Coherent and Incoherent Addition of Waves: Definition, Differences

There are two kinds of sources of lights: Coherent and incoherent. Coherent waves are those which have the same fequency and zero or constant phase difference. Incoherent waves have random frequencies and phase differences. Addition of waves dealt with the interference patterns that are created by the superposition of two waves.

Key Takeaways: Coherent Light Waves, Coherent Sources, Temporal Coherence, Spatial Coherence, Incoherent Sources, Scattering of Light Waves, Light, Radiation

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Coherent Light Waves

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Coherent light is light where the beam occurs for all the photons at the same time. There will be no sudden change in the phase within the beam. For example, the light produced by the laser is both coherent and monochromatic.

Coherence can be defined as a set relationship between the phases of waves during a beam of radiation of one frequency. Two light beams can be called coherent if the phase distinction between their waves is constant; they're noncoherent if there's a random or dynamic phase relationship. Radiation from coherent sources are responsible for stable interference patterns which are produced when a single beam of light gets separated into two or more beams of light.

For example, a laser, in contrast to an incandescent source of light, produces a beam where all the parts bear a set relationship with each other.

Coherence can also be defined as a property that allows waves to have stationary interference. Apart from that,the number of coherence is sometimes measured by interference visibility. As an example, two parallel slits lighted by a ray are classified as two coherent point sources.

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Characteristics of Coherent Sources

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• The waves generated have a constant phase distinction.
• The waves are of one frequency.
• The waves ought to have identical amplitude.

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Types of Coherence

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Coherent sources can be classified into following categories - 

Temporal Coherence

• Temporal coherence is a measure of the relationship between the value of a wave and itself creating a delay of _T at any wide combination of times.
• Measurement of how monochromatic a particular source is carried out using temporal coherence. This includes determining how well a wave can interfere with itself at a distinct time.
• The delay by a phase or amplitude which ought to be by a substantial amount is known as the coherence time.

Spatial Coherence

• In case of systems like optics or water waves, the dimension of the wave extends from one or two spaces.
• Spatial coherence is known as the ability of two points denoted by x1 and x2 within the area of a wave that may interfere. 
• Thus in simple words, it can be defined as cross-relation between two points during a wave at any given time.
• When a wave possesses a single amplitude value over an infinite length, we can say that it has a perfect spatial coherence.

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Examples of Coherent sources

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• Sound waves generated from speakers are driven by electrical signals and have a constant frequency.
• Lasers are normally used as coherent sources as it makes use of a mechanism known as stimulated emission to get extremely coherent light.
• Small sources of sunshine are partially coherent due to which we can observe interference patterns on soap bubbles and appreciate the brightness of butterfly wings.

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Incoherent Sources

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Incoherent light is a type of light source where there is a frequent and random change in the phase between the photons. For example, conventional light sources such as night bulbs, fluorescent tubes and metal filament lamps produce incoherent lightweight waves. All standard sources are incoherent sources. We don't get an interference pattern with incoherent sources of waves.

Consider two waves that are emitted from two sources of intensities I₁ and I₂. The intensity of these two waves is, I = I₁ + I₂

Difference between Coherent and Incoherent Light Waves 

• Coherent light waves are usually stronger compared to the incoherent source of light waves. 
• Furthermore, coherent light waves are unidirectional and Incoherent light waves are Omni-directional.

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Scattering of Light Waves

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When a light wave confronts a matter, it diverges from its straight path and digresses into different directions. This phenomenon is termed as scattering of light waves. All molecules of matter scatter light. Scattering is often classified as coherent and incoherent based on phase delays of waves.

The scattering of the wave is found to be coherent and constructive if the phase delay is the same for all scattered waves. If the phase delay is varying uniformly from 0 to 2 π, then it is said to be coherent and damaging. If it varies in random, then it's incoherent. Coherent scattering happens in one or a number of directions. Coherent damaging scattering happens in all alternative directions.

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Things to Remember

• There are two kinds of sources of lights: Coherent and incoherent.
• Coherent waves are those which have the same fequency and zero or constant phase difference. Incoherent waves have random frequencies and phase differences.
• Characteristics of Coherent Sources: The waves generated have a constant phase distinction. The waves are of one frequency.
• Coherent sources can be classified into following categories -  Temporal Coherence and Spatial Coherence
• Incoherent light is a type of light source where there is a frequent and random change in the phase between the photons. For example, conventional light sources such as night bulbs.
• Coherent light waves are usually stronger compared to the incoherent source of light waves. 

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Previous Year Questions

1. Unpolarized light of intensity I is incident on a system of two polarizers, A followed by B…? [JEE Mains 2018]
2. Light of wavelength 550nm falls normally on a slit of width 22.0×10⁻⁵cm. The angular position…? [JEE Mains 2018]
3. In an interference experiment, the ratio of amplitudes of coherent waves is…? [JEE Mains 2019]
4. Diameter of the objective lens of a telescope is 250cm. For light of wavelength 600nm…? [JEE Mains 2019]
5. An observer is moving with half the speed of light towards a stationary microwave source…? [JEE Mains 2017]
6. A plane polarized light is incident on a polariser with its pass axis making angle ‘a’ with x-axis…? [JEE Mains 2018]
7. Two light sources are said to be coherent if they are obtained from … [VITEEE 2010]
8. The Brewsters angle … [NEET 2020]
9. A linear aperture whose width is … [NEET 2016]
10. At the first minimum adjacent to the central maximum of single-slit diffraction … [NEET 2015]
11. In a diffraction pattern due to a single slit of width 'a' … ​[NEET 2016]
12. In a Young' double slit experiment … ​[NEET 2019]
13. In the Young's double slit experiment, the intensity of light … ​[NEET 2014]
14. In Young's double slit experiment, the slits are 2mm apart … ​[NEET 2013]
15. Young's double slit experment is first performed in air … [NEET 2017]
16. When the angle of incidence on a material is 60^∘ … ​[KEAM]
17. The ratio of the intensities of two waves is 16 : 9 … [KEAM]
18. A monochromatic source of wavelength 60nm … [KEAM]
19. A narrow slit of width 2mm … [KEAM]
20. A slit of width a is illuminated by red light of wavelength … [KEAM]

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