Interference is a phenomenon that occurs when two or more waves overlap and combine their amplitudes. The resulting wave pattern depends on the phase relationship between the waves. If the waves are in phase, they constructively interfere, resulting in a wave with greater amplitude. Conversely, if the waves are out of phase, they destructively interfere, resulting in a wave with smaller or zero amplitude.


Coherent sources are waves that have a constant phase difference between them. When two coherent sources interfere, their phase relationship remains constant, resulting in a stable interference pattern. In other words, the phase difference between the sources does not change over time.


Completely destructive interference occurs when the two coherent sources are perfectly out of phase. This means that the phase difference between the sources is exactly half a wavelength or an odd multiple of half a wavelength. As a result, the waves from the sources cancel each other out at certain points, creating regions of zero amplitude called nodes.


In this question, we are given that completely destructive interference occurs at point P. This implies that the waves from the two coherent sources cancel each other out at point P, resulting in a node. To find the phase difference required for this, we can consider the path difference between the two sources at point P.


The path difference is the difference in distance traveled by the waves from the two sources to reach a certain point. In the case of completely destructive interference, the path difference between the two sources at point P is equal to an odd multiple of half a wavelength.


The expression "S2P - S1P" represents the path difference between the two sources at point P. By calculating this value, we can determine the phase difference required for completely destructive interference.

In conclusion, "S2P - S1P" represents the path difference between the two coherent sources at point P. By setting this value equal to an odd multiple of half a wavelength, we can achieve completely destructive interference.

(2n+1)λ/2