An intuitive, deep-dive tutorial into electromagnetic field theory: from vector calculus tools through Maxwell's equations, to electromagnetic waves, skin depth, and the Poynting vector.
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Wave Optics: A Complete
An intuitive deep-dive into wave optics: interference, thin films, Newton's rings, diffraction, diffraction gratings, dispersive power, and resolving power — explained with physics, not just formulas.
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Fiber Optics and Laser
An intuitive deep-dive into fiber optics and laser physics: from total internal reflection and numerical aperture, through stimulated emission and population inversion, to understanding how lasers and optical fibers power modern communication.
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Superconductors and Nano
An intuitive deep-dive into superconductivity and nanotechnology: from zero resistance and the Meissner effect, through Type I/II superconductors, to quantum dots, quantum wells, and fabrication methods like sol-gel and CVD.
Engineering Physics provides the fundamental concepts of modern physics and their applications in engineering and technology. This course covers quantum mechanics, electromagnetic field theory, wave optics, fiber optics, lasers, superconductors, and nanomaterials.
These topics help students understand the physical principles behind modern electronic devices, optical communication systems, laser technology, superconducting materials, and nanoscale engineering.
Unit 1 — Quantum Mechanics
Contact Hours: 9
Quantum mechanics describes the behavior of matter and energy at atomic and subatomic scales. Classical mechanics cannot explain several microscopic phenomena, so quantum theory introduces concepts such as matter waves, wave functions, and probability.
1. Inadequacy of Classical Mechanics
Classical mechanics successfully explains the motion of macroscopic objects but fails to explain several microscopic phenomena.
Important limitations include:
Black body radiation
Photoelectric effect
Compton effect
Atomic spectra
Stability of atoms
Wave-particle duality
These limitations led to the development of quantum mechanics.
2. Planck's Theory of Black Body Radiation
A black body is an ideal body that absorbs and emits radiation at all wavelengths.
According to Planck's quantum hypothesis, energy is emitted or absorbed in discrete packets called quanta.
The energy of a quantum is:
E=hν
where:
E = energy of radiation
h = Planck's constant
ν = frequency of radiation
Thus, energy exchange at the microscopic level is quantized rather than continuous.
3. Compton Effect
The Compton effect is the increase in wavelength of X-rays or other electromagnetic radiation when they are scattered by electrons.
The Compton wavelength shift is:
Δλ=λ′−λ
and
Δλ=mech(1−cosθ)
where:
λ = incident wavelength
λ′ = scattered wavelength
me = electron mass
c = velocity of light
θ = scattering angle
The Compton effect provides strong evidence for the particle nature of electromagnetic radiation.
4. de Broglie Matter Waves
Louis de Broglie proposed that moving particles can exhibit wave-like behavior.
The wavelength associated with a particle is called the de Broglie wavelength:
λ=ph
For a non-relativistic particle:
λ=mvh
where m is the particle mass and v is its velocity.
This concept established the idea of wave-particle duality.
5. Davisson and Germer Experiment
The Davisson-Germer experiment experimentally demonstrated the wave nature of electrons.
Electrons were accelerated and directed toward a nickel crystal. The electrons produced a diffraction pattern, confirming that electrons behave as waves.
The experimental result agreed with the de Broglie relation:
λ=mvh
Therefore, the experiment provided experimental verification of matter waves.
6. Phase Velocity and Group Velocity
The phase velocity is the velocity with which a particular phase of a wave propagates.
vp=kω
where ω is angular frequency and k is the wave number.
The group velocity is the velocity with which the wave packet or information propagates.
vg=dkdω
For matter waves, group velocity is associated with the velocity of the particle.
7. Schrödinger Wave Equations
The Schrödinger equation is the fundamental equation of non-relativistic quantum mechanics.
Time-Dependent Schrödinger Equation
iℏ∂t∂ψ=[−2mℏ2∇2+V]ψ
where:
ψ = wave function
ℏ = reduced Planck's constant
m = particle mass
V = potential energy
Time-Independent Schrödinger Equation
For a stationary state:
−2mℏ2∇2ψ+Vψ=Eψ
or
H^ψ=Eψ
where H^ is the Hamiltonian operator.
8. Physical Interpretation of Wave Function
The wave function ψ itself does not directly represent a measurable physical quantity.
According to Born's interpretation:
∣ψ∣2
represents the probability density of finding the particle at a particular position.
The wave function must satisfy appropriate conditions such as being finite, single-valued, continuous, and normalizable.
The normalization condition is:
∫∣ψ∣2dτ=1
9. Particle in a One-Dimensional Box
Consider a particle confined inside an infinitely deep one-dimensional potential box of width L.
The allowed energy levels are:
En=8mL2n2h2
where:
n=1,2,3,…
The corresponding wave functions are:
ψn(x)=L2sin(Lnπx)
The important result is that the particle can possess only discrete energy values. This phenomenon is called quantization of energy.
Unit 1 Key Points
Planck introduced the quantum concept.
Compton effect demonstrates photon momentum.
de Broglie proposed matter waves.
Davisson-Germer experiment verified electron diffraction.
Schrödinger equation describes quantum states.
∣ψ∣2 represents probability density.
A particle in a box has quantized energy levels.
Unit 2 — Electromagnetic Field Theory
Contact Hours: 8
Electromagnetic field theory describes the relationship between electric fields, magnetic fields, electric charges, and currents. Maxwell's equations provide the mathematical foundation of classical electromagnetism.
1. Stoke's Theorem
Stoke's theorem relates a line integral around a closed path to a surface integral over the surface bounded by that path.
∮CA⋅dl=∫S(∇×A)⋅dS
It is useful for converting integral forms of electromagnetic laws into differential forms.
2. Divergence Theorem
The divergence theorem relates the flux through a closed surface to the volume integral of divergence.
∮SA⋅dS=∫V(∇⋅A)dV
It is particularly useful in deriving differential forms of Gauss's laws.
3. Basic Laws of Electricity and Magnetism
Important electromagnetic laws include:
Gauss's law for electric fields
Gauss's law for magnetism
Ampere's law
Faraday's law of electromagnetic induction
Lorentz force law
The Lorentz force is:
F=q(E+v×B)
4. Continuity Equation for Current Density
The conservation of electric charge leads to the continuity equation:
∇⋅J+∂t∂ρ=0
where:
J = current density
ρ = charge density
This equation states that electric charge cannot be created or destroyed.
5. Displacement Current
Maxwell introduced displacement current to make Ampere's law consistent with charge conservation.
The displacement current density is:
Jd=∂t∂D
where D is electric flux density.
The modified Ampere-Maxwell law is:
∇×H=J+∂t∂D
6. Maxwell's Equations
Maxwell's equations can be written in integral and differential forms.
Gauss's Law for Electricity
∇⋅D=ρ
Integral form:
∮SD⋅dS=Q
Gauss's Law for Magnetism
∇⋅B=0
Integral form:
∮SB⋅dS=0
Faraday's Law
∇×E=−∂t∂B
Ampere-Maxwell Law
∇×H=J+∂t∂D
These four equations form the foundation of classical electromagnetic theory.
7. Maxwell Equations in Vacuum
In vacuum:
ρ=0,J=0
and:
D=ϵ0E
B=μ0H
The electromagnetic wave velocity is:
c=μ0ϵ01
which is equal to the speed of light in vacuum.
8. Maxwell Equations in Conducting Medium
For a conducting medium:
J=σE
where σ is electrical conductivity.
The presence of conductivity causes electromagnetic energy to be dissipated as heat and results in attenuation of electromagnetic waves.
9. Poynting Vector
The Poynting vector represents the electromagnetic energy flow per unit area.
S=E×H
Its direction represents the direction of propagation of electromagnetic energy.
10. Poynting Theorem
Poynting theorem represents conservation of electromagnetic energy.
In differential form:
∇⋅S+J⋅E+∂t∂u=0
where u is electromagnetic energy density.
11. Plane Electromagnetic Waves in Vacuum
Electromagnetic waves consist of oscillating electric and magnetic fields.
For a plane wave:
E⊥B
and both fields are perpendicular to the direction of propagation.
Thus electromagnetic waves are transverse waves.
The relation between electric and magnetic fields in vacuum is:
BE=c
Also:
HE=η0
where η0 is the intrinsic impedance of free space.
12. Electromagnetic Waves in Conducting Medium
When an electromagnetic wave travels through a conducting material, its amplitude decreases with distance.
This attenuation occurs because electromagnetic energy is converted into heat through the conductivity of the medium.
Skin Depth
Skin depth is the distance over which the amplitude of an electromagnetic wave falls to 1/e of its value at the surface.
For a good conductor:
δ=ωμσ2
where:
δ = skin depth
ω = angular frequency
μ = permeability
σ = conductivity
Higher frequency and higher conductivity generally result in smaller skin depth.
Poynting vector represents electromagnetic power flow.
Electromagnetic waves are transverse.
Conducting media produce attenuation and skin effect.
Unit 3 — Wave Optics
Contact Hours: 10
Wave optics explains optical phenomena using the wave nature of light. The major topics include interference, diffraction, thin films, Newton's rings, and diffraction gratings.
1. Coherent Sources
Two sources are coherent when they produce waves having:
The same frequency
A constant phase difference
Coherent sources are essential for obtaining stable interference fringes.
2. Interference of Light
Interference is the redistribution of intensity produced when two or more coherent light waves superpose.
For constructive interference:
Δ=nλ
For destructive interference:
Δ=(n+21)λ
where Δ is the path difference.
3. Interference in Uniform Thin Films
When light falls on a thin transparent film, part of the light is reflected from the upper surface and another part from the lower surface.
The two reflected waves can interfere.
The optical path difference depends on:
Film thickness
Refractive index
Angle of refraction
Phase change on reflection
Thin-film interference is responsible for many colors observed in soap bubbles and oil films.
4. Interference in Wedge-Shaped Films
A wedge-shaped film is formed when two transparent surfaces are inclined at a small angle.
The film thickness gradually changes along the wedge, producing interference fringes.
For an air wedge under suitable conditions, the fringe width is:
β=2θλ
where θ is the wedge angle.
Wedge-shaped films can be used to determine:
Wavelength of light
Thickness of thin sheets
Small angles
5. Necessity of Extended Sources
Extended sources can produce poor or unclear interference patterns because different points of the source may produce different fringe systems.
For clear interference, appropriate coherence conditions and suitable source geometry are required.
6. Newton's Rings
Newton's rings are concentric circular interference fringes produced by interference between light reflected from the upper and lower surfaces of a thin air film between a curved lens and a plane glass plate.
For dark rings in reflected light:
Dn2=4nRλ
where:
Dn = diameter of the nth dark ring
R = radius of curvature
λ = wavelength
Applications of Newton's Rings
Newton's rings can be used to determine:
Wavelength of monochromatic light
Radius of curvature of a lens
Refractive index of a liquid
7. Diffraction
Diffraction is the bending and spreading of waves when they encounter an obstacle or pass through a narrow aperture.
Diffraction becomes significant when the size of the aperture is comparable to the wavelength.
Two major types are:
Fresnel diffraction
Fraunhofer diffraction
8. Fraunhofer Diffraction at a Single Slit
For a single slit of width a, minima occur when:
asinθ=nλ
where:
n=1,2,3,…
The central maximum is wider and more intense than the secondary maxima.
9. Fraunhofer Diffraction at Double Slit
For two slits, interference and diffraction occur simultaneously.
Interference maxima are approximately given by:
dsinθ=nλ
where d is the separation between corresponding points of the two slits.
10. Absent Spectra
In a diffraction grating, some expected spectral orders may be missing because an interference maximum can coincide with a diffraction minimum.
These are called absent spectra or missing orders.
11. Diffraction Grating
A diffraction grating contains a large number of equally spaced parallel slits.
The grating equation is:
dsinθ=nλ
where:
d = grating element
θ = diffraction angle
n = order of spectrum
λ = wavelength
12. Spectra with Grating
A grating separates different wavelengths because each wavelength is diffracted at a different angle.
This makes diffraction gratings useful for spectroscopic analysis.
13. Dispersive Power
Dispersive power indicates the ability of an optical system to separate different wavelengths.
For a grating, angular dispersion is:
dλdθ=dcosθn
Higher dispersion allows wavelengths that are close together to be separated more effectively.
14. Resolving Power
Resolving power represents the ability of an optical instrument to distinguish two closely spaced wavelengths.
For a grating:
R=Δλλ=nN
where:
n = order of spectrum
N = number of illuminated grating lines
15. Rayleigh's Criterion
According to Rayleigh's criterion, two close spectral lines are just resolved when the principal maximum of one diffraction pattern coincides with the first minimum of the other.
This criterion provides a standard method for determining the resolution of optical instruments.
Unit 3 Key Points
Interference requires coherent sources.
Thin films produce interference due to multiple reflections.
Newton's rings are circular interference fringes.
Diffraction occurs due to the wave nature of light.
A diffraction grating separates wavelengths.
Dispersive power measures wavelength separation.
Resolving power measures the ability to distinguish close wavelengths.
Unit 4 — Fiber Optics and Laser
Contact Hours: 9
Fiber optics uses total internal reflection to transmit optical signals through thin fibers. Lasers generate highly directional, coherent, and nearly monochromatic light.
Part A — Fiber Optics
1. Principle of Optical Fiber
An optical fiber is a thin, flexible optical waveguide made primarily from glass or suitable polymeric materials.
It generally consists of:
Core
Cladding
Protective coating
The core has a higher refractive index than the cladding.
Light propagates through the core primarily by total internal reflection.
2. Acceptance Angle
The maximum angle at which light can enter the fiber and still propagate through it by total internal reflection is called the acceptance angle.
For a fiber in air:
NA=sinθa
where θa is the acceptance angle.
3. Numerical Aperture
Numerical aperture represents the light-gathering capability of an optical fiber.
For a step-index fiber in air:
NA=n12−n22
where:
n1 = refractive index of core
n2 = refractive index of cladding
4. Acceptance Cone
The set of directions from which light can enter the fiber and be guided through it forms a cone called the acceptance cone.
Its half-angle is the acceptance angle.
A larger numerical aperture generally means a larger acceptance cone.
5. Step-Index Fiber
In a step-index fiber, the refractive index of the core is approximately constant and changes abruptly at the core-cladding boundary.
It can support multiple modes depending on its dimensions and numerical aperture.
6. Graded-Index Fiber
In a graded-index fiber, the refractive index gradually decreases from the center of the core toward the cladding.
This reduces modal dispersion compared with a typical multimode step-index fiber and can improve bandwidth.
7. Fiber Optic Communication
A basic fiber-optic communication system consists of:
Information source
Optical transmitter
Optical fiber
Optical receiver
Output system
The electrical information is converted into an optical signal, transmitted through the fiber, and converted back into an electrical signal at the receiver.
8. Attenuation
Attenuation is the reduction in optical power as light travels through a fiber.
Major causes include:
Absorption
Rayleigh scattering
Bending losses
Connector and splice losses
Attenuation is commonly expressed in dB/km.
9. Dispersion
Dispersion causes optical pulses to spread as they travel through a fiber.
Major types include:
Material dispersion
Waveguide dispersion
Modal dispersion
Excessive dispersion limits the bandwidth and transmission distance.
10. Applications of Optical Fiber
Optical fibers are used in:
Internet communication
Telephone networks
Cable television
Medical endoscopy
Industrial inspection
Fiber optic sensors
Data centers
High-speed communication systems
Part B — Laser
11. Absorption of Radiation
When an atom in a lower energy state absorbs a photon of suitable energy, it moves to a higher energy state.
The photon energy must satisfy:
hν=E2−E1
12. Spontaneous Emission
An excited atom can return to a lower energy state without external stimulation and emit a photon.
This process is called spontaneous emission.
The emitted photons generally have random phase and direction.
13. Stimulated Emission
When a photon interacts with an excited atom, it can stimulate the atom to emit another photon.
The emitted photon has the same:
Frequency
Phase
Direction
Polarization
as the stimulating photon.
Stimulated emission is the fundamental process responsible for laser amplification.
14. Population Inversion
Normally, more atoms occupy lower energy states than higher energy states.
For laser action, the population of the upper laser level must exceed that of the lower laser level:
N2>N1
This condition is called population inversion.
15. Einstein's Coefficients
Einstein introduced three coefficients to describe radiation processes:
A21 — spontaneous emission
B12 — absorption
B21 — stimulated emission
These coefficients establish the relationship between absorption, spontaneous emission, and stimulated emission.
16. Principle of Laser Action
LASER stands for:
Light Amplification by Stimulated Emission of Radiation.
A laser system generally requires:
Active medium
Pumping mechanism
Population inversion
Optical resonator
The optical resonator usually consists of two mirrors, one highly reflecting and another partially transmitting.
17. Ruby Laser
Ruby laser is a solid-state laser.
Its active medium is a ruby crystal containing chromium ions.
Important features include:
Solid-state active medium
Optical pumping
Three-level laser system
Red laser output
Wavelength approximately 694.3 nm
18. He-Ne Laser
The helium-neon laser is a gas laser containing a mixture of helium and neon gases.
Electrical discharge excites helium atoms, which transfer energy to neon atoms and help produce laser action.
A commonly used He-Ne laser wavelength is:
λ=632.8 nm
19. Applications of Lasers
Lasers are used in:
Optical communication
Medical surgery
Industrial cutting and welding
Barcode scanning
Laser printing
Holography
Measurement systems
Material processing
Scientific research
Unit 4 Key Points
Optical fibers work primarily through total internal reflection.
Step-index and graded-index fibers differ in refractive-index profile.
Attenuation reduces optical power.
Dispersion causes pulse broadening.
Laser action depends on stimulated emission and population inversion.
Ruby is a solid-state laser.
He-Ne is a gas laser.
Unit 5 — Superconductors and Nanomaterials
Contact Hours: 8
This unit introduces superconductivity and nanotechnology. Superconductors exhibit remarkable electrical and magnetic properties, while nanomaterials show size-dependent properties because of their nanoscale dimensions.
Part A — Superconductors
1. Temperature Dependence of Resistivity
A superconductor is a material whose electrical resistance falls dramatically to essentially zero below a characteristic temperature called the critical temperatureTc.
For:
T<Tc
the material enters the superconducting state.
Above Tc, the material behaves as a normal conductor.
2. Meissner Effect
The Meissner effect is the expulsion of magnetic flux from the interior of a superconductor when it is cooled below its critical temperature.
This demonstrates that superconductivity is not simply zero electrical resistance; it also involves a special magnetic state.
3. Critical Magnetic Field
The superconducting state can be destroyed when the applied magnetic field exceeds a critical value.
The temperature dependence of the critical field is commonly represented by:
Hc(T)=Hc(0)[1−(TcT)2]
where:
Hc(0) = critical field at absolute zero
Tc = critical temperature
4. Persistent Current
A current established in a superconducting closed loop can continue for a very long time without measurable resistance.
Such a current is called a persistent current.
This property demonstrates the extremely low electrical resistance of the superconducting state.
5. Type I Superconductors
Type I superconductors generally have a single critical magnetic field.
They show complete Meissner behavior below the critical field and transition relatively abruptly to the normal state.
Examples include:
Mercury
Lead
Tin
6. Type II Superconductors
Type II superconductors have two critical magnetic fields:
Hc1
and
Hc2
Between these fields, the material enters a mixed or vortex state.
Type II superconductors can withstand much stronger magnetic fields and are therefore important for practical applications.
7. High-Temperature Superconductors
High-temperature superconductors have comparatively high critical temperatures.
Many are ceramic materials, such as copper-oxide-based compounds.
Their relatively high transition temperatures make them important for research and technological applications.
8. Properties of Superconductors
Important properties include:
Nearly zero electrical resistance
Meissner effect
Persistent current
Critical temperature
Critical magnetic field
Magnetic flux quantization in appropriate superconducting systems
Strong magnetic-field response
9. Applications of Superconductors
Superconductors are used or investigated in:
MRI systems
Particle accelerators
Superconducting magnets
Magnetic levitation
Quantum technologies
Sensitive magnetic sensors
Power transmission research
High-field scientific instruments
Part B — Nanomaterials
10. Introduction to Nanomaterials
Nanomaterials are materials having at least one characteristic dimension approximately in the nanoscale range, commonly around 1–100 nm.
At this scale, materials can exhibit properties significantly different from their bulk counterparts.
Important reasons include:
Large surface-to-volume ratio
Quantum confinement
Size-dependent optical properties
Size-dependent electrical properties
Enhanced catalytic activity
11. Properties of Nanomaterials
Nanomaterials may exhibit unique:
Mechanical properties
Electrical properties
Optical properties
Magnetic properties
Thermal properties
Chemical properties
For example, reducing particle size can significantly increase the surface area available for chemical reactions.
12. Quantum Dots
Quantum dots are nanoscale semiconductor structures in which charge carriers are confined in three dimensions.
Because of quantum confinement, their optical and electronic properties depend strongly on their size.
Smaller quantum dots generally exhibit larger effective energy gaps and can emit light at different wavelengths.
13. Quantum Wires
Quantum wires are nanoscale structures in which charge carriers are confined in two dimensions and can move primarily along one dimension.
They show quantum-confinement effects and can have unusual electronic and optical properties.
14. Quantum Wells
A quantum well confines charge carriers primarily in one dimension while allowing movement in the other two dimensions.
Quantum wells are widely used in semiconductor devices such as:
Semiconductor lasers
LEDs
High-electron-mobility devices
Photodetectors
15. Fabrication of Nanomaterials
Nanomaterials can be produced using two broad strategies:
Top-Down Approach
The top-down approach starts with bulk material and reduces its dimensions to the nanoscale.
Examples include:
Lithography
Ball milling
Etching
Bottom-Up Approach
The bottom-up approach builds nanostructures from atoms, molecules, or smaller building blocks.
Examples include:
Sol-gel process
Chemical vapor deposition (CVD)
Chemical synthesis
Self-assembly
Important: CVD is generally classified as a bottom-up fabrication technique because nanostructures are formed through chemical reactions and deposition from gaseous precursors.
16. Sol-Gel Method
The sol-gel process is a bottom-up technique used to produce various nanomaterials.
The general process involves:
Precursor→Sol→Gel→Drying→Nanomaterial
It provides good control over composition, particle size, and material structure.
17. Chemical Vapor Deposition
Chemical vapor deposition is a technique in which gaseous precursors react or decompose on a substrate to form a solid material.
CVD is widely used for producing:
Thin films
Nanowires
Carbon nanotubes
Semiconductor structures
Advanced coatings
18. Applications of Nanomaterials
Nanomaterials are used in:
Electronics
Solar cells
Sensors
Drug delivery research
Energy storage
Catalysis
Nanomedicine
Water purification
Coatings
Semiconductor devices
Environmental applications
Unit 5 Key Points
Superconductors exhibit nearly zero electrical resistance below Tc.
The Meissner effect describes magnetic flux expulsion.
Type I and Type II superconductors differ in their magnetic-field behavior.
Nanomaterials have dimensions in the nanoscale range.
Quantum dots provide three-dimensional confinement.
Quantum wires provide two-dimensional confinement.
Quantum wells provide one-dimensional confinement.
Top-down methods reduce bulk materials to nanoscale structures.
Bottom-up methods construct nanostructures from atoms or molecules.
Sol-gel and CVD are commonly used bottom-up techniques.
Important Formula Summary
Quantum Mechanics
E=hν
λ=ph=mvh
Δλ=mech(1−cosθ)
En=8mL2n2h2
∫∣ψ∣2dτ=1
Electromagnetic Field Theory
∇⋅D=ρ
∇⋅B=0
∇×E=−∂t∂B
∇×H=J+∂t∂D
S=E×H
c=μ0ϵ01
δ=ωμσ2
Wave Optics
asinθ=nλ
dsinθ=nλ
R=Δλλ=nN
Dn2=4nRλ
Fiber Optics
NA=n12−n22
NA=sinθa
Superconductivity
Hc(T)=Hc(0)[1−(TcT)2]
Exam-Oriented Learning Strategy
For effective preparation, focus on the following:
Understand the physical meaning of every major concept.
Memorize important definitions and laws.
Practice numerical problems based on the major formulas.
Learn the derivations of important equations.
Draw diagrams for optical fibers, lasers, diffraction, Newton's rings, and superconductors.
Compare related concepts such as phase velocity vs group velocity, interference vs diffraction, step-index vs graded-index fiber, and Type I vs Type II superconductors.
Practice previous-year university questions after completing each unit.
Quick Revision Checklist
Quantum mechanics and matter waves
Compton effect
Davisson-Germer experiment
Schrödinger equations
Particle in a one-dimensional box
Stoke's and divergence theorems
Maxwell's equations
Poynting theorem
Electromagnetic waves
Skin depth
Thin-film interference
Newton's rings
Fraunhofer diffraction
Diffraction grating
Resolving and dispersive power
Optical fiber and numerical aperture
Fiber attenuation and dispersion
Laser action and Einstein coefficients
Ruby and He-Ne lasers
Superconductivity and Meissner effect
Type I and Type II superconductors
Nanomaterials
Quantum dots, wires, and wells
Top-down and bottom-up fabrication
Sol-gel and CVD
Applications of nanomaterials
Instructor
Name: Ankit kushwaha
Email: ankitkushwaha909@gmail.com
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