1. Dr. Vishal Jain will be giving a lecture series on engineering physics covering topics such as wave optics and interference.
2. The document discusses the principles of wave optics including interference, diffraction, polarization and introduces the Michelson interferometer.
3. Examples of how the Michelson interferometer can be used to measure wavelength and the difference between two nearby wavelengths are shown through problems and solutions.
The document provides an overview of lasers, including their introduction, characteristics, population inversion, types of coherence, and applications. It discusses key laser concepts such as spontaneous emission, stimulated emission, optical pumping, threshold inversion density, and optical feedback. Examples of specific laser types are given, including ruby lasers, HeNe lasers, and semiconductor lasers. The document concludes with applications of lasers in areas like welding, medicine, data storage, printing, and military weapons.
1. The document discusses various theories of light propagation including Newton's corpuscular theory, Huygens' wave theory, Maxwell's electromagnetic wave theory, Einstein's quantum theory, and de Broglie's dual theory of light. It explains the key aspects of each theory and whether they can explain various optical phenomena.
2. Topics covered include the nature of light waves, wave fronts, interference and diffraction of light waves, types of interference (constructive and destructive), and Young's double-slit experiment. Key findings of the double-slit experiment are summarized such as the formation of bright and dark interference fringes on the screen.
3. Formulas for path difference, phase difference, resultant amplitude
This document provides an overview of Planck's quantum theory and the photoelectric effect. It begins by outlining the key learning outcomes for understanding Planck's quantum theory, which distinguished energy of electromagnetic radiation as quantized rather than continuous. It then describes the photoelectric effect and defines important concepts like work function and stopping potential. Finally, it presents Einstein's explanation of the photoelectric effect using photon energy and provides examples demonstrating how to use the photoelectric equations.
Polarized light occurs when light vibrations are restricted to a single plane. There are three main types of polarized light: linear, elliptical, and circular polarization. Polarization can be produced through dichroism, double reflection, scattering, and reflection. Polarization has many applications including sunglasses, 3D movies, mineral identification, astronomy, communication technologies, and ophthalmic instruments. Polarizers and analyzers are used to produce and detect polarized light. Laws like Malus' law and Brewster's law describe the behavior of polarized light.
Laser is a device that emits light through a process of optical amplification based on the stimulated emission of electromagnetic radiation. It differs from other sources of light in that it emits light coherently, which allows for a high intensity beam with low divergence. The key components are an amplifying medium that can be pumped to invert a population of atoms or molecules to higher energy levels, and an optical resonator formed by two or more mirrors to provide feedback of the light emitted from the amplifying medium. When the population inversion condition is achieved, stimulated emission produces a cascade of photons with the same phase and wavelength.
This document summarizes an experiment on interference fringes using a sodium lamp as a monochromatic light source. Rays from the source were reflected through a plano convex lens and formed circular interference patterns known as Newton's rings on the glass surface. The width of the fringes could be measured using a traveling microscope and used to calculate the wavelength of light from the sodium lamp through a formula accounting for the air gap between the lens and glass surface. The circular fringes resulted from the plano-convex lens shaping the light waves into concentric rings.
This document discusses blackbody radiation and the laws that describe it. It defines a blackbody as an ideal absorber of all incident radiation. It then explains the four main blackbody radiation laws: 1) The Rayleigh-Jeans law applies to long wavelengths but fails at short wavelengths, 2) The Planck law provides accurate predictions across all wavelengths, 3) The Wien displacement law describes how the peak wavelength shifts to shorter wavelengths at higher temperatures, and 4) The Stefan-Boltzmann law establishes that total radiation emitted increases with the fourth power of temperature. Real objects can be compared to blackbodies, and the document provides an example application calculating the Earth's surface temperature from its energy balance.
1. Every magnet has two poles, north and south, and magnetic fields are described by field lines that run from the north to the south pole.
2. A current-carrying wire in a magnetic field experiences a force perpendicular to both the current and the magnetic field. Fleming's left hand rule can be used to determine the direction of this force.
3. Charged particles like electrons moving through a magnetic field experience a force perpendicular to their motion, causing them to travel in a circular path. The magnetic field provides the centripetal force.
The document provides an overview of lasers, including their introduction, characteristics, population inversion, types of coherence, and applications. It discusses key laser concepts such as spontaneous emission, stimulated emission, optical pumping, threshold inversion density, and optical feedback. Examples of specific laser types are given, including ruby lasers, HeNe lasers, and semiconductor lasers. The document concludes with applications of lasers in areas like welding, medicine, data storage, printing, and military weapons.
1. The document discusses various theories of light propagation including Newton's corpuscular theory, Huygens' wave theory, Maxwell's electromagnetic wave theory, Einstein's quantum theory, and de Broglie's dual theory of light. It explains the key aspects of each theory and whether they can explain various optical phenomena.
2. Topics covered include the nature of light waves, wave fronts, interference and diffraction of light waves, types of interference (constructive and destructive), and Young's double-slit experiment. Key findings of the double-slit experiment are summarized such as the formation of bright and dark interference fringes on the screen.
3. Formulas for path difference, phase difference, resultant amplitude
This document provides an overview of Planck's quantum theory and the photoelectric effect. It begins by outlining the key learning outcomes for understanding Planck's quantum theory, which distinguished energy of electromagnetic radiation as quantized rather than continuous. It then describes the photoelectric effect and defines important concepts like work function and stopping potential. Finally, it presents Einstein's explanation of the photoelectric effect using photon energy and provides examples demonstrating how to use the photoelectric equations.
Polarized light occurs when light vibrations are restricted to a single plane. There are three main types of polarized light: linear, elliptical, and circular polarization. Polarization can be produced through dichroism, double reflection, scattering, and reflection. Polarization has many applications including sunglasses, 3D movies, mineral identification, astronomy, communication technologies, and ophthalmic instruments. Polarizers and analyzers are used to produce and detect polarized light. Laws like Malus' law and Brewster's law describe the behavior of polarized light.
Laser is a device that emits light through a process of optical amplification based on the stimulated emission of electromagnetic radiation. It differs from other sources of light in that it emits light coherently, which allows for a high intensity beam with low divergence. The key components are an amplifying medium that can be pumped to invert a population of atoms or molecules to higher energy levels, and an optical resonator formed by two or more mirrors to provide feedback of the light emitted from the amplifying medium. When the population inversion condition is achieved, stimulated emission produces a cascade of photons with the same phase and wavelength.
This document summarizes an experiment on interference fringes using a sodium lamp as a monochromatic light source. Rays from the source were reflected through a plano convex lens and formed circular interference patterns known as Newton's rings on the glass surface. The width of the fringes could be measured using a traveling microscope and used to calculate the wavelength of light from the sodium lamp through a formula accounting for the air gap between the lens and glass surface. The circular fringes resulted from the plano-convex lens shaping the light waves into concentric rings.
This document discusses blackbody radiation and the laws that describe it. It defines a blackbody as an ideal absorber of all incident radiation. It then explains the four main blackbody radiation laws: 1) The Rayleigh-Jeans law applies to long wavelengths but fails at short wavelengths, 2) The Planck law provides accurate predictions across all wavelengths, 3) The Wien displacement law describes how the peak wavelength shifts to shorter wavelengths at higher temperatures, and 4) The Stefan-Boltzmann law establishes that total radiation emitted increases with the fourth power of temperature. Real objects can be compared to blackbodies, and the document provides an example application calculating the Earth's surface temperature from its energy balance.
1. Every magnet has two poles, north and south, and magnetic fields are described by field lines that run from the north to the south pole.
2. A current-carrying wire in a magnetic field experiences a force perpendicular to both the current and the magnetic field. Fleming's left hand rule can be used to determine the direction of this force.
3. Charged particles like electrons moving through a magnetic field experience a force perpendicular to their motion, causing them to travel in a circular path. The magnetic field provides the centripetal force.
The Zeeman effect is the splitting of a spectral line into multiple spectral lines when in the presence of a magnetic field. It was first observed in 1896 by Dutch physicist Pieter Zeeman when he placed a sodium flame between magnetic poles and observed the broadening of spectral lines. Zeeman's discovery earned him the 1902 Nobel Prize in Physics. The pattern and amount of splitting provides information about the strength and presence of the magnetic field.
The document summarizes Bohr's atomic model and developments that followed. It discusses:
1) Bohr's postulates that electrons orbit in discrete orbits with angular momentum an integer multiple of Planck's constant and atoms emit photons when electrons jump orbits.
2) Spectral series of hydrogen and critical, excitation, and ionization potentials.
3) Sommerfeld extended Bohr's model to elliptical orbits and relativistic electron mass.
4) Vector atomic model introduced spatial quantization and electron spin, with quantum numbers like orbital and spin to describe electron states.
This document summarizes the use of a mica quaterwaveplate to produce circularly polarized light from plane polarized light. It first explains the theory behind how quaterwaveplates function as uniaxial crystals that introduce a phase difference of π/2 between the ordinary and extraordinary rays. It then describes the experimental procedure which involves passing plane polarized light through a quaterwaveplate and analyzing the emerging light with a rotating analyzer to observe no change in intensity, indicating circular polarization. The document concludes by stating the key result is that a quaterwaveplate converts plane polarized light to circularly polarized light when the optic axis is at 45 degrees to the plane of polarization.
Diffraction is the bending of light around obstacles. Light diffracts through small openings more noticeably than larger openings, producing interference patterns of bright and dark fringes. A double slit experiment demonstrates diffraction through two slits, with light and dark fringes appearing from constructive and destructive interference. Diffraction gratings split light into multiple beams like how light spreads on a CD. Diffraction is used in microscopes and telescopes to resolve images by separating blurred images into distinct ones.
The document discusses the nature of light and how our understanding of it has changed over time. It was originally thought to be a particle (Newton) or a wave (Huygens), but is now understood to have a dual nature, exhibiting both wave-like and particle-like properties. The key wave properties are interference, diffraction, and polarization, while the particle properties are traveling in straight lines, reflection, and refraction. Light can be thought of as packets of energy called photons.
A normally clear substance can appear colorful when found in a very thin layer due to constructive and destructive interference of light waves. When light hits the surface of a thin film, some light is reflected and some passes through, with further reflections and refractions at each boundary. The thickness of the film determines whether light waves interfere constructively or destructively, producing different colors. For example, a soap bubble appears green when the thickness of the soapy water layer is approximately 95.8 nm.
- Diffraction occurs when waves pass through small openings, around obstacles, or by sharp edges. This causes the waves to spread out after passing through the openings.
- A single slit placed between a light source and screen produces a diffraction pattern of alternating bright and dark bands called interference fringes. The spacing and intensity of the fringes depends on the wavelength of light and the width of the slit.
- In single-slit diffraction, each part of the slit acts as a secondary source, and the light interferes depending on the path differences between waves, causing constructive and destructive interference at different angles.
Refraction is the bending of light when passing from one medium to another. It occurs because the speed of light is decreased in denser mediums, causing the light's path to bend toward the normal. Snell's law describes the mathematical relationship between the angle of incidence and angle of refraction, stating that for two mediums, the ratio of sines of the incidence and refraction angles is equal to the ratio of the indexes of refraction. The index of refraction is a number that represents how much a medium slows light down relative to a vacuum.
What is Polarization?
Types of polarized light
Few related terms
Few laws related to polarization
Applications
FOR MORE VISIT: https://tariqalfayad.blogspot.com/
1. Light has both wave and particle properties, though historically there were separate theories proposing one or the other.
2. Thomas Young's double slit experiment provided early evidence of light's wave nature by producing interference patterns. Other experiments like thin film interference and diffraction around obstacles further supported this.
3. Albert Einstein explained the photoelectric effect by proposing light also behaves as discrete packets of energy called photons, providing evidence of its particle nature.
Huygen's principle describes how each point on a wavefront acts as a secondary source of waves, and that the new wavefront is the envelope of these secondary waves. It provides a method for determining the propagation and behavior of light waves. The principle is based on assuming each point on the initial wavefront emits spherical wavelets, and the new wavefront is the envelope of these secondary waves. It can be used to understand phenomena like interference and diffraction of light.
The document discusses interference of light using Michelson's interferometer. It begins with an introduction to light as an electromagnetic wave and the principles of superposition and interference. It then describes Young's double slit experiment and details the construction, working principle and applications of Michelson's interferometer, including determining the wavelength of light and wavelength separation of nearby wavelengths. Examples of problems using the interferometer are given along with solutions. The document provides a comprehensive overview of interference and Michelson's interferometer.
The index of refraction of air is approximately 1. The Brewster's angle θB is given by tanθB = n2/n1.
Plugging in the values given, we get:
tanθB = 1.52/1
θB = arctan(1.52) = 56.3°
Therefore, the Brewster's angle when the glass plate (n2 = 1.52) is in air (n1 = 1) is 56.3°.
This document contains information about a team of 5 students and milestones in quantum physics. It discusses J.J. Thomson's discovery of the electron, Einstein's explanation of the photoelectric effect using the photon model, and key observations about the photoelectric effect that classical physics could not explain but quantum theory could.
- The document discusses the photoelectric effect where ultraviolet (UV) light causes a zinc plate to emit electrons called photoelectrons.
- It describes several experiments where changing the intensity and frequency of the UV light impacts the number and kinetic energy of the emitted photoelectrons.
- Key concepts explained include the work function, which is the minimum energy needed to remove an electron from a metal, and how it differs for different metals. The threshold frequency is the minimum frequency needed to cause photoemission for a given metal.
The document describes an experiment to determine the separation between the plates of a Fabry Perot etalon. It provides background on the Fabry Perot interferometer and the principle of interference in the etalon. The experimental setup involves illuminating the etalon with a laser and measuring the angular diameters of interference fringes observed on a screen. By plotting the order of interference versus the cosine of the fringe angles and determining the slope, the separation between the etalon plates is calculated as approximately 2-3 mm, remaining constant despite varying the screen distance.
1) The document discusses key concepts in optics, including geometrical optics, physical optics, and quantum optics.
2) Geometrical optics deals with light rays and concepts like reflection and refraction. Physical optics examines light as waves and topics such as interference and diffraction. Quantum optics views light as particles.
3) Images formed by a concave mirror depend on the object's location relative to the mirror's center of curvature and focal point. If beyond the center, the image is real, inverted, and smaller.
Polarization is a property of transverse waves where the oscillations occur in one direction rather than randomly in all directions perpendicular to the propagation direction. Unpolarized waves have oscillations in any direction, while linearly polarized waves oscillate in only one direction. Polarization of electromagnetic waves is defined by the electric field. Polarization can occur through selective absorption by materials that preferentially absorb certain oscillation directions, such as Polaroid which absorbs oscillations parallel to its long molecular chains. Many applications rely on polarization, including Polaroid sunglasses, LCD displays, and antennas.
1. Diffraction refers to the bending of light around obstacles or through openings, and results in interference patterns.
2. There are two main types of diffraction: Fresnel diffraction occurs when light passes near an obstacle, while Fraunhofer diffraction occurs when light passes through or around objects and the observation is made far from the obstacle.
3. Diffraction gratings consist of many parallel slits and cause light to diffract into several beams. The angles and intensities of these beams can be determined through analysis of interference from the multiple slits.
This document describes Newton's rings experiment to observe the interference of light. When a plano-convex lens is placed on a glass slide, a thin air film is formed of varying thickness. Circular interference fringes called Newton's rings are seen when monochromatic light is shone on the setup. The rings appear as alternating bright and dark circles whose diameters are used to determine the wavelength of light through mathematical formulas derived from light interference principles.
1. Diffraction refers to the bending of light around the corners of an obstacle or aperture into the region of geometrical shadow.
2. Fraunhofer diffraction occurs when there is a planar wavefront and the observation is at infinity, producing fixed diffraction patterns. Fresnel diffraction involves cylindrical wavefronts and a finite observation distance, producing patterns that change as you propagate downstream.
3. In single-slit diffraction, the intensity at the center maximum is highest, while the principal minima occur when the path difference is equal to odd multiples of half the wavelength. Secondary maxima occur at positions satisfying the condition derived by equating the intensity equation to zero.
The document discusses Michelson's interferometer. It begins by explaining interference and interference fringes. It then describes how Michelson's interferometer works by splitting light into two beams using a beam splitter, sending the beams to mirrors with one fixed and one movable, and recombining the beams to produce an interference pattern. Key applications of Michelson's interferometer include measuring the wavelength of light, measuring small wavelength separations, detecting gravitational waves, and its role in the Michelson-Morley experiment.
The Zeeman effect is the splitting of a spectral line into multiple spectral lines when in the presence of a magnetic field. It was first observed in 1896 by Dutch physicist Pieter Zeeman when he placed a sodium flame between magnetic poles and observed the broadening of spectral lines. Zeeman's discovery earned him the 1902 Nobel Prize in Physics. The pattern and amount of splitting provides information about the strength and presence of the magnetic field.
The document summarizes Bohr's atomic model and developments that followed. It discusses:
1) Bohr's postulates that electrons orbit in discrete orbits with angular momentum an integer multiple of Planck's constant and atoms emit photons when electrons jump orbits.
2) Spectral series of hydrogen and critical, excitation, and ionization potentials.
3) Sommerfeld extended Bohr's model to elliptical orbits and relativistic electron mass.
4) Vector atomic model introduced spatial quantization and electron spin, with quantum numbers like orbital and spin to describe electron states.
This document summarizes the use of a mica quaterwaveplate to produce circularly polarized light from plane polarized light. It first explains the theory behind how quaterwaveplates function as uniaxial crystals that introduce a phase difference of π/2 between the ordinary and extraordinary rays. It then describes the experimental procedure which involves passing plane polarized light through a quaterwaveplate and analyzing the emerging light with a rotating analyzer to observe no change in intensity, indicating circular polarization. The document concludes by stating the key result is that a quaterwaveplate converts plane polarized light to circularly polarized light when the optic axis is at 45 degrees to the plane of polarization.
Diffraction is the bending of light around obstacles. Light diffracts through small openings more noticeably than larger openings, producing interference patterns of bright and dark fringes. A double slit experiment demonstrates diffraction through two slits, with light and dark fringes appearing from constructive and destructive interference. Diffraction gratings split light into multiple beams like how light spreads on a CD. Diffraction is used in microscopes and telescopes to resolve images by separating blurred images into distinct ones.
The document discusses the nature of light and how our understanding of it has changed over time. It was originally thought to be a particle (Newton) or a wave (Huygens), but is now understood to have a dual nature, exhibiting both wave-like and particle-like properties. The key wave properties are interference, diffraction, and polarization, while the particle properties are traveling in straight lines, reflection, and refraction. Light can be thought of as packets of energy called photons.
A normally clear substance can appear colorful when found in a very thin layer due to constructive and destructive interference of light waves. When light hits the surface of a thin film, some light is reflected and some passes through, with further reflections and refractions at each boundary. The thickness of the film determines whether light waves interfere constructively or destructively, producing different colors. For example, a soap bubble appears green when the thickness of the soapy water layer is approximately 95.8 nm.
- Diffraction occurs when waves pass through small openings, around obstacles, or by sharp edges. This causes the waves to spread out after passing through the openings.
- A single slit placed between a light source and screen produces a diffraction pattern of alternating bright and dark bands called interference fringes. The spacing and intensity of the fringes depends on the wavelength of light and the width of the slit.
- In single-slit diffraction, each part of the slit acts as a secondary source, and the light interferes depending on the path differences between waves, causing constructive and destructive interference at different angles.
Refraction is the bending of light when passing from one medium to another. It occurs because the speed of light is decreased in denser mediums, causing the light's path to bend toward the normal. Snell's law describes the mathematical relationship between the angle of incidence and angle of refraction, stating that for two mediums, the ratio of sines of the incidence and refraction angles is equal to the ratio of the indexes of refraction. The index of refraction is a number that represents how much a medium slows light down relative to a vacuum.
What is Polarization?
Types of polarized light
Few related terms
Few laws related to polarization
Applications
FOR MORE VISIT: https://tariqalfayad.blogspot.com/
1. Light has both wave and particle properties, though historically there were separate theories proposing one or the other.
2. Thomas Young's double slit experiment provided early evidence of light's wave nature by producing interference patterns. Other experiments like thin film interference and diffraction around obstacles further supported this.
3. Albert Einstein explained the photoelectric effect by proposing light also behaves as discrete packets of energy called photons, providing evidence of its particle nature.
Huygen's principle describes how each point on a wavefront acts as a secondary source of waves, and that the new wavefront is the envelope of these secondary waves. It provides a method for determining the propagation and behavior of light waves. The principle is based on assuming each point on the initial wavefront emits spherical wavelets, and the new wavefront is the envelope of these secondary waves. It can be used to understand phenomena like interference and diffraction of light.
The document discusses interference of light using Michelson's interferometer. It begins with an introduction to light as an electromagnetic wave and the principles of superposition and interference. It then describes Young's double slit experiment and details the construction, working principle and applications of Michelson's interferometer, including determining the wavelength of light and wavelength separation of nearby wavelengths. Examples of problems using the interferometer are given along with solutions. The document provides a comprehensive overview of interference and Michelson's interferometer.
The index of refraction of air is approximately 1. The Brewster's angle θB is given by tanθB = n2/n1.
Plugging in the values given, we get:
tanθB = 1.52/1
θB = arctan(1.52) = 56.3°
Therefore, the Brewster's angle when the glass plate (n2 = 1.52) is in air (n1 = 1) is 56.3°.
This document contains information about a team of 5 students and milestones in quantum physics. It discusses J.J. Thomson's discovery of the electron, Einstein's explanation of the photoelectric effect using the photon model, and key observations about the photoelectric effect that classical physics could not explain but quantum theory could.
- The document discusses the photoelectric effect where ultraviolet (UV) light causes a zinc plate to emit electrons called photoelectrons.
- It describes several experiments where changing the intensity and frequency of the UV light impacts the number and kinetic energy of the emitted photoelectrons.
- Key concepts explained include the work function, which is the minimum energy needed to remove an electron from a metal, and how it differs for different metals. The threshold frequency is the minimum frequency needed to cause photoemission for a given metal.
The document describes an experiment to determine the separation between the plates of a Fabry Perot etalon. It provides background on the Fabry Perot interferometer and the principle of interference in the etalon. The experimental setup involves illuminating the etalon with a laser and measuring the angular diameters of interference fringes observed on a screen. By plotting the order of interference versus the cosine of the fringe angles and determining the slope, the separation between the etalon plates is calculated as approximately 2-3 mm, remaining constant despite varying the screen distance.
1) The document discusses key concepts in optics, including geometrical optics, physical optics, and quantum optics.
2) Geometrical optics deals with light rays and concepts like reflection and refraction. Physical optics examines light as waves and topics such as interference and diffraction. Quantum optics views light as particles.
3) Images formed by a concave mirror depend on the object's location relative to the mirror's center of curvature and focal point. If beyond the center, the image is real, inverted, and smaller.
Polarization is a property of transverse waves where the oscillations occur in one direction rather than randomly in all directions perpendicular to the propagation direction. Unpolarized waves have oscillations in any direction, while linearly polarized waves oscillate in only one direction. Polarization of electromagnetic waves is defined by the electric field. Polarization can occur through selective absorption by materials that preferentially absorb certain oscillation directions, such as Polaroid which absorbs oscillations parallel to its long molecular chains. Many applications rely on polarization, including Polaroid sunglasses, LCD displays, and antennas.
1. Diffraction refers to the bending of light around obstacles or through openings, and results in interference patterns.
2. There are two main types of diffraction: Fresnel diffraction occurs when light passes near an obstacle, while Fraunhofer diffraction occurs when light passes through or around objects and the observation is made far from the obstacle.
3. Diffraction gratings consist of many parallel slits and cause light to diffract into several beams. The angles and intensities of these beams can be determined through analysis of interference from the multiple slits.
This document describes Newton's rings experiment to observe the interference of light. When a plano-convex lens is placed on a glass slide, a thin air film is formed of varying thickness. Circular interference fringes called Newton's rings are seen when monochromatic light is shone on the setup. The rings appear as alternating bright and dark circles whose diameters are used to determine the wavelength of light through mathematical formulas derived from light interference principles.
1. Diffraction refers to the bending of light around the corners of an obstacle or aperture into the region of geometrical shadow.
2. Fraunhofer diffraction occurs when there is a planar wavefront and the observation is at infinity, producing fixed diffraction patterns. Fresnel diffraction involves cylindrical wavefronts and a finite observation distance, producing patterns that change as you propagate downstream.
3. In single-slit diffraction, the intensity at the center maximum is highest, while the principal minima occur when the path difference is equal to odd multiples of half the wavelength. Secondary maxima occur at positions satisfying the condition derived by equating the intensity equation to zero.
The document discusses Michelson's interferometer. It begins by explaining interference and interference fringes. It then describes how Michelson's interferometer works by splitting light into two beams using a beam splitter, sending the beams to mirrors with one fixed and one movable, and recombining the beams to produce an interference pattern. Key applications of Michelson's interferometer include measuring the wavelength of light, measuring small wavelength separations, detecting gravitational waves, and its role in the Michelson-Morley experiment.
This document discusses interference and diffraction techniques in optics. It describes several methods for obtaining interference patterns, including wavefront splitting using devices like Young's double slits, and amplitude splitting using beam splitters. It then discusses several examples in more detail, including Fresnel's biprism, Lloyd's mirror, Newton's rings, and multiple beam interference in thin films. The key techniques discussed are used to determine the wavelength of light through measurement of fringe widths and distances.
The document describes how to set up and use a Michelson interferometer to study the interference of light waves. Key steps include:
1. Aligning a diode laser, beam splitter, and two mirrors on an optical breadboard to split and recombine the laser light.
2. Using the interference fringes formed to calibrate the sub-micrometer movement of one of the mirrors and determine the laser wavelength.
3. Observing how the contrast of the interference fringes is affected by the path difference between the light beams and their relative plane of polarization.
1. Michelson's interferometer uses a beam splitter to split light into two beams that travel different paths and are recombined, creating interference patterns of light and dark fringes.
2. The document discusses the conditions for constructive and destructive interference for Michelson's interferometer and how changing the orientation of the mirrors or using a glass plate as the beam splitter affects the interference patterns.
3. Methods for using Michelson's interferometer to determine properties are described, such as finding the wavelength of light, measuring differences in wavelengths, and determining the refractive index or thickness of transparent materials.
The blue color of Morpho butterfly wings is due to optical interference, which causes the color to shift with viewing angle. Interference occurs when two coherent light waves superimpose and their amplitudes combine, potentially constructively or destructively. In a thin film between materials with different refractive indices, partial reflection occurs at each interface, and the reflected waves can interfere. For constructive interference producing bright fringes, the optical path difference of the waves must be equal to integer multiples of the wavelength. [/SUMMARY]
Measure the refractive index of air using a Michelson interferometer.UCP
The document describes using a Michelson interferometer to measure the refractive index of air. It begins with introductions on refractive index and how a Michelson interferometer works by splitting and recombining light beams to produce interference patterns. It then details the experimental procedure, which involves counting interference fringe shifts as air pressure is decreased in one beam path. Calculations show this allows determining the refractive index of air as about 0.000192 based on the fringe shifts measured.
Newton's rings are an interference pattern caused when monochromatic light reflects off a spherical surface, like a lens, and an adjacent flat surface, like a glass sheet. This forms a thin air film between the surfaces that varies in thickness. At points of constructive interference, bright rings appear; at points of destructive interference, dark rings appear. The spacing between the rings gets smaller further from the center. The formula for the radius of the nth bright ring is derived from considering the optical path difference between light reflecting off the two surfaces.
This document describes Newton's rings experiment to determine the wavelength of sodium light. When a spherical glass surface is placed on a flat surface, interference patterns of concentric bright and dark rings are formed due to the varying thickness of the air gap between the surfaces. By measuring the diameter of different rings and using the known radius of curvature, the wavelength can be calculated using an interference equation. The experiment involves using a monochromatic light source to illuminate the surfaces and observing the ring patterns under a microscope to measure ring diameters and calculate the wavelength.
This document provides instructions for building and using a Michelson interferometer to precisely measure the wavelength of light. It consists of 3 parts: 1) an overview of how the Michelson interferometer works, 2) technical details of the experimental setup, and 3) a procedure for aligning the mirrors and measuring the wavelength of a He-Ne laser. The goal is to achieve an accuracy of one part in 10,000 by translating one mirror and counting the number of interference fringes that pass a photodiode.
The document summarizes the theory and operation of the Michelson interferometer. It describes how the interferometer uses a beam splitter and two mirrors to split an incoming light beam into two paths that later recombine, creating an interference pattern. Key points covered include the factors that influence the interference patterns observed, such as the coherence and wavelength of the light source. Applications like measuring refractive indices and displacements are also mentioned. Instructions for setting up and using a basic Michelson interferometer in the laboratory are provided.
This document discusses diffraction patterns and polarization of light. It begins by introducing diffraction and showing examples of diffraction patterns from single slits and circular apertures. It then derives the equations for intensity of diffraction patterns from single and double slits. It also discusses the resolution limit of single slits and circular apertures. The document further explains diffraction gratings and Bragg's law. Finally, it covers various methods of polarization including selective absorption, reflection, double refraction, scattering, and optical activity.
This article discusses the basics of Interference phenomenon of light. Young's Double Slit Experiment is discussed to understand the phenomenon of Interference and also to understand the wave behaviour of light. Newton's Ring experiment, Lloyd's Mirror experiment, Fresnel's Biprism experiment are studued here to establish the wave nature of light. Also the bright and the dark fringes and there mathematical expressions are elaborated here in this article.
1. Young's experiment demonstrated interference using a single wavefront that was split into two coherent secondary sources by passing the wavefront through two slits. The overlapping waves from the two slits interfered and produced an interference pattern.
2. Thin film interference occurs when a beam of light is split by reflection and transmission at the interfaces of a thin film. The optical path difference between the reflected and transmitted beams depends on factors like the film thickness and refractive indices, leading to constructive or destructive interference and the appearance of colored fringes.
3. Interferometers like Michelson's use arrangements of mirrors and beamsplitters to split a light beam into two paths that recombine to produce interference patterns, which can
Optical interferometry uses light interference to provide extremely precise measurements. When two light waves are combined, they can produce interference fringes of light and dark bands that contain information about the optical path differences between the waves. Recent advances in lasers, fiber optics, and digital processing have expanded applications of optical interferometry from measuring molecular sizes to diameters of stars.
Paras Sundriyal presented on the topic of interference to Mrs. Ramna Tripathi. They discussed key concepts of interference including coherent sources, conditions for interference, and types of interference like constructive and destructive. Specific experiments were covered like Young's double slit experiment, fringe width, displacement of fringes, Stokes treatment, and Newton's rings experiment using a plano-convex lens and glass plate to form interference patterns. The presentation aimed to provide a clearer understanding of interference beyond the typical syllabus.
Interference diffraction and polarization.pptxbagadeamit1
1) Interference occurs when two waves superpose to form a resultant wave of greater, lower, or equal amplitude. Newton's rings experiment demonstrates interference using a plano-convex lens on a glass plate where concentric bright and dark rings appear.
2) Polarization is when light vibrations are restricted to one plane. It can be produced through reflection, refraction, or double refraction. A diffraction grating uses a series of parallel slits to diffract light into different orders, with the grating equation relating grating spacing to diffraction angle and wavelength.
3) A spectrometer uses a diffraction grating to determine the wavelength of monochromatic light by measuring the diffraction angle of the first order maximum
Mapping WGMs of erbium doped glass microsphere using near-field optical probe...NuioKila
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1. Engineering Physics
Lecture Series
By
Dr.Vishal Jain,
Associate Professor
Department of Physics
Geetanjali Institute of Technical Studies
Udaipur, Rajasthan
Experience =10 Years, Research Publications =25
Unit 1. Wave Optics
2. wave optics, is the branch of optics that studies interference,
diffraction, polarization, and other phenomena for which the ray
approximation of geometric optics is not valid.
3. What is Light?
Light is an electromagnetic radiation refers to visible regions of
electromagnetic spectrum corresponding to the wavelength range of
380nm to 750nm which has transverse vibrations.
4. Basic Definitions
The Wavelength of a sin
wave, λ, can be measured
between any two points with
the same phase, such as
between crests, or troughs, as
shown.
The frequency, f, of a wave is
the number of waves passing a
point in a certain time. We
normally use a time of one
second, so this gives
frequency the unit hertz (Hz),
since one hertz is equal to one
wave per second.
5.
6. Principle of Superposition
“Whenever two or more waves superimpose in a medium, the
total displacement at any point is equal to the vector sum of
individual displacement of waves at that point”
If Y1
, Y2
, Y3
…are different
displacement vector due to the
waves 1,2,3 …acting
separately then according to
the principle of superposition
the resultant displacement is
given by
Y=Y1
+Y2
+Y3
+……
7. INTERFERENCE is the process in which two or more waves
of the same frequency - be it light, sound, or other electromagnetic waves -
either reinforce or cancel each other, the amplitude of the resulting wave being
equal to the sum of the amplitudes of the combining waves.
8.
9. MICHELSON’S INTERFERROMETER
The Michelson interferometer is a common
configuration for optical interferometer and was
invented by Albert Abraham Michelson in 1887.
Using a beam splitter, a light source is split into two
arms.
10. Principle:- The MI works on the principle of division of amplitude.
When the incident beam of light falls on a beam splitter which divided
light wave in two part in different directions. These two light beams
after traveling different optical paths, are superimposed to each other
and due to superposition interferences fringes formed.
11. Construction:- It consists of two highly polished plane mirror M1
and M2
, with
two optically plane glass plate G1
and G2
which are of same material and same
thickness. The mirror M1
and M2
are adjusted in such a way that they are
mutually perpendicular to each other. The plate G1
and G2
are exactly parallel to
each other and placed at 45° to mirror M1
and M2
. Plate G1
is half silvered from
its back while G2
is plane and act as compensating plate. Plate G1
is known as
beam-splitter plate.
The mirror M2
with screw on its back can slightly titled about vertical and
horizontal direction to make it exactly perpendicular to mirror M1
. The mirror M1
can be moved forward or backward with the help of micrometer screw and this
movement can be measured very accurately.
Working: Light from a broad source is made paralied by using a convex lens L.
Light from lens L is made to fall on glass plate G1
which is half silver polished
from its back. This plate divides the incident beam into two light rays by the
partial reflection and partial transmission, known as Beam splitter plate. The
reflected ray travels towards mirror M1
and transmitted ray towards mirror M2
.
These rays after reflection from their respective mirrors meet again at 'O' and
superpose to each other to produce interference fringes. This firings pattern is
observed by using telescope.
12. Functioning of Compensating Plate: In absence of plate G2
the reflected ray passes
the plate G1
twice, whereas the transmitted ray does not passes even once.
Therefore, the optical paths of the two rays are not equal. To equalize this path the
plate G2
which is exactly same as the plate G1
is introduced in path of the ray
proceeding towards mirror M2
that is why this plate is called compensating plate
because it compensate the additional path difference.
Formation of fringes in MI
13.
14.
15. The shape of fringes in MI depends on inclination of mirror M1
and M2
. Circular fringes are
produced with monochromatic light, if the mirror M1
and M2
are perfectly perpendicular to
each other. The virtual image of mirror M2
and the mirror M1
must be parallel. Therefore it is
assumed that an imaginary air film is formed in between mirror M1
and virtual image mirror
M'2
. Therefore, the interference pattern will be obtained due to imaginary air film enclosed
between M1
andM'2
.
From Fig. if the distance M1
and M2
and M'2
is'd', the
distance between S'1
and S'2
will be 2D.
If the light ray coming from two virtual sources
making an angle θ with the normal then the path
difference between the two beams from S1
and S2
will becomes
As one of the ray is reflecting from denser medium
mirror M1, a path change of λ/2 occurs in it. Hence
the effective path difference between them will be
16. If this path difference is equal to an integral number of wavelength λ, the condition for
constructive interference is satisfied. Thus the bright fringe will formed.
If this path difference is equal to an integral number of wavelength (2n±1)λ/2, the condition
for destructive interference is satisfied. Thus the dark fringe will formed.
17. Radius of Fringes
The Condition for maxima and minima in MI is given by
It is clear that on moving away from center the value of angle θ increases and the value of
cos θ decreases hence the order of fringe also decrease so n maximum at center, The
condition for nth dark ring at center is
On moving m number of rings away from the center, the
order of mth
ring will be ( n-m). If mth
ring make an angle
θm
with the axis of telescope then from equation
For maxima For minima
……………Eq 1
……………Eq 2
D
θm
rm
n n-1
n-2
m
n-m
On Subtracting eq 1 and 2
…Eq 3
Here
…Eq 4
18. By eq 3 and 4
This equation gives the radius of mth
ring
……………Eq 5
……………Eq 6
……………Eq 7
……………Eq 8
……………Eq 9
……………Eq 10
19. Applications of MI
(1) Measurement of the wavelength of monochromatic light : The mirror M1
and
M2
adjusted such that circular fringes are formed. For this purpose mirror M1 and
M2 are made exactly perpendicular to each other.
Now set the telescope at the center of fringe and move the mirror M1 in any
direction, number of fringes shifted in field of view of telescope is counted.
Let on moving mirror M1 through x distance number of fringes shifted is N So the
path difference
By using both equations we will calculate wavelength corresponding to distance
and number of fringes shifted through telescope.
(2) Determination of the difference in between two nearby wavelengths :- Suppose
a source has two nearby wavelengths λ1 and λ2. Each wavelength gives rise its own
fringe pattern in MI. By adjusting the position of the mirror M1, aposition will be
found where fringes from both wavelength will coincide and form highly contrast
fringes.
20. So the condition is given by
When a mirror M1
has been moved through a certain distance, the bright fringe due to
wavelength λ1
coincide with dark fringe due to wavelength λ2
and no fringe will be seen.
On further movies mirror M1
the bright fringes again distinct, this is the position where
n1
+m order coincide with n2
+m+1.
So the condition given by
Subtracting eq 2 by eq 1
So by eq 4 and 3
……………Eq 1
……………Eq 2
……………Eq 3
……………Eq 4
21. Problems & Solution
Q.1. In MI 200 fringes cross the field of view when the movable mirror is displaced through
0.05896mm. Calculate the wavelength of the monochromatic light used.
Solution:- Given
N=200
x= 0.05896mm = 0.05896 X 10-3
m
So the wavelength Å
Q.2. The initial and final readings of MI screw are 10.7347 mm and 10.7057mm
respectively, when 100 fringes pass trough the field of view. Calculate the wavelength of
light used.
Solution:- Given
N=100
x=x2
-x1
= 10.7347-107057=0.029mm=0.029 X 10-3
m
So the wavelength
Å
22. Problems & Solution
Q.3. MI is set to form circular fringes with light of wavelength 5000Å. By Changing the path
length of movable mirror slowly, 50 fringes cross the center of view How much path length
has been changed?
Solution:- Given
N=50
λ= 5000 X 10-10
m
So the path length
Q.4. In a Michelson Interferometer, when 200 fringes are shifted, the final reading of the
screw was found to be 5.3675mm. If the wavelength of light was 5.92 X 10-7
m, What was
the critical reading of the screw?
Solution:- Given
N=200
x=x2
-x1
= 5.3675 X10-3
m - ?
and wavelength λ = 5.92 X 10-2
m
So the wavelength
Now initial reading of screw d1
=d2
± x = 5.3675 x 10-3
m + 0.0592 x10-3
m =5.4267 x 10-3
m
23. NEWTONS RING
Newton's rings seen in two plano-convex lenses with their flat surfaces in contact. One surface is
slightly convex, creating the rings. In white light, the rings are rainbow-colored, because the
different wavelengths of each color interfere at different locations.
Newton's rings is a phenomenon
in which an interference pattern is
created by the reflection of light
between two surfaces—a spherical
surface and an adjacent touching
flat surface. It is named for Isaac
Newton, who first studied the effect
in 1717. When viewed with
monochromatic light, Newton's
rings appear as a series of
concentric, alternating bright and
dark rings centered at the point of
contact between the two surfaces.
26. Theory Explanation
When a Plano convex lens of long focal length is placed in contact on a plane glass
plate (Figure given below), a thin air film is enclosed between the upper surface of
the glass plate and the lower surface of the lens. The thickness of the air film is
almost zero at the point of contact O and gradually increases as one proceeds
towards the periphery of the lens. Thus points where the thickness of air film is
constant, will lie on a circle with O as center.
By means of a sheet of glass G, a parallel beam of monochromatic light is
reflected towards the lens L. Consider a ray of monochromatic light that strikes the
upper surface of the air film nearly along normal. The ray is partly reflected and
partly refracted as shown in the figure. The ray refracted in the air film is also
reflected partly at the lower surface of the film. The two reflected rays, i.e. produced
at the upper and lower surface of the film, are coherent and interfere constructively
or destructively. When the light reflected upwards is observed through microscope
M which is focused on the glass plate, series of dark and bright rings are seen with
center as O. These concentric rings are known as " Newton's Rings ".
At the point of contact of the lens and the glass plate, the thickness of the film is
effectively zero but due to reflection at the lower surface of air film from denser
medium, an additional path of λ/2 is introduced. Consequently, the center of Newton
rings is dark due to destructive interference.
27.
28.
29. Diffraction of Light
Diffraction refers to various phenomena that occur when a wave
encounters an obstacle or a slit. It is defined as the bending of light
around the corners of an obstacle or aperture into the region of
geometrical shadow of the obstacle.
Diffraction pattern of red
laser beam made on a
plate after passing
through a small circular
aperture in another plate
Thomas Young's sketch of two-slit diffraction, which
he presented to the Royal Society in 1803.
30. Fresnel's Diffraction Fraunhofer diffraction
Cylindrical wave fronts Planar wave fronts
Source of screen at finite distance from the
obstacle
Observation distance is infinite. In practice,
often at focal point of lens.
Move in a way that directly corresponds with
any shift in the object.
Fixed in position
Fresnel diffraction patterns on flat surfaces Fraunhofer diffraction patterns on spherical
surfaces.
Change as we propagate them further
‘downstream’ of the source of scattering
Shape and intensity of a Fraunhofer diffraction
pattern stay constant.
Classification of Diffraction
Diffraction phenomena of light can be divided into two different classes
31. Fraunhofer Diffraction at a Single Slit
Let us consider a slit be rectangular aperture
whose length is large as compared to its
breath. Let a parallel beam of wavelength be
incident normally upon a narrow slit of AB.
And each point of AB send out secondary
wavelets is all direction. The rays proceeding
in the same direction as the incident rays are
focused at point O and which are diffracted at
angle θ are focused at point B. The width of
slit AB is small a.
The path difference between AP and BP is
calculated by draw a perpendicular BK.
According to figure the path difference
the phase difference
……………..
eq 1
……………..
eq 2
32. According to Huygens wave theory each point of slit AB spread out secondary wavelets which
interfere and gives diffraction phenomena. Let n be the secondary wavelets of the wave front
incident on slit AB . The resultant amplitude due to all equal parts of slit AB at the point P can
be determine by the method of vector addition of amplitude. This method is known as
polygon method
For this construct a polygon of vector that magnitude Ao
represent the amplitude of each
wavelets and direction of vector represented the phase of each wavelets
nɸ=δ
δ/2
δ/2 N
A
B
C
δ
2δ
nδ
r
nɸ=δ
A
B
R
R/2
R/2
33. Now a perpendicular CN is draw from the center C of an arc on the line A, which will
divide the amplitude R in two parts
from triangle ACN and BCN
By assuming polygon as a arc of a circle of radius r we can calculate the angle
AC=BC = r so
By putting the values of r
By assuming δ/2 =α=π/λ a sinθ
and the intensity I is given by
34. Intensity distribution by single slit diffraction
Central Maxima
For the central point P on the screen θ = 0 and hence α = 0
Hence intensity at point P will be
Hence intensity at point P will be maximum
Principal Minima
For the principal minima intensity should be zero
Where n = 1, 2, 3,4……
n = 0
35. Secondary Maxima
To find out direction of secondary maxima we
differentiate intensity equation with respect to
α and equivalent to zero
This is the condition for secondary
maximas and can be solved by plotting a
graph between y= tanα and y=α as shown
The point of intersection of two curves gives
the position of secondary maxima. The
positions are α1
= 0, α2
= 1.43π, α3
= 2.46π,
α4
= 3.47π,..
36. Intensity distribution by single slit diffraction
Central
maxima
Secondary
maxima’s
Principal
Minima’s
37. Width of the central maximum
The width of he central maximum can be
derived as the separation between the first
minimum on either side of the central
maximum.
If he first maximum is at distance x from the
central maximum then
x
x
D
f
We know that
From the diagram
θ1
If θ is very small sinθ1
= tanθ1
= θ1
……………..
eq 1
…..eq
2
…..eq
3
…..eq
4
38. Diffraction Grating
A diffraction grating is an arrangement equivalent to a large number of parallel slits of
equal widths and separated from one another by equal opaque spaces.
Construction
Diffraction grating can be made by
drawing a large number of equidistant
and parallel lines on an optically plane
glass plate with the help of a sharp
diamond point. The rulings scatter the
light and are effectively opaque, while
the unruled parts transmit light and act
as slits. The experimental arrangement
of diffraction grating is shown
They are two type refection and
transmission gratings
39. A very large reflecting
diffraction grating
An incandescent light
bulb viewed through a
transmissive diffraction
grating.
40. Theory for transmission grating
(resultant intensity and amplitude)
Let AB be the section of a grating having
width of each slit as a, and b the width of each
opaque space between the slits. The quantity
(a + b) is called grating element, and two
consecutive slits separated by the distance (a
+ b) are called corresponding points.
The schematic ray diagram of grating has
been shown in figure
Let a parallel beam of light of wavelength λ incident normally on the grating using
the theory of single slit & Huygens principle, the amplitude of the wave diffracted at
angle θ by each slit is given by
……………………eq 1
41. Diffraction by n parallel slit at an angle θ is equivalent to N parallel waves of amplitude R
That emitted from each slit s1
, s2
, s3
…..sN
Where α = π/λ (a sinθ), These N parallel waves interfere
and gives diffraction pattern consisting of maxima and minima on the screen.
The path difference between the waves emitted from two consecutive slits given by.
The corresponding Phase Difference
Thus there are N equal waves of equal amplitude and with a increasing phase difference of δ
……………………eq 2
……………………eq 3
……………………eq 4
42. To find the resultant amplitude of these N parallel waves we use the vector polygon method.
Waves from each slit is represented by vectors where its magnitude represented by amplitude
and direction represents the phase.
Thus joining the N vectors tail to tip we get a polygon of N equal sides and the angle between
two consecutive sides is δ
The phase difference between waves from first to last slit is Nδ obtained by drawing the
tangents at A and B
Nδ
Nδ/2
Nδ/2
A
B
C
δ
2δ
Nδ
r
Nδ
A
B
RN
RN
N
43. Diffraction by n parallel slit at an angle θ is equivalent to N parallel waves of amplitude RN.
Consider a triangle ACN and DCN
C
A N D
δ/2 δ/2
R/2 R/2
Since AC=CD we can rewrite
……………………eq 5
In triangle ABC
……………………eq 6
Here
44. So the resultant intensity
……………………eq 7
The above equation gives the resultant intensity of N parallel waves diffracted at an angle θ.
The resultant intensity is the product of two terms
Due to diffraction from each slit
Due to Interference of N slits
Intensity distribution by diffraction Grating
Central Maxima
Hence intensity at point P will be maximum
Principal Minima
Where m = 1, 2, 3,4……
1. Due to Diffraction from Each Slit
45. Secondary Maxima
2. Due to Interference of N slits
Principal Maxima’s
Position of Principal maxima’s obtained when
Where n= 0, 1, 2, 3………..
Then sinNβ is also equal to zero and becomes indeterminate so by using L’ Hosptal
Rule
Hence the intensity of principal maxima is given by
46. Manima’s
The intensity will be minimum when I = 0 i.e. sinNβ = 0 but sinβ ≠ 0
Nβ = ±pπ here p = 1, 2, 3………..(N-1)(N+1)…….(2N-1)(2N+1)…….. i.e. p ≠ N, 2N……
hence
Secondary
Maxima’s
To find out direction of secondary maxima we differentiate intensity equation with respect to
α and equivalent to zero
The solution of the above equation
except p=±nπ gives the position of the
secondary maxima’s
47. Intensity of Secondary Maxima’s
The position of secondary maxima is given by using this equation a
right triangle can be formed as shown
Nβ
(1+N
2 tan
2 β)
1/2
A
B
C
Ntanβ
From figure
As increase in number of slit the
number of secondary maxima also
increases
49. Formation of Spectra with Diffraction Grating
With White
Light
With Monochromatic
Light
50. Characteristics of Grating Spectra
If the angle of diffraction is such that, the minima due to diffraction component in the
intensity distribussion falls at the same position of principal maxima due to interference
component, then the order of principal maxima then absent. If mth
order minima fall on nth
order principal maxima then
Now we consider some cases
A. If b=a, i.e. width of opaque space in equal to width of slit then from equation 3. n = 2m
since m=1, 2, 3 …. Then n = 2nd
, 4th
, 6th
….spectra will be absent
B. If b=2a, i.e. width of opaque space in equal to width of slit then from equation 3. n = 3m
since m=1, 2, 3 …. Then n = 3rd
, 6th
, 9th
….spectra will be absent
1. ABSENT SPECTRA
……………
eq 1
……………
eq 2
……………
eq 3
51. 2. Maximum Number of Order Observed by Grating
Principal maximum in grating spectrum is given by
Maximum possible angle of diffraction is 90 degree therefore
So
Q.1. A plane transmission grating has 6000 lines/cm. Calculate the higher order of spectrum
which can be seen with white light of wavelength 4000 angstrom
Sol. Given a+b=1/6000, Wavelength 4000X 10-8
cm
As we know that gratings equation written as
For maximum order
Maximum order will be 4th
……………..
eq 1
……………..
eq 2
52. 3. Width of principal maxima
The angular width of principal maxima of nth order is defined as the angular separation between
the first two minima lying adjacent to principal maxima on either side
θn
2δθ
n
θn
-
δθn
θn
+δθ
n
A O
If θn
is the position of nth order principal maxima
θn
+δθn,
θn
-δθn
are positions of first minima
adjacent to principal minima then the width of
nth principal maxima = 2δθn
From the Grating Equation nth
order maxima
And the position of minima is given by
Hence equation rewritten as
……………
eq 1
…eq
2
On dividing eq 2 by eq 1
If dθn
is very small than cosdθn
= 1, sindθn
= dθn
53. 4. Dispersive Power of Diffraction Gratings
For a definite order of spectrum, the rate of change of angle of diffraction θ with respect to the
wavelength of light ray is called dispersive power of Grating.
Dispersive Power = dθ/dλ
We know that gratings equation
Also written as
……………..
eq 1
……………..
eq 2
……………..
eq 3
56. Resolving Power
Resolving Power
The ability of an optical instrument to produce two distinct separate images of two objects located very close to
each other is called the resolution power
Limit of resolution
The smallest distance between two object, when images
are seen just as separate is known as limit of resolution
For eye limit of resolution is 1 minutes
Resolution
When two objects or their images are very close to each other they appeared as a one and it not be possible for the
eye to seen them separate. Thus to see two close objects just as separate is called resolution
57. Rayleigh Criterion for Resolution
Lord Rayleigh (1842-1919) a British Physicist proposed a criterion which can manifest
when two object are seen just separate this criterion is called Rayleigh’s Criterion for
Resolution
Well Resolved
Just resolved
Not resolved
58. Resolving power of a telescope
Resolving power of telescope is defined as the reciprocal of the smallest angle sustained
at the object by two distinct closely spaced object points which can be just seen as
separate ones through telescope.
Let a is the diameter of objective telescope as shown in fig and P1
and P2
are the
positions of the central maximum of two images. According to Rayleigh criterion these
two images are said to be separated if the position of central maximum of the second
images coincides with the first minimum or vice versa.
P
1
P
2
A
B
dθ
dθ
dθ
a
The path difference between AP2
and
BP2 is zero and the path difference
between AP1
and BP1
is given by
If dθ is very small sin dθ = dθ
C
For rectangular
aperture
For circular
aperture
……………..
eq 1
………e
q 2
59. Resolving power of a Diffraction Grating
The resolving power of a grating is the ability to separate the spectral lines which are very close to each other.
When two spectral lines in spectrum produced by diffraction grating are just resolved, then in this position the
ratio of the wavelength difference and the mean wave length of spectral lines are called resolution limit of
diffraction Grating
Q
dθ
Let parallel beams of light of wavelength λ and λ+dλ be
incident normally on the diffraction grating. If nth
principal maxima of λ and λ+dλ are formed in the
direction of θn
, θn
+dθn
respectively
For the principal maximum by wavelength λ the gratings
equation written as
for wavelength d λ
θn
λ+dλ
δθn
A
λ P
……………………….....eq 1