Introduction:
In the study of interference phenomena, destructive interference occurs when two waves combine to produce a resulting wave with a smaller amplitude. This is achieved by introducing a phase difference between the waves. In the case of light waves, a phase difference of (2n-1)π is often used.

Explanation:
Phase Difference:
The phase of a wave represents the position of a point on the wave at a particular time. It is usually measured in radians or degrees. When two waves interfere constructively, their crests and troughs align, resulting in reinforcement. Conversely, when they interfere destructively, their crests and troughs misalign, leading to cancellation.

Path Difference and Phase Difference:
The path difference is the physical difference in the distance traveled by two waves. When this path difference corresponds to half a wavelength (λ/2), the waves are said to be in phase opposition or have a phase difference of π radians (180 degrees). This results in destructive interference. However, to achieve destructive interference, a phase difference of (2n-1)π is used.

2n-1π Phase Difference:
The reason for using a phase difference of (2n-1)π is to account for the possibility of multiple reflections or refractions that can occur in the interference phenomenon. Each reflection or refraction introduces an additional π phase shift.

Multiple Reflections or Refractions:
When light waves encounter a medium with a different refractive index or reflect off multiple surfaces, the waves undergo phase shifts. These shifts can be caused by changes in the propagation speed or reflections at boundaries. For example, when light reflects off a denser medium, there is a phase shift of π radians.

Compensating for Phase Shifts:
To ensure destructive interference, the phase difference needs to account for the accumulated phase shifts due to multiple reflections or refractions. By using a phase difference of (2n-1)π, where n is an integer, the interference pattern can be adjusted to cancel out the waves completely.

Conclusion:
In summary, a phase difference of (2n-1)π is used in destructive interference of light waves to compensate for the phase shifts introduced by multiple reflections or refractions. This ensures that the waves align in such a way that they cancel each other out, resulting in a diminished amplitude or complete destructive interference.