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 → Geometrical Optics ↓


Reflection and Refraction


In the field of optics, which is an important branch of physics, there are two important concepts known as reflection and refraction. Understanding these concepts is important for understanding how light behaves when it hits different mediums. In geometrical optics, these phenomena are essential in explaining how we see objects, how lenses and mirrors work, and in the design of various optical devices.

Reflection of light

Reflection occurs when light bounces back from a surface. This phenomenon can be observed in mirrors or any shiny surface where the incoming light reflects, allowing us to see images. There is a fundamental law governing reflection called the law of reflection, which states:

Angle of Incidence = Angle of Reflection

To elaborate further, the angle of incidence is the angle between the incoming ray of light and the normal - the line perpendicular to the surface. The angle of reflection is the angle between the reflected ray and the normal.

incident ray Reflected ray normal line

For example, imagine you are standing directly in front of a flat mirror. The angle at which your ray of sight meets the mirror will be equal to the angle at which it exits the mirror, allowing you to see your reflection.

Refraction of light

Refraction is the bending of light as it passes from one transparent medium to another. This change in direction is caused by the change in the speed of light in different media. When light enters a more dense medium at an angle, it slows down and bends toward the normal, and when it exits into a less dense medium, it speeds up and bends away from the normal.

The law governing refraction is called Snell's law, which is expressed as:

n₁ * sin(θ₁) = n₂ * sin(θ₂)

Where, n₁ and n₂ are the refractive index of the first and second medium respectively, θ₁ is the angle of incidence, and θ₂ is the angle of refraction.

incident ray Refracted ray normal line

Consider an example in which a ray of light enters water from air. The refractive index of air is about 1.00 and that of water is about 1.33. If the ray of light enters the water at an angle of 30°, we can calculate the angle of refraction using Snell's law.

Reflection example

Everyday examples of reflection include looking at yourself in a mirror, seeing the tops of clouds in a deep pool of water, or seeing a reflection in a glass window. In each of these cases, light reflects off the surface and into your eyes, allowing you to see the reflected image.

In technology, reflection is used in the design of optical instruments such as telescopes and cameras. For example, reflecting telescopes use curved mirrors to reflect light from distant stars and focus it to form an image.

Examples of refraction

The experience of refraction is more common than we realize. A common example is a straw placed in a glass of water appearing bent or broken on the surface of the water. This happens because light bends as it passes from water to air.

Another example is in lenses, which use refraction to focus light. Eyeglasses, cameras, and microscopes all use lenses to focus light, making distant objects appear larger or farther away.

The concept of refraction is also applied to the eyes. The lens of the eye refracts incoming light to focus it accurately on the retina. This is why people need glasses if their eyes cannot refract light properly.

Conclusion

The principles of reflection and refraction are fundamental in optics. Every day we see light colliding with surfaces and passing through lenses, controlling and manipulating light in many ways in science and technology. Understanding these concepts gives a clear idea of how light interacts with the environment and leads to many applications in design, engineering and the natural sciences.

Through the continued study and exploration of these phenomena, optical innovations continue to evolve, providing clearer images, improved optical instruments, and advances in our exploration and understanding of the universe.


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Reflection and Refraction

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