No, in the context of double-slit interference, you cannot simply add the intensities from each of the two slits to calculate the overall intensity. The interference pattern that arises in the double-slit experiment is a result of the wave nature of the particles (such as photons or electrons) passing through the slits.
When two coherent waves (such as those emerging from the two slits) interact, they can either reinforce each other (constructive interference) or cancel each other out (destructive interference), depending on the phase relationship between the waves at a particular point.
To determine the overall intensity pattern resulting from the interference, you need to consider the complex amplitudes of the waves from each slit and take into account the interference effects.
Mathematically, if the complex amplitudes of the waves from the two slits are represented as A₁ and A₂, respectively, then the total amplitude at a given point will be given by the sum of these amplitudes:
Total amplitude = A₁ + A₂
To calculate the overall intensity at that point, you need to square the magnitude of the total amplitude:
Overall intensity = |Total amplitude|² = (A₁ + A₂)²
Importantly, when you expand this expression, you will get cross-terms that involve the product of the amplitudes from each slit, which leads to interference terms. These interference terms determine the resulting intensity pattern on a screen placed to detect the particles.
The interference pattern will exhibit regions of constructive interference, where the intensities add up and become larger, and regions of destructive interference, where the intensities cancel out or become smaller.
So, in summary, simply adding the intensities from each of the two slits is an incorrect approach. Instead, the interference effects arising from the wave nature of the particles must be considered by taking into account the complex amplitudes and their interference terms to calculate the overall intensity pattern.