Conditions for Destructive Interference

Interference is a phenomenon in which two waves with the same or different amplitude meet each other. In this regard, it should be mentioned that destructive interference is a specific type of interference in which the two superposing waves are seen to completely cancel each other out. In nature, several interesting activities can be noticed whose description cannot be given with an individual or single wave. To properly understand destructive interference a person needs to analyze the combination of the waves. Hence, the principle of superposition must be applied. According to this principle, if two waves that are traveling within the same medium superpose then the resultant wave will be given as the algebraic sum of the two superposing waves. 

Destructive interference equation

The destructive interference equations have been outlined in the following table.

The above equations for destructive interference (2n – 1) refer to an odd multiple, Δ is the path difference, λ is the wavelength, θ = time interval, and T = period.

Conditions for interference

To know about destructive interference and analyze the conditions of destructive interference, firstly we need to know about the conditions for interference. The conditions for interference have been outlined in the following. 

• The sources from which the two light waves are coming need to be coherent. 

• The frequency of the two coherent sources must be the same. This means that the source can be taken as the monochromatic source of light. 

• The two waves coming from the coherent sources must have the same amplitude. 

Conditions for destructive interference

There are some specific conditions for destructive interference to occur. Destructive interference specifically occurs when the two superposing waves collide in a way such that they cancel on one another. Another condition for destructive interference is that when the two waves superpose destructively then they must have the same amplitude. However, it should be in the opposite direction. When two waves having comparable frequencies travel within the same medium, then the resultant is variable for variable points due to their superposition as well as their intensities. This point is often negligible and this is known as destructive interference. 

In the case of constructive interference, the necessary condition is that the frequencies of the two interfering waves must be the same and the crest of one of the superposing waves must overlap with another wave’s crest. In constructive interference, a similar phenomenon should also happen in the case of the trough of the two interfering waves. On the other hand in the case of destructive interference, the necessary condition states that the frequencies of the two superposing waves must be the same. Moreover, the one wave’s crest must overlap with the trough of another wave. A similar phenomenon should occur with the first wave’s trough and the second wave’s crest. Lastly, constructive interference happens only when 1st and 2nd waves have a phase difference between them. This phase difference must be an even multiple of the value of π. On the other hand when the phase difference between 1st and 2nd wave is an odd multiple of the value of π then destructive interference is seen to occur. 

Mathematically the conditions for destructive interference can be given as follows.

Difference in phase = π(2n – 1)

Difference in phase = λ/2 * (2n – 1)

For destructive interference, I = Imin = I2 + I1 – 2√ I2 I1 = (√ I2  – √ I1)2

Conclusion

The overall article has been written to identify the key conditions of destructive interference. Destructive interference is a vital topic in the UPSC exams and has immense importance in the subject of Physics and chemistry. To discuss every aspect of the topic, firstly the destructive interference equation has been discussed, followed by identifying the conditions for interference. Lastly, the Conditions for destructive interference have been provided.