What Is Destructive Interference
In destructive interference When two light waves superpose with each other in such a way that the crest of one wave coincides with the trough of the second wave, then the amplitude and intensity of the resultant wave become zero.
Some of its effects are:
- two waves cancel the effects of each other.
- Due to a dark fringe is obtained on the screen.
Wave Interference And Spatial Patterns
- When we speak about interference we primarily concernedwith spatial patterns of the combined wave.
- Let us consider inerference pattern between two spherical waves producedby two coherent sources
- coherent means that the sources have the same frequency, and, in our example, oscillate in phase
|One source||Two sources at the same position|
|Two source separated by d =||Two source separated by d = 2|
Constructive Interference Vs Destructive Interference
So, we know that the waves making a big wave is constructive interference whereas two waves canceling each other is destructive interference. The difference between the two types of interference is described in the form of the following graph:
In this graph, we can see that the crest and troughs of the two waves overlap each other. The same scenario is observable when we drop a stone in water, the waves spread in the form of concentric circles, and the point of this overlap is the interference this is for constructive interference.
Now, talking about the destructive interference, another stone is dropped in the vicinity of these already formed concentric circular waves. So, here, the waves of another stone may cancel out the already formed waves. Now, this canceling may produce no effect and thats the point where we get the destructive interference.
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Thomas Young’s Double Slit Experiment
Among the pioneers in early physics was a nineteenth century English scientist named Thomas Young, who convincingly demonstrated the wave-like character of light through the phenomenon of interference using diffraction techniques. Young’s experiments provided evidence in contrast to the popular scientific opinion of the period, which was based on Newton’s corpuscular theory for the nature of light. In addition, he is also responsible for concluding that different colors of light are made from waves having different lengths, and that any color can be obtained by mixing together various quantities of light from only three primary colors: red, green, and blue.
In 1801, Young conducted a classical and often-cited double-slit experiment providing important evidence that visible light has wave-like properties. His experiment was based on the hypothesis that if light were wave-like in nature, then it should behave in a manner similar to ripples or waves on a pond of water. Where two opposing water waves meet, they should react in a specific manner to either reinforce or destroy each other. If the two waves are in step , then they should combine to make a larger wave. In contrast, when two waves meet that are out of step , the waves should cancel and produce a flat surface in that area.
Figure 5 – Thomas Young’s Double Slit Experiment
Figure 6 – Newton’s Ring Experiment
Visibility = – I)/ + I)
Interference Of Light Examples
Interference of light is defined as: When two or more light waves having the same frequency, same wavelength and same amplitude meet together in a medium at a point, they cancel or enhance the effect of each other at that point. This phenomenon is called interference of light waves.There are two types of interference of light:
- Constructive interference
- Destructive interference
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Between Two Plane Waves
A simple form of interference pattern is obtained if two plane waves of the same frequency intersect at an angle.Interference is essentially an energy redistribution process. The energy which is lost at the destructive interference is regained at the constructive interference.One wave is travelling horizontally, and the other is travelling downwards at an angle to the first wave. Assuming that the two waves are in phase at the point B, then the relative phase changes along the x-axis. The phase difference at the point A is given by
It can be seen that the two waves are in phase when
and are half a cycle out of phase when
Constructive interference occurs when the waves are in phase, and destructive interference when they are half a cycle out of phase. Thus, an interference fringe pattern is produced, where the separation of the maxima is
and df is known as the fringe spacing. The fringe spacing increases with increase in wavelength, and with decreasing angle .
The fringes are observed wherever the two waves overlap and the fringe spacing is uniform throughout.
Between Two Spherical Waves
A point source produces a spherical wave. If the light from two point sources overlaps, the interference pattern maps out the way in which the phase difference between the two waves varies in space. This depends on the wavelength and on the separation of the point sources. The figure to the right shows interference between two spherical waves. The wavelength increases from top to bottom, and the distance between the sources increases from left to right.
When the plane of observation is far enough away, the fringe pattern will be a series of almost straight lines, since the waves will then be almost planar.
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Things To Remember Based On Destructive Interference
- Interference is a wave interaction phenomenon, when two waves collide at a point, they cause interference. The two waves cancel out in destructive interference, resulting in decreased amplitude at the point where they meet.
- The largest absolute value of a varying quantity is called amplitude.
- When two stones are put into a pool of water, waves from each source spread out, causing interference where they contact.
- The superposition of two waves with slightly different frequencies but identical amplitudes produce beats.
- The ear’s function is to convert the signals in bouncing air molecules into electrical nerve signals while maintaining as much information as possible in the signals.
- Ships can utilise sound waves to navigate by transmitting sound waves and measuring the time between transmissions and receiving the reflection. This is referred to as sonar.
- Destructive interference is only effective for a short period of time. Where the displacement of the medium is smaller than the displacement of the wave with the maximum amplitude.
What Is The Difference Between Constructive And Destructive Interference
This dynamic interplay of colors derives from the simultaneous reflection of light from both the inside and outside surfaces of the bubble. The two surfaces are very close together , and light reflected from the inner surface interferes both constructively and destructively with light reflected from the outer surface. This is because light reflected from the inner surface of the bubble must travel further than light reflected from the outer surface. When the light waves reflected from the inner and outer surface combine, they will interfere with each other, removing or reinforcing some parts of white light by destructive or constructive interference. This results in color. If the extra distance traveled by the inner light waves is exactly the wavelength of the outer light waves, then they will recombine constructively, and bright colors of those wavelengths will be produced. In places where the waves are out of step, destructive interference will occur, canceling the reflected light .
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Reflection Due To Phase Change
Light exhibits wave characteristics in various media as well as in a vacuum. When light goes from a vacuum to some medium its speed and wavelength change, but its frequency f remains the same. The speed of light in a medium is v = c/n, where n is the index of refraction. For example, water has an index of refraction of n = 1.333. When light is reflected off a medium with a higher index of refraction, crests get reflected as troughs and troughs get reflected as crests. In other words, the wave undergoes a 180 degree change of phase upon reflection, and the reflected ray jumps ahead by half a wavelength.
What Is Diffraction Of Light
The bending of light around corners such that it spreads out and illuminates places is known as diffraction. In general, it’s difficult to distinguish between diffraction and interference since they both happen at the same time. A silver line appears in the sky as sunlight penetrates through or strikes a cloud. This is due to diffraction of sunlight.
Diffraction of Waves
Interference is the phenomenon in which two or more waves collide and superimpose to generate a new wave. The resultant wave may be of larger, lower, or of equal amplitude depending on the nature of the superimposition or alignment of the overlapping waves’ peaks and troughs.
Interference of Light
Interference is a feature caused by waves from two independent coherent sources, whereas Diffraction is caused by secondary wavelets that originate from the same wave but occur in various areas of it. It’s essential to understand the fundamental differences between them by looking at the region of least intensity in interference, this region is extremely dark, but in diffraction, it’s less dark. There are a few other criteria that distinguish diffraction from interference, in addition to these few distinctions which are tabulated below.
Interference pattern of Light
In Physics, the difference between interference and diffraction is well explained in the table above. Let us now distinguish between light interference and diffraction:
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Equation Of Interference In Physics
Constructive Interference: When the phase difference is an even multiple of , then cos /2 =1, so the sum of the two waves is a wave with twice the amplitude.
W1+W2 = 2A cosW1+W2=2A cos
Destructive interference: When the phase difference is an odd multiple of , then cos /2 = 0, so the sum of the two waves will be zero.
The equations for constructive interference are as follows:
y1 = Cos , and
String Instruments And Transverse Standing Waves
In general, the special cases are given by:
The first three harmonics are shown in the following diagram:
When you pluck a guitar string, for example, waves at all sorts of frequencies will bounce back and forth along the string. However, the waves that are NOT at the harmonic frequencies will have reflections that do NOT constructively interfere, so you won’t hear those frequencies. On the other hand, waves at the harmonic frequencies will constructively interfere, and the musical tone generated by plucking the string will be a combination of the different harmonics.
Example – a particular string has a length of 63.0 cm, a mass of 30 g, and has a tension of 87.0 N. What is the fundamental frequency of this string? What is the frequency of the fifth harmonic?
The first step is to calculate the speed of the wave :
The fundamental frequency is then found from the equation:
So the fundamental frequency is 42.74 / = 33.9 Hz.
The second harmonic is double that frequency, and so on, so the fifth harmonic is at a frequency of 5 x 33.9 = 169.5 Hz.
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The Double Slit Experiment
The basic setup of the double-slit experiment is illustrated in Figure 4. Coherent laser light is allowed to illuminate a barrier containing two pinhole apertures that allow only some of the light to pass through. A screen is placed in the region behind the slits, and a pattern of bright red and dark interference bands becomes visible on the screen. The key to this experiment is the mutual coherence between the light diffracted from the two slits at the barrier. Young achieved this coherence through the diffraction of sunlight from the first slit, and we are using a coherent laser source for the purposes of this discussion.
What Is Light Wave Interference
An important characteristic of light waves is their ability, under certain circumstances, to interfere with one another. The definition of interference in physics is the superposition of waves, causing an increase or decrease in the amplitude of the resulting wave. Most people observe some type of optical interference every day, but do not realize what is occurring to produce this phenomenon. One of the best examples of the interference of light is demonstrated by the light reflected from a film of oil floating on water. Another example is the soap bubble illustrated in Figure 1 that reflects a variety of beautiful colors when illuminated by natural or artificial light sources.
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Difference Between Diffraction And Interference
Exams Prep Master| Updated On -Jun 20, 2022
Diffraction is the bending of waves when it is passed through a narrow aperture. Whereas interference is the addition of two waves to result in another wave of similar amplitude. Diffractionand interference occur in all waves. The major difference between diffraction and interference is that in diffraction, secondary waves are formed from different parts of the same wave. Whereas, in interference, waves from different sources are merged together to form a resultant wave.
Key Terms: Diffraction, Interference, Waves, Light, Superimposing of waves, Fringe width, Constructive and Destructive interference
The Principle Of Linear Superposition
The principle of linear superposition applies to any number of waves states that when two or more waves of the same type are incident on the same point, the resultant amplitude at that point is equal to the vector sum of the amplitudes of the individual waves and to simplify matters just consider what happens when two waves come together.
For example, sound reaching you simultaneously from two different sources, or two pulses traveling towards each other along a string. When these waves come together, the result is superimposed waves and they add together, with the amplitude at any point being the addition of the amplitudes of the individual waves at that point. Although these waves interfere with each other when they meet, they continue traveling as if they had never encountered each other.
What Are Interference Fringes
As laser light is diffracted through the two barrier slits, each diffracted wave meets the other in a series of steps, as illustrated in Figure 4 . Sometimes the waves meet in step , sometimes they meet out of step , and sometimes they meet partially in step. When the waves meet in step, they add together owing to constructive interference, and a bright area is displayed on the screen. In areas where the waves meet totally out of step, they will subtract from each other towing to destructive interference, and a dark area will appear in that portion of the screen. The resulting patterns on the screen, a product of interference between the two diffracted beams of laser light, are often referred to as interference fringes.
Other types of experiments have been devised to demonstrate the wave-like nature of light and interference effects. Most notable are the single mirror experiment of Lloyd and the double mirror and biprism experiments devised by Augustin Fresnel. These experiments are described in detail in many of the physics books listed in our bibliography.
Previous Years Questions Based On Destructive Interference
Ques: Write down two conditions in order to obtain the sustained interference fringe pattern of light. State the effect on the interference fringes in Youngs double slit experiment, when monochromatic source is replaced by a source of white light?
Ans: The conditions for sustained interference are:
The two sources of light need to be coherent in order to emit light of constant phase difference.
The amplitude of electric field vector of interfering wave must be identical so that it can have greater contrast between intensity of constructive and destructive interference.
When monochromatic light is replaced by white light, the coloured fringe pattern will be appeared on the screen.
Ques:Write the importance of coherent sources in the phenomenon of interference. In Youngs double slit experiment to produce interference pattern, find out the conditions for constructive and destructive interference. Therefore, deduce the expression for the fringe width. If the entire experimental apparatus of YDSE is immersed in water, how does the fringe width get affected?
Ans: In order to observe interference fringe pattern, there must have coherent sources of light which can produce light of constant phase difference.
Let two coherent sources of light S1 and S2 are derived from a source S. These two slits S1 and S2 are equidistant from source S. now, suppose S1 and S2 are divided by distance d. The slit and screen are distance D apart.
For the constructive interference:
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What Is Constructive Interference
When two light waves superpose with each other in such a way that the crest of one wave falls on the crest of the second wave, and the trough of one wave falls on the trough of the second wave, then the resultant wave has larger amplitude and intensity. Such type of interference is called constructive interference. Some of its effects are:
- In constructive interference, two waves of light reinforce each other.
- In constructive interference, a bright fringe is obtained on the screen.
Introduction To Light Interference
The formation of an image in the microscope relies on the complex interplay between two critical optical phenomena: diffraction and interference. Light passing through the specimen is scattered and diffracted into divergent waves by tiny details and features present in the specimen. Some of the divergent light scattered by the specimen is captured by the objective and focused onto the intermediate image plane, where the superimposed light waves are recombined or summed through the process of interference to produce a magnified image of the specimen.
Figure 1 – Soap Film Interference Patterns
The seemingly close relationship between diffraction and interference occurs because they are actually manifestations of the same physical process and produce ostensibly reciprocal effects. Most of us observe some type of optical interference almost every day, but usually do not realize the events in play behind the often-kaleidoscopic display of color produced when light waves interfere with each other. One of the best examples of interference is demonstrated by the light reflected from a film of oil floating on water. Another example is the thin film of a soap bubble , which reflects a spectrum of beautiful colors when illuminated by natural or artificial light sources.
Figure 2 – Reflected Light Pathways Through Soap Bubbles
Figure 3 – Interference Structures in Butterfly Wings
Figure 4 – Interference Between Coincident Light Waves
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