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Light interference is a fascinating phenomenon that occurs when two or more light waves converge and combine with each other. This results in the formation of a new wave pattern, which can either amplify or diminish the light intensity in certain areas. Interference patterns are created when the waves are coherent, meaning they have the same frequency and a stable phase relationship.

When light passes through two narrow slits, as in the exercise, it behaves like waves spreading out from each slit. These waves overlap and interfere with each other, creating a pattern of bright and dark fringes on a screen. Bright fringes, known as interference maxima, occur where the waves enhance each other, while dark fringes appear where they cancel out.

The exercise illustrates how varying the frequency of light affects the position of these interference maxima. By calculating the wavelengths for two different frequencies and using the interference condition, one can determine the separation between the slits, as this distance dictates the specific pattern of light and dark bands observed.

The double slit experiment is a classic demonstration of the wave-like behavior of light and is central to the field of quantum mechanics. It reveals the interference pattern, which is one of the most direct pieces of evidence that light can behave as a wave.

In the experiment, coherent light shines through two closely spaced slits, producing a pattern of bright and dark fringes on a screen behind the slits. From the experiment in the exercise, we see that when light of a certain frequency causes an interference maximum at a set angle, a different frequency of light can produce a maximum at the same angle—indicating that the interference pattern is a function of both the frequency of light and the slit separation.

Through careful measurements and calculations, such as those presented in the problem solution, the separation between the slits can be determined. The logic applied in the example uses the assumption about the ratio of the maxima's orders derived from the ratio of frequencies to decode the underlying pattern and conclude the sought value of the slit separation.

Wave-particle duality is a cornerstone concept of quantum mechanics proposing that every particle or quantum entity can exhibit both wave-like and particle-like properties. In the context of light, this concept was proposed to reconcile the particle theory of light, which includes photons, with its wave-like behavior, such as diffraction and interference.

Even though the exercise focuses primarily on the wave aspect of light to explain the interference pattern, the underlying principle of wave-particle duality is also implicitly at play. The fact that light can generate an interference pattern demonstrates its wave-like property; meanwhile, its particle aspect is acknowledged when considering that light is made up of photons—discrete packets of energy.

Realizing that matter and energy can switch between particle-like and wave-like behaviors depending on the conditions and measurements is pivotal in understanding the fundamentals of quantum phenomena. This is also essential in grasping the full scope of the double slit experiment, where not just waves of light but individual photons can produce interference patterns, a result that's deeply intertwined with the nature of wave-particle duality.