Coherent and Incoherent addition of waves: Overview, Questions, Preparation

Understanding the core concepts of coherent and incoherent addition of waves are extremely crucial for candidates who are aspiring to prepare for JEE MAINS. These fundamentals help develop the foundations of wave optics and quantum mechanics.

Here’s a quick comparison between these two which can help you understand the basic mechanism of addition of waves:

Coherent waves are the types of waves who have a constant phase difference i.e. the peaks and troughs of the wave perfectly overlap with each other in a predictable way over a particular time period. These waves have almost the same frequency and are generally emitted by the same source or synchronized sources. Example: laser beam.

Mathematically, if 2 waves have the same amplitude, the resultant value can be denoted by:

2Acos(ϕ/2​)

Where,

A = Amplitude

Φ = Phase difference

As a result, the interference pattern is stable in this case.

This is the type of interference that occurs when the crest of one wave aligns with the crest of another, due to which amplitude increases.

This is the type of interference that occurs when the crest of one wave meets the trough of the other, due to which amplitude decreases.

Incoherent waves are another category of waves that occur when the waves have rapidly varying phase differences i.e. their peaks and troughs do not align with each other. The frequencies of these waves differ and are usually emitted from independent sources. Example: lights from 2 different bulbs.

So if 2 waves of different intensities are added, the answer is:

I (total) = I1​+I2​

As a result, there is no stable interference pattern in this case.