Grade 12
  1. Advanced mechanics  1.1. Dynamics  1.1.1. Motion in two and three dimensions  1.1.2. Advanced Projectile Motion and Range Equations  1.1.3. Relative motion in different reference frames  1.1.4. Motion of charged particles in electric and magnetic fields  1.1.5. Non-uniformly accelerated motion in multiple dimensions  1.2. Dynamics  1.2.1. Newton's laws and applications in non-inertial frames  1.2.2. Dynamics of particle systems  1.2.3. Non-conservative forces and energy dissipation  1.2.4. Momentum in variable mass systems (rocket momentum)  1.2.5. Lagrangian and Hamiltonian Mechanics (Introduction)  1.3. Work, Energy and Power  1.3.1. Work done by non-conservative forces  1.3.2. Power in rotational and translational motion  1.3.3. Advanced Conservation Laws and Applications  1.3.4. Potential energy surface and stability  1.4. Advanced rotational speed  1.4.1. Torque in three dimensions  1.4.2. Moment of inertia for irregular bodies  1.4.3. Gyroscopic motion and precession  1.4.4. Rotational work–energy theorem  1.4.5. Euler's equations of rotational motion  1.5. Gravitational force  1.5.1. Advanced Orbital Mechanics  1.5.2. Lagrange points and stability of orbits  1.5.3. Gravitational time dilation  1.5.4. Escape velocity and energy considerations  1.5.5. Tidal force and the Roche limit
  2. Fluid mechanics and thermodynamics  2.1. Fluid dynamics  2.1.1. Applications of Bernoulli's Principle  2.1.2. Navier-Stokes equations and fluid resistance  2.1.3. Turbulent vs. Laminar Flow  2.1.4. Surface tension and capillary action  2.2. Advanced Thermal Physics  2.2.1. Thermodynamic equilibrium and heat engines  2.2.2. Entropy and the Second Law of Thermodynamics  2.2.3. Maxwell's demon and statistical thermodynamics  2.2.4. Thermodynamic potential and free energy
  3. Oscillations and waves  3.1. Advanced Simple Harmonic Motion  3.1.1. Coupled oscillations and common modes  3.1.2. Damped and driven oscillations  3.1.3. Phase space and resonance  3.1.4. Anharmonic oscillations  3.2. Wave motion  3.2.1. Advanced wave equations and dispersion  3.2.2. Shock Waves and Sonic Booms  3.2.3. Doppler effect in electromagnetic waves  3.2.4. Wave–particle duality
  4. Electromagnetism  4.1. Electrostatics  4.1.1. Gauss's law in unilateral charge distribution  4.1.2. Electric potential for complex charge configuration  4.1.3. Electrostatic energy and self-energy of a system  4.1.4. Dielectrics and Polarization  4.2. Current Electricity  4.2.1. Advanced Circuit Analysis (Thevenin and Norton theorems)  4.2.2. RC, RL and RLC circuits in AC and DC  4.2.3. Superconductivity and applications  4.3. Advanced Magnetism and Electromagnetic Induction  4.3.1. Magnetic fields in conductors and plasma  4.3.2. Lenz's law in time-dependent magnetic fields  4.3.3. Eddy Currents and Applications  4.3.4. Magnetic dipole moment and torque on electric current loops  4.4. Alternating Current and Electromagnetic Waves  4.4.1. LC Circuits and Resonance  4.4.2. Maxwell's equations and electromagnetic wave transmission  4.4.3. Applications of Electromagnetic Waves  4.4.4. Polarization and reflection of EM waves
  5. Optics  5.1. Geometrical Optics  5.1.1. Aberrations in optical systems  5.1.2. Advanced lens and mirror formulas  5.1.3. Optical Instruments and Adaptive Optics  5.2. Wave optics  5.2.1. Diffraction at single and multiple slits  5.2.2. Optical Coherence and Interferometry  5.2.3. Holography and applications
  6. Modern and quantum physics  6.1. Special relativity  6.1.1. Time expansion and length contraction  6.1.2. Relativistic energy and mass  6.1.3. Relativistic Doppler effect  6.2. Quantum mechanics  6.2.1. Schrödinger equation and wave function  6.2.2. Quantum tunneling and applications  6.2.3. Heisenberg uncertainty principle  6.2.4. Quantum superposition and entanglement  6.3. Nuclear physics  6.3.1. Binding energy and mass defect  6.3.2. Neutrino physics and beta decay  6.3.3. Nuclear Fission and Fusion  6.4. Particle physics  6.4.1. Standard Model and fundamental interactions  6.4.2. The Higgs boson and symmetry breaking  6.4.3. Antimatter and CP violation
  7. Astrophysics and cosmology  7.1. General relativity and gravity  7.1.1. Einstein's field equations  7.1.2. Gravitational waves and their detection  7.1.3. Black holes and event horizons  7.2. Cosmology  7.2.1. Dark matter and dark energy  7.2.2. Cosmic microwave background radiation  7.2.3. The expansion of the universe and Hubble's law

Grade 12 ↓


Optics


Optics is the branch of physics that studies light and its interactions with various substances. It helps us understand how we see the world around us, how lenses and mirrors work, and many other phenomena involving light.

Basic concepts of lighting

Let us first understand what light is. Light is a type of energy that travels in waves. These waves can travel in a vacuum, which means they do not need any physical medium to move through. Light travels at an incredible speed of about 299,792 kilometers per second in a vacuum. This speed is known as the speed of light, represented by the letter c.

c = 299,792 km/s

Waves and particles

Light behaves like both a wave and a particle. This duality is one of the most striking features of light. When light behaves like a wave, it can be described in terms of wavelengths and frequencies. Wavelength is the distance between two successive peaks of the wave, and frequency is how many wave peaks pass a point in one second. The unit of frequency is Hertz (Hz).

Wave speed (v) = frequency (f) × wavelength (λ)
V = F × λ

When light behaves like particles, these particles are called photons. Photons are tiny packets of energy. The energy of a photon is related to its frequency as follows:

Energy (E) = Planck's constant (h) × Frequency (f)
E = H × F

The Planck constant h is approximately 6.626 × 10^-34 Joule second.

Transmission of light

Light travels in straight lines. This property is the basis of how we see the world and is used in a variety of optical instruments.

Reflection

Reflection occurs when light bounces off a surface. Mirrors are common examples that use reflection to create an image. There are two types of reflection:

  • Reflection: Occurs on smooth surfaces like mirrors and water surface.
  • Diffuse reflection: occurs on rough surfaces, scattering light in different directions.

The laws of reflection describe how light behaves when it reflects off a surface:

incident ray Reflected ray General angle of incidence angle of reflection

The angle of incidence is equal to the angle of reflection.

Refraction

Refraction occurs when light passes from one medium to another and changes speed, which changes its direction. A common example of refraction is the bending of a straw when placed in a glass of water.

Snell's law describes refraction. It relates the angles and refractive indices of the two media:

n1 × sin(θ1) = n2 × sin(θ2)

Here, n1 and n2 are the refractive indices of the two media, and θ1 and θ2 are the angles of incidence and refraction, respectively.

Air Water incident ray Refracted ray General

While going from a less dense medium to a more dense medium the ray of light bends towards the normal.

Optical instruments

Optical instruments such as cameras, telescopes, and microscopes use lenses and mirrors to control light and create images. Understanding how these instruments work helps us learn about everything from the smallest bacteria to the most distant galaxies.

Lens

Lenses are curved pieces of glass or plastic that refract light. They can converge or diverge light rays, forming images.

  • Convex lens: Converges light rays to a point called the focal point. These lenses are thicker in the middle than at the edges. Convex lenses are used in magnifying glasses and glasses for farsightedness.
  • Concave lens: Spreads light rays away from a point. These lenses are thinner in the middle than at the edges. Concave lenses are used in glasses for nearsightedness.

The focal length of a lens, denoted by f, is the distance from the lens to the focal point. The lens formula is:

1/F = 1/V + 1/U

Where f is the focal length, v is the image distance, and u is the distance of the object from the lens.

object Main axis Concave lens

This diagram shows how a concave lens diverges light rays.

Optical phenomenon

Apart from the basic laws, optics also explains fascinating phenomena like rainbow, mirage, etc.

Spread

Dispersion occurs when different colors of light spread out due to being refracted by different amounts. A prism is a well-known device that spreads out white light into its component colors, creating a beautiful spectrum commonly known as a rainbow.

Red orange Yellow Green Blue Indigo Purple white Glasses

When white light passes through a prism, it splits into a spectrum of colours.

Interference and diffraction

Interference occurs when two or more waves overlap, creating a new wave pattern. This can result in regions of constructive interference, where the wave amplitudes add up, and destructive interference, where they cancel each other out.

Diffraction refers to when light bends around an obstacle or hole. A simple example of this is how light spreads out when it passes through a narrow hole.

light beam Obstacle

Due to diffraction the light spreads out when passing through small holes.

Applications of optics

Optics has many applications in everyday life and advanced technology:

  • Glasses: Correct vision by refracting light and focusing it properly on the retina.
  • Camera: Use the lens to focus light and create a sharp picture.
  • Fiber optics: Use total internal reflection to transmit data over long distances via light signals.
  • Microscopes: Use a series of lenses to magnify small objects.
  • Telescopes: Collect light to observe distant objects in space.

These examples demonstrate the fundamental importance of optics in modern scientific progress.

Conclusion

Optics provides important information about the behavior of light, which contributes greatly to our understanding of physics and the technological world. Knowing how light interacts with surfaces, bends through lenses, and creates various phenomena prepares us to use its properties for telescopic applications.


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Optics

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