Destructive interference occurs when two coherent waves combine in such a way that their amplitudes cancel each other out. In other words, the crests of one wave line up with the troughs of the other wave, resulting in a net amplitude of zero. The resultant intensity at a point of destructive interference is therefore zero.

To understand this concept more clearly, let's break down the interference pattern and analyze the superposition of the two waves.

Interference Pattern:
When two identical coherent waves meet, they create an interference pattern consisting of alternating regions of constructive and destructive interference. These regions are characterized by the addition or subtraction of the amplitudes of the waves at each point.

Constructive Interference:
In regions of constructive interference, the amplitudes of the two waves add up, resulting in an increased amplitude and intensity. The maximum intensity at these points is given by the sum of the individual intensities of the waves, resulting in an intensity of 2I0.

Destructive Interference:
In regions of destructive interference, the amplitudes of the waves cancel each other out, resulting in a net amplitude of zero. Since intensity is proportional to the square of the amplitude, the resultant intensity at these points is zero.

Explanation of the Correct Answer:
Therefore, in the case of two identical coherent waves of intensity I0 producing an interference pattern, the resultant intensity at points of destructive interference would be zero. This is because the waves interfere in such a way that their amplitudes cancel each other out, resulting in no net intensity at those points.

In summary, destructive interference occurs when two waves combine to produce a net amplitude of zero. As a result, the resultant intensity at points of destructive interference is zero, as observed in the given options.