Wave optics is a branch of physics that studies various phenomena such as interference, diffraction, and polarization. It involves the behavior of light and its interaction with different mediums, leading to studying wavefronts, waves normal, coherent and incoherent sources, and other related concepts.
In this article, we will have a comprehensive study of Wave Optics, including its theories, concepts, and more.
What is Wave Optics?
Wave optics, also known as physical optics, is a branch of optics that deals with studying various phenomena such as interference, diffraction, and polarization, among others, where the ray approximation of geometric optics is not valid. It involves treating light as an electromagnetic wave and using wave theory to explain the behavior of light.
Wave Optic Theories
The wave theory of light has a long history, dating back to the 17th century. In the 1670s, Dutch physicist Christiaan Huygens proposed that light was a wave motion, and he developed the principle of wavefronts and secondary wavelets to explain the behavior of light.
However, the wave theory faced opposition from the corpuscular theory of light, which was supported by Isaac Newton. Newton’s theory proposed that light was composed of small particles called corpuscles that traveled in a straight line and interacted with the external environment. Newton conducted experiments to explain light’s reflection, refraction, and rectilinear propagation. However, his corpuscular theory could not explain diffraction, which is a typical wave property.
Huygens’ Wave Theory
Huygens’ wave theory of light is a fundamental concept in wave optics that explains the behavior of light as a wave motion. According to Huygens’ principle, every point in a wavefront is a source of wavelets, and these wavelets combine to produce a new wavefront that propagates through the transmission medium.
Huygens’ wave theory can explain various phenomena such as reflection, refraction, diffraction, and interference of light. However, Huygens’ wave theory also has some limitations. Which include:
- Huygens’ wave theory cannot explain the photoelectric effect. This phenomenon can only be explained by the particle nature of light.
- The polarization of light is also one of the phenomena that Huygen’s wave theory failed to explain.
- The theory was able to explain some aspects of diffraction. Still, it could not explain it fully as Newton’s corpuscular theory does.
- It could not explain the wave-particle duality of light, which is a fundamental principle of quantum mechanics.
Read More, Huygens’s Wave Theory
Maxwell Electromagnetic Theory
In 1864, James Clerk Maxwell proposed that light is an electromagnetic wave in its electromagnetic theory. The theory means that light consists of electric and magnetic fields. It states that light has a transverse nature and finite speed, which is as follows:
C = 1/√(μ₀ × ε₀) = 3 x 108 m/s
- μo is Permeability = 4π x 10-7
- εo is Permittivity = 8.854 x 10-12
Wavefront and Wave Normal
Wavefront and wavenormal are two important feature of a wave. The detailed explanation of each of them is given below:
What is Wavefront?
A wavefront is an imaginary surface representing a wave’s corresponding points that vibrate in the same phase. It is the set of all locations in a medium where the wave is at the same phase. Wavefront are classified into three types:
Spherical Wavefront
A spherical wavefront is produced when a light source is far from the observer. The wavefronts are spherical surfaces that expand with the wave.
The amplitude of a spherical wavefront decreases as the distance from the source increases.
A ∝ 1/r
The intensity of a spherical wavefront is inversely proportional to the square of the distance from the source.
I ∝ 1/r2
Cylindrical Wavefront
A cylindrical wavefront is formed when the source of light is linear in shape.
The amplitude of a cylindrical wavefront remains constant along the length of the cylinder and is inversely proportional to the square root of the distance from the source.
A ∝ 1/√r
The intensity of a cylindrical wavefront is inversely proportional to the distance from the source.
I ∝ 1/r
Plane Wavefront
A plane wavefront is formed when the light rays are coming from a very distant object. These wavefronts are perpendicular to the direction of propagation.
The amplitude of a plane wavefront remains constant along the wavefront. The intensity of a plane wavefront is constant along the wavefront and does not change with the change in distance from the source.
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What is Wave Normal?
Wave normal is a unit vector that is perpendicular to an equiphase surface of a wave and has its positive direction on the same side of the surface as the direction of propagation.
Wave normal is a vector that points in the direction of the wave’s energy flow and describes the direction of wave propagation in a medium.
In optics, the direction of wave propagation is often described using the wave vector, which is a vector that points in the direction of wave propagation and has a magnitude equal to the wave’s wavenumber.
Coherent and Incoherent Sources
Coherent and incoherent sources refer to the characteristics of light waves emitted by different sources.
Coherent Sources
A coherent source emits light waves with the same frequency, wavelength, and phase or with a constant phase difference. Light from a coherent source forms sustained interference patterns when the waves superimpose.
Examples of coherent sources include lasers and sound waves produced by speakers driven by electrical signals with the same frequency.
Read More, Coherent Sources
Incoherent Sources
An incoherent source emits light waves with different frequencies, wavelengths, and phases. Light from incoherent sources has frequent and random phase changes between the photons.
Examples of incoherent sources include tungsten filament lamps and ordinary fluorescent tubes emitting incoherent light.
Read More, Incoherent Sources
Interference of Light
Interference of light is a phenomenon where multiple light waves interact with one another under certain circumstances, causing the combined amplitudes of the waves to either increase or decrease.
Interference can be observed in both coherent and incoherent sources of light. However, the interference patterns are more pronounced in coherent sources, which emit light waves with the same frequency, wavelength, and phase.
The tabular representation of important formulas used in wave optics is illustrated below:
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Wave Equation Formula: The speed of light (c) is equal to the product of wavelength (λ) and frequency (f).
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c = λf
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Young’s Double Slit Interference Formula: Determines the distance between the central maximum and the nth bright fringe in a double-slit experiment.
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y = nDλ/d
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Diffraction Grating Formula: Determines the angles (θ) at which constructive interference occurs for a diffraction grating.
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mλ = dsinθ
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Snell’s Law Formula: Describes the relationship between the angles of incidence and refraction in two different media.
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n1sinθ1 = n2sinθ2
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Polarization Formula: Intensity (I) of polarized light after passing through an analyzer at an angle (θ).
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I = I0cos2θ
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Diffraction of Light
Diffraction of light is a phenomenon where light waves bend around corners or pass through an aperture and spread out. This bending is known as diffraction. The diffraction of light can be observed in various situations, such as when light passes through a narrow slit or aperture or when it reflects on a thin film of oil on water or off the surfaces of a soap bubble.
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Refraction of Light
Refraction in wave optics is the change in direction and phase velocity of a wave due to a change in the medium it is passing through. The most common way to observe this phenomenon is when a wave passes from one medium to another at any angle.
Refraction is described by Snell’s law, which states that the ratio of the sines of the angle of incidence and angle of refraction is equivalent to the ratio or, equivalently, to the inverse relationship between the two indices of refraction.
Read More, Refraction of Light
Reflection of Light
Reflection in wave optics is the change in the direction of a wavefront at an interface between two different media so that the wavefront returns to the medium from which it originated. This phenomenon is observed in various waves, such as light, sound, and water waves.
The law of reflection states that for specular reflection (e.g., at a mirror), the angle at which the wave approaches the surface is equal to the angle at which it is reflected.
Reflection is important in various fields, such as acoustics, which causes echoes and is used in sonar. It is also significant in the study of seismic waves in geology. It is observed with surface waves in bodies of water.
Also Check, Reflection of Light
Polarization of Light
Polarization is a property of waves that describes the orientation of the oscillations of the wave. In the case of light waves, polarization refers to the direction of the electric field vector of the wave.
Linear Polarization, Circular Polarization, and Elliptical Polarization are different ways in which light waves can be polarized. Polarization can be affected by passing light through polarizing filters or by reflection from certain surfaces.
Polarization is important in various areas of science and technology, including seismology, optics, radio, and microwaves.
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Wave Theory Frequently Asked Questions
What is Principle of Wave Optics?
The basic principle of wave optics is the modified Huygens principle, also known as the Huygens-Fresnel principle which states that every point on the wavefront may be considered a source of secondary spherical wavelets which spread out in the forward direction at the speed of light.
What is Optical Wave Theory?
The optical wave theory of light is a model that explains reflection and refraction. Wave optics is a branch of physics that studies the wave nature of light and how it interacts with matte
What is Ray Optics and Wave Optics?
Ray optics is based on rectilinear propagation of light, and deals with mirrors, lenses, reflection, refraction, etc. Wave optics is based on the behavior of light and its interaction with different mediums, leading to studying wavefronts, waves normal, coherent and incoherent sources, and other related concepts.
Who Proposed Wave Theory of Light?
Dutch physicist Christiaan Huygens proposed the wave theory of light in the 1670s.
What are Differences Between Coherent and Incoherent Sources of Light?
Coherent sources emit light waves with the same frequency, wavelength, and phase. In contrast, incoherent sources have different frequencies, wavelengths, and phases.
What is Interference of Light?
Interference is the phenomenon where light waves interact, causing combined amplitudes to increase or decrease.
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