A Study to Understand the Condition for Constructive Interference

The interference of light is a natural phenomenon observed almost everywhere. A pair of light waves pass over each other and create interference. Interference typically takes place in electromagnetic waves, and the most obvious example of interference is seen in light. Optical interference is responsible for the formation of rainbows, or even the visibility of various colours in a soap bubble.

Interference of light refers to the superimposition of waves to form a resultant wave, which can be of the higher, lower, or the same amplitude. Amplitude is the height of the wave. When two light waves form a superimposed wave of higher amplitude, the phenomenon is called constructive interference.

Constructive Interference

When two crests or troughs of a wave align with each other to give a resultant amplitude that is higher, it is called constructive interference. Typically, it is the sum of the individual amplitudes of the waves. Such waves are said to be in phase, which means their phase difference is 0, or an even multiple of π.

The effects of constructive interference between two waves with the same amplitude and frequency (ω) can be described by these equations:

 y1 = cos (kx – ωt) and y2 = cos (kx – ωt + 𝛅)

where δ is the phase difference between the waves,
k is the wavenumber,
x is the wave position,
and t is time.

Sources of Constructive Interference

Light waves are randomly generated by most sources. This is why for examples like soap bubbles or rainbows, you won’t observe a constant interference resulting in the colours. This usually means that the sources of light yielding these interferences do not have a constant amplitude, or frequency, or are not aligned in the same phase.

Basically, the source can be emitting light in all directions and may have a starting maxima, minima or any point in the middle. There is no determining way of predicting the phase that these waves begin with. Such sources are incoherent sources of light.

In contrast, when a source of light has the same phase, frequency or amplitude, it is said to be a coherent course of light. Examples are lasers or any other focused beams of light.

Conditions for the interference of light

To obtain a light interference pattern that is sustained or retained, the following conditions must be met:

1. The light source must be coherent and in the same state of polarisation.
2. The amplitudes and intensities of the light sources should be equal. This will ensure there is sufficient contrast between the maxima and minima of the interference pattern.
3. The light source must be monochromatic and a point source. For example, lasers.
4. The sources of light must be near enough to produce clear and sharp fringes.
5. The source and screen should be far enough to produce wide but sharp fringes.

Experiment to understand the conditions for constructive interference

Thomas Young, in 1801, performed the double-slit experiment which helped understand the interference of light. This experiment helped prove the wave nature of light.

By proving that light also moved as waves, Young successfully established that like all electromagnetic waves, light also underwent interference of light when two light waves passed over each other. 

He used one source of light, the sun, but passed it through two small openings or holes small enough that they could be called slits. This ensured that clear and sharp fringes of light are produced and that the source of light would now be coherent. A single source of light also ensured that it was monochromatic. This way, he observed an interference pattern on the screen, depending on whether the light waves were crest to crest or crest to trough, i.e., same phase or opposite phase, respectively.

Let us consider the plane light waves arrive at a barrier that contains two parallel slits, S1 and S2. These two slots serve as a pair of coherent light sources because waves emerging from them originate from the same wavefront, and therefore maintain a same-phase relationship. The light from S1 and S2 produces a visible pattern of bright and dark parallel bands called fringes on the screen. When the light from S1 and S2 arrive in the same phase, constructive interference takes place, making a bright fringe appear.

A dark fringe signals opposite phases of source waves, and destructive interference.

Conclusion 

Constructive interference of light is when two waves of light arrive in the same phase. It results in the formation of a wave that has a higher amplitude than the source waves. Typically, the resultant amplitude is a sum of individual amplitudes of source waves. 

For obtaining a bright fringe, which is the result of constructive interference, certain conditions are required which we have studied in detail. Young’s double-slit experiment was used to obtain the conditions required to obtain constructive interference.