Two light waves represented by y₁ = a ( ₁ t - k₁ x) and y₂ = a ( ₂ t - k₂ x + ₀) arrive at a point P on a screen. It is observed that a sustained (steady) interference pattern is formed on the screen. For this sustained pattern to exist, what must be the primary condition regarding the phase difference ( ) between the two waves at point P?

Step-by-step solution

For a sustained (steady) interference pattern to be observed, the positions of maxima and minima on the screen must not shift over time. The resultant intensity at any point depends on the phase difference between the interfering waves. If changes with time, the intensity at point P will fluctuate rapidly, resulting in a uniform average illumination rather than a steady pattern. Therefore, the fundamental requirement for sustained interference (coherence) is that the phase difference between the two waves must rema