slits. And you are asking whether if you shoot 100 photons after each other, and 40 will go through the left slit, 60 the right, and we repeat the experiment, with another 100 photons, will the same amount of 40 on the left and 60 on the right go through? The answer is no. You are asking whether the randomness of this comes from the direction of the laser beam. The answer is no. The randomness comes from the QM phenomenon called photon, and that our universe is basically QM. There are a few things that are important to understand:
- photon are not localized spatially between emission and absorption
The photon position is only well defined when we interact with it and collapse its wave function. This interaction would normally be with the detector. If we interact with the photon, to define its position, before it reaches the slits then the diffraction pattern disappears.
- each photon (in case there is a pattern) goes through both slits
The photons do not have a well defined trajectory. The diagram shows them as if they were little balls travelling along a well defined path, however the photons are delocalised and don't have a specific position or direction of motion. The photon is basically a fuzzy sphere expanding away from the source and overlapping both slits. That's why it goes through both slits.
Shooting a single photon through a double slit
- if you want to know which slit the photon went through, you will not see the pattern anymore, and you need to interact with the photon, that is, the detector on the slits will inelastically scatter the photon, changing its energy, and phase, and thus spatially localizing the photon. The reason you see a bright dot on the screen when the detector on one of the slits interacted with the photon, is that only the untouched slit will create the dot.
A detector after one of the slits intercepting the photon, changes the boundary conditions to a different system, and thus a different Ψ∗Ψ. It is no longer the same experimental setup. It should be obvious that if the detecting instrument after the slit , absorbs the photon like the screen does, only the untouched slit will give a signal on the far screen, which could not interfere with itself .( A sophisticated experiment with electrons which tries to minimally show the effect came to the conclusion that the detecting level acts as a point source for the electrons going through it, i.e. a different Ψ∗Ψ for the electron which is no longer coherent so as to show the interference pattern.)
Detection at the screen has picked ("collapsed ")an instance of (x,y,z) of the original wavefunction and removed that photon from the final screen. In general after the detection of "which slit" the photons are in a different wave function with new boundary conditions.
Double Slit Experiment. What effect does the detector actually cause?
- each and every photon (that was shot) will leave a bright spot on the screen
In a double slit experiment, does each and every photon leave a dot on the screen in the bright area?
You are asking about the randomness, which slit the photon goes through (actually which slit we will detect it at), and it comes from the QM phenomenon of the photon itself, being not localized as it travels through space.
What actually waves is the wave function of the photon, spreading as a Gaussian wave.
Do photons oscillate or not?
You are basically asking whether the randomness of the photons going through (being detected at) certain slits is because of the setup of the laser, and the original direction. The answer is no. The randomness comes along the way as the photon travels through space (and is not localized) before actually being absorbed at the screen creating a bright spot.