When two rays intersect each other, they do not disturb each other. This is what the "Principle of mutual independence of rays" states Why is that so? When a ray of ultro violet light and one of visible light intersect each other, they contain particles of different energies and also they are of different wave lengths Would they not interact at all? If there could be any interaction we can think about, what could that be?
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This is the assumption of linearity. If there were finite amplitude interactions, then many different things could happen. For instance, for water waves resonance modifies the spectral energy distribution, and can modify the dispersion relationship, and hence the ray trajectories. – Nick P Mar 11 '17 at 14:08