The heart of quantum mechanics – Interference as vector sums

We consider a continuous laser beam on the single slit, and explain the interference pattern based on the wave theory. The laser is, in that context, described as an electromagnetic wave.
Light travels in all possible directions. Starting with the straight path, we will divide the slit into six segments of equal size, and consider the phase differences that emerge.

For the straight path, there is no phase difference, that is, all vectors point in the same direction. Let us now observe the red point on the screen. The six partial waves interfere there. Adding up the six vectors, we obtain the square root of the intensity I_S, which constitutes the maximum.

Next, we consider the first minimum. What path difference Δ do the six partial waves take on at this location? After adding the six vectors, we see that the vector sum is zero. Thus, the phase difference between two successive partial waves is 60°. The resulting phase difference is
Φ = 6•60° = 360° or 2π.
The phases of the six vectors always keep rotating in a circle, depending on the path difference Δ. The first secondary maximum is reached once the path difference has increased by a further half wavelength to Δ = 3/2 λ.

Once the second slit has been opened, it can be seen that the path difference between the individual partial waves at the central maximum is zero again.
In case of the double slit, the first minimum emerges much closer than in the case of the single slit. At the first minimum, the path difference Δ is half a wavelength. The partial waves of the first slit and the partial waves of the second slit exactly eliminate one another.

If the path difference Δ between the two slits corresponds exactly to one wavelength λ, we obtain the secondary maximum.
Overall, the intensity distribution measured can be well explained based on this model of interfering partial wave.