Final Answer:
For maximum constructive interference at point P, the two beams of coherent light must travel paths that differ by a distance equivalent to a whole number of wavelengths or multiples thereof for the specific light being used.
Step-by-step explanation:
Constructive interference occurs when two waves are in phase and their amplitudes reinforce each other. In this scenario, to achieve maximum constructive interference at point P, the two beams of coherent light must traverse paths that result in them being in phase upon arrival. This necessitates a path difference corresponding to a whole number of wavelengths or an integral multiple of the light's wavelength.
Let λ represent the wavelength of the light. To ascertain the path difference required for constructive interference, the condition for constructive interference is \(Δd = mλ\), where m is an integer representing the number of wavelengths of path difference. For instance, if m = 1, the path difference Δd would equal one wavelength; for m = 2, Δd would be two wavelengths, and so on.
For maximum constructive interference, the additional path length traveled by one beam compared to the other must fulfill this condition. If the paths differ by an integral multiple of the wavelength (mλ), the waves will constructively interfere at point P due to their in-phase alignment. Any deviation from this condition will result in a phase shift, leading to interference patterns other than maximum constructive interference.
Therefore, the fundamental principle for achieving maximum constructive interference at point P is ensuring that the path difference between the two beams corresponds precisely to a whole number of wavelengths or multiples thereof, allowing the waves to meet in phase and reinforce each other's amplitudes.
Here is completed question:
"Two beams of coherent light (waves are in phase with each other) start from the same point in phase and travel different paths to arrive at point P. If the maximum constructive interference is to occur at point P, the two beams must travel paths that differ by a distance that corresponds to a whole number of wavelengths or multiples of the wavelength of the light being used."