Undergraduate
  1. Classical mechanics  1.1. dynamics  1.1.1. Motion in one dimension  1.1.2. Motion in two dimensions  1.1.3. projectile motion  1.1.4. Relative speed  1.1.5. Uniform circular motion  1.1.6. Non-uniform circular motion  1.1.7. Reference frames and transformations  1.2. Newton's Laws of Motion  1.2.1. First law of motion  1.2.2. Second law of motion  1.2.3. Third Law of Motion  1.2.4. Applications of Newton's Laws  1.2.5. Friction and its types  1.2.6. Free Body Diagram  1.2.7. Constraints and pseudo-forces  1.3. Work and Energy  1.3.1. work done by the force  1.3.2. Work–energy theorem  1.3.3. Kinetic energy  1.3.4. Potential energy in classical mechanics  1.3.5. Conservative and non-conservative forces  1.3.6. Energy Conservation  1.3.7. Power and efficiency  1.4. Speed and collisions  1.4.1. Linear momentum  1.4.2. Conservation of momentum  1.4.3. Impulse and impact force  1.4.4. Elastic and inelastic collision  1.4.5. Center of mass and speed  1.4.6. Rocket Propulsion  1.5. Rotational motion  1.5.1. Torque and Angular Momentum  1.5.2. Moment of inertia  1.5.3. Rotational Kinematics  1.5.4. Rotational Energy  1.5.5. Rolling Motion  1.5.6. Precession and gyroscopic motion  1.6. Gravitational force  1.6.1. Newton's law of universal gravitation  1.6.2. Gravitational potential energy  1.6.3. Orbital mechanics  1.6.4. Kepler's laws of planetary motion  1.6.5. Gravitational field and potential  1.7. Fluid mechanics  1.7.1. Pressure and Pascal's Principle  1.7.2. Buoyancy and Archimedes' principle  1.7.3. Fluid Dynamics and Bernoulli's Principle  1.7.4. Viscosity and Poiseuille's law  1.7.5. Surface tension and capillarity  1.8. Oscillations and waves  1.8.1. Simple Harmonic Motion  1.8.2. Damped and driven oscillations  1.8.3. Coupled oscillations and common modes  1.8.4. Wave properties and types  1.8.5. Sound Waves and the Doppler Effect  1.8.6. Wave interference and superposition
  2. Electromagnetism  2.1. Electrostatics  2.1.1. Electric charge and properties  2.1.2. Coulomb's law  2.1.3. Electric field and electric potential  2.1.4. Gauss's Law  2.1.5. Capacitance and Dielectric  2.1.6. Electric dipole and potential energy  2.2. Electric circuits  2.2.1. Current and Resistance  2.2.2. Ohm's law  2.2.3. Kirchhoff's Laws  2.2.4. RC Circuit  2.2.5. AC Circuits and Reactance  2.2.6. Electric power and energy  2.3. Magnetism  2.3.1. Magnetic Fields and Forces  2.3.2. Ampere's Law  2.3.3. Magnetic dipole moment  2.3.4. Biot-Savart law  2.3.5. Magnetic Materials and Hysteresis  2.4. Electromagnetic induction  2.4.1. Faraday's Law  2.4.2. Lenz's law  2.4.3. Self and mutual induction  2.4.4. Transformers and Inductive Circuits  2.5. Maxwell's equations  2.5.1. Gauss's law for electricity  2.5.2. Gauss's law for magnetism  2.5.3. Faraday's law of induction  2.5.4. Ampere-Maxwell law  2.5.5. Electromagnetic waves
  3. Thermodynamics  3.1. Laws of Thermodynamics  3.1.1. Zeroth law of thermodynamics  3.1.2. First law of thermodynamics  3.1.3. Second Law  3.1.4. Third Law  3.2. Heat and work  3.2.1. Heat transfer (conduction, convection, radiation)  3.2.2. Thermal expansion  3.2.3. Heat engines and refrigerators  3.2.4. Carnot cycle and efficiency  3.3. Statistical mechanics  3.3.1. Maxwell–Boltzmann distribution  3.3.2. Entropy and Probability  3.3.3. Partition function  3.3.4. Fermi–Dirac and Bose–Einstein statistics
  4. Optics  4.1. Geometrical Optics  4.1.1. Reflection and Refraction  4.1.2. Mirrors and lenses  4.1.3. Optical Instruments  4.1.4. Fermat's principle  4.2. Wave optics  4.2.1. Interference in wave optics  4.2.2. Diffraction  4.2.3. Polarization  4.2.4. Coherence and holography
  5. Quantum mechanics  5.1. Wave–particle duality  5.1.1. Blackbody radiation in wave–particle duality in quantum mechanics  5.1.2. Photoelectric effect  5.1.3. Compton scattering  5.1.4. De Broglie wavelength  5.2. Schrödinger Equation  5.2.1. Time-independent Schrödinger equation  5.2.2. Particle in a box  5.2.3. Quantum Tunneling  5.2.4. Potential wells and obstacles  5.3. Quantum States  5.3.1. Wave function  5.3.2. Quantum operators  5.3.3. Heisenberg uncertainty principle  5.3.4. Angular momentum and spin
  6. Relativity  6.1. Special relativity  6.1.1. Lorentz transformations  6.1.2. Time expansion and length contraction  6.1.3. Relativistic energy and momentum  6.2. General relativity  6.2.1. Principle of Equivalence  6.2.2. Schwarzschild metric  6.2.3. Gravitational waves  6.2.4. Black holes and event horizons
  7. Solid state physics  7.1. Crystal structure  7.1.1. Bravais lattices  7.1.2. X-ray diffraction  7.1.3. Band theory  7.1.4. Phonons and lattice vibrations  7.2. Electrical and Magnetic Properties  7.2.1. Conductors, Semiconductors and Insulators  7.2.2. Superconductivity  7.2.3. Hall effect
  8. Nuclear and particle physics  8.1. Atomic Structure  8.1.1. Atomic Model  8.1.2. Nuclear binding energy  8.2. Radioactivity  8.2.1. Alpha, beta, gamma decay  8.2.2. Half life  8.2.3. Nuclear Fission and Fusion  8.3. Particle physics  8.3.1. Standard Model  8.3.2. Quarks and Leptons  8.3.3. antimatter  8.3.4. Fundamental interactions
  9. Astrophysics and cosmology  9.1. Stellar evolution  9.1.1. Star formation  9.1.2. Black holes and neutron stars  9.1.3. White dwarfs and supernovae  9.2. Cosmology  9.2.1. The Big Bang Theory  9.2.2. Dark matter and dark energy  9.2.3. Cosmic microwave background

Undergraduate ↓


Optics


Optics is a branch of physics that studies the behavior, properties, and phenomena of light. Light is an electromagnetic wave, but for most introductory courses, we simplify it into rays and waves to understand its behavior. This lesson will cover various fundamental concepts in optics, including reflection, refraction, lens and mirror equations, wave optics, and more.

Nature of light

Light can be viewed in two main ways: as a wave and as a particle. However, for this discussion, we will focus on its wave nature and view it as a beam of light for the sake of simplification.

Light waves are transverse, meaning they vibrate perpendicular to the direction in which they travel. The speed of light in a vacuum is approximately c = 299,792,458 m/s. In other mediums, light travels slower due to interactions with particles within the medium.

Reflection

Reflection occurs when light strikes a surface. The law of reflection states that the angle of incidence is equal to the angle of reflection. This can be represented by the equation:

Angle of incidence = Angle of reflection

If a ray of light falls on a plane mirror, then the angle θ i (angle of incidence) will be equal to the angle θ r (angle of reflection).

θ iθRGeneral

Real life example: Mirrors in cars use the principles of reflection to help drivers see what is behind them.

Refraction

Refraction is the bending of light when it passes from one medium to another medium with different density. The light bends due to the change in the speed of light while entering the new medium.

Snell's law relates the angles of incidence and refraction to the indices of refraction of the two media:

n 1 * sin(θ 1) = n 2 * sin(θ 2)

where n is the refractive index of the medium.

Medium 1 (n 1)Medium 2 (n 2)θ 1θ 2

Real life example: A straw placed in a glass of water appears to bend on the surface of the water due to refraction.

Lens

Lenses are transparent objects that refract light to make it converge or diverge. Common lenses include convex lenses (which converge light) and concave lenses (which diverge light).

Convex lens

Convex lenses are thick in the middle and thin at the edges. They converge parallel light rays to a focal point in the opposite direction.

1/f = (n - 1)(1/r 1 - 1/r 2)

where f is the focal length, R 1 and R 2 are the radii of curvature of the lens surfaces.

F

Real life example: Magnifying glasses use convex lenses to make objects appear larger.

Concave lens

Concave lenses are thin in the middle and thick at the edges. They diverge parallel light rays.

F

Real life example: Glasses for nearsightedness use concave lenses, which cause the light to diverge before it hits the eye.

Mirror

Concave mirror

Concave mirrors, or converging mirrors, are curved inward. They reflect light inward to a focal point. They are used in applications where converging light is beneficial.

Convex mirror

Convex mirrors or diverging mirrors have surfaces that curve outward. They scatter light but allow a wider field of view.

Real life example: Car park mirrors and security mirrors are usually convex mirrors.

Lens and mirror equation

We can use the following mirror and lens equations to solve for various properties:

1/f = 1/ d + 1/ di

where f is the focal length, d o is the object distance, and d i is the image distance.

Wave optics

While the ray model of light helps us explain many phenomena, it fails when the wave nature of light is evident. In such cases, wave optics becomes important to understand interference, diffraction, and polarization.

Interference

Interference occurs when two or more light waves combine to form a new wave pattern. This can occur as constructive or destructive interference.

d * sin(θ) = m * λ

Where d is the distance between the slits, θ is the interference angle, m is the serial number, and λ is the wavelength of light.

Diffraction

Diffraction is the bending of light waves around obstacles and holes. The extent of diffraction depends on the size of the obstacle relative to the wavelength of the light.

Polarization

Polarization is the process in which waves of light or other electromagnetic radiation are restricted to certain directions of vibration. This is why polarized sunglasses are useful in reducing glare.

Conclusion

Optics is a vast and fascinating field of physics that explores how light behaves. By understanding the principles of reflection, refraction, lenses, mirrors, and wave optics, we can solve real-life problems and innovate in a variety of technological fields. The study of light is foundational to our understanding of the natural world and continues to be an area of important scientific inquiry.


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Optics

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