What is the significance of phase difference in interference?

The phase difference in interference determines the constructive or destructive nature of the resultant wave.

In the phenomenon of interference, two or more waves superpose to form a resultant wave of greater, lower, or the same amplitude. This superposition often occurs when the waves are coherent, meaning they have a constant phase difference and the same frequency. The phase difference between these waves plays a crucial role in determining the nature of the resultant wave.

When the phase difference is a multiple of a complete cycle (i.e., 0, 2π, 4π, and so on), the waves are said to be 'in phase'. In this case, the crests and troughs of the waves align, leading to constructive interference. This results in a resultant wave with an amplitude that is the sum of the amplitudes of the individual waves. This is why you observe bright fringes in the interference pattern of light.

On the other hand, when the phase difference is an odd multiple of a half cycle (i.e., π, 3π, 5π, and so on), the waves are 'out of phase'. Here, the crest of one wave aligns with the trough of the other, leading to destructive interference. The resultant wave has an amplitude that is the difference of the amplitudes of the individual waves. This results in dark fringes in the interference pattern of light.

Moreover, the phase difference also determines the position of these bright and dark fringes in the interference pattern. A greater phase difference corresponds to a fringe further from the centre of the pattern. This is why the interference pattern consists of alternating bright and dark fringes.

In summary, the phase difference in interference is significant as it determines whether the interference is constructive or destructive, and it also influences the position of the fringes in the interference pattern. Understanding this concept is crucial for interpreting and predicting the outcomes of experiments involving wave interference, such as Young's double-slit experiment.