An experiment with bullets

Figure 18.1: Double slit experiment with bullets

We consider an experiment where bullets are sprayed randomly on screen A which has two slits $1$ and $2$ as shown in Figure 18.1. The bullets that hit the screen are stopped, the bullets that pass through the slits reach screen B. The number of bullets arriving at different points on screen B is recorded.

The experiment is first performed with slit $2$ closed. The bullets can now arrive at screen B only through slit $1$. We use $N1$ to denote the number of bullets arriving at different points on screen B through slit $1$. As shown in Figure 18.1, $N1$ peaks at the point just behind slit $1$, and falls off as we move away from this point . The experiment is next repeated with slit $2$ open and slit $1$ closed. The bullets can now reach screen B only though slit $2$, and $N2$ is very similar to $N1$ except that the peak is shifted.

Finally the experiment is performed with both slits open. Bullets can now reach screen B through slits $1$ or slit $2$, and the number of bullets at any point on screen B is $N1+N2$.

Salient points that should be noted are

1. Any point on screen B is hit by either one, or two or a larger integer number of bullets. Half bullets or other fractions are never detected.
2. If the rate of shooting is increased, the frequency of arrival increases.
3. The counts can be converted to probability of a bullet arriving at a point x on the screen.
4. A bullet arrives at a point on screen B either through slit $1$ or slit $2$. Denoting the associated probabilities as $P_1$ and $P_2$ respectively, the probability when both slits are open is $P_{12}=P_1+P_2$.