Lesson 1

• This learning area is focused on the profound impact of electricity and magnetism, optics, the basics of special relativity, atomic and nuclear phenomena using the methods and concepts of algebra, geometry, trigonometry, graphical analysis, and basic calculus
• Observation of Magnetic and Electric Phenomena: The ancient Greeks observed natural magnetic materials such as lodestone attracting iron. Similarly, they noted static electricity produced by rubbing certain objects together
• Link between Magnetism and Electricity: In the 18th century, scientists like Hans Christian Oersted and André-Marie Ampère conducted experiments that suggested a relationship between electricity and magnetism. Oersted's famous experiment in 1820 showed that an electric current produces a magnetic field around it
• Faraday's Discoveries: Michael Faraday, in the early 19th century, made significant contributions to understanding electromagnetism. His experiments with electric currents and magnetic fields led to the discovery of electromagnetic induction, demonstrating that a changing magnetic field can induce an electric current in a nearby circuit
• Maxwell's Equations: James Clerk Maxwell, in the 19th century, formulated a set of equations that described the behavior of electric and magnetic fields. His equations unified electricity and magnetism into a single electromagnetic force and predicted the existence of electromagnetic waves
• Gauss law for static electric fields


  It says that a lone charge like an electron will produce an electric field
• Gauss law for static magnetic fields


  It says you cannot have a loan magnetic pole or monopole since a north pole must come with a south pole and form a closed loop
• Faraday's law of electromagnetic induction


  It says that a changing magnetic field produces an electric field
• Ampere's law extension


  It says that a changing electric field produces a magnetic field
• Source-Free Equation


  1. Take the curl of the equation

  2. Use the identity: ∇ × ∇ × Ԧ𝐴 = ∇ ∇ × Ԧ𝐴 − ∇2 Ԧ𝐴

  3. ∇ ∇ × 𝐸 − ∇2𝐸 = ∇ × − 𝜕𝐵 𝜕𝑡

  4. −∇2𝐸 = ∇ × − 𝜕𝐵 𝜕𝑡

  5. ∇2𝐸 = 2 𝜕𝑡 1 𝑐2 𝜕𝐸 𝜕𝑡

  6. ∇2𝐸 = 1 𝑐2 𝜕2𝐸 𝜕𝑡2
• Wave Equation


  • ∇ × 𝐸 = 𝜕𝐵 𝜕𝑡
  • ∇ × 𝐵 = 1 𝐶2 𝜕𝐸 𝜕𝑡
• Maxwell's Equations


  A set of four fundamental equations in electromagnetism
• Source-Free Equation


  1. Take the curl of the equation

  2. Use the identity: ∇ × ∇ × A = ∇(∇ · A) - ∇^2 A
• Maxwell's equations have profound implications for optics because they predict the existence of electromagnetic waves, including light
• These waves travel at the speed of light and have both electric and magnetic components oscillating perpendicular to each other and to the direction of propagation
• Maxwell's equations provide a theoretical framework for understanding various optical phenomena, such as reflection, refraction, diffraction, interference, and polarization
• They form the basis of classical electromagnetism and are essential for understanding the behavior of light and other electromagnetic radiation
• Electromagnetic wave


  A form of energy that is in the form of an electromagnetic wave and is almost everywhere around us
• Light


  The visible light has wavelengths measuring between 400–700 nanometers
• The Sun is the primary source of light by which plants utilize this to produce their energy
• In physics, the term light also refers to electromagnetic radiation of different kinds of wavelengths, whether it is visible to the naked eye or not
• Types of objects

  • Luminous objects (objects that can emit their own light)
  • Non-luminous objects (objects that cannot emit their own light)
• Reflection


  The phenomenon in which a light ray is sent back into the same medium from which it is coming
• Laws of Reflection


  • The incident ray, the reflected ray, and the normal all lie in the same plane
  • The angle of incidence is equal to the angle of reflection
• Types of Reflection

  • Regular reflection (rays are reflected from a smooth surface parallel to parallel incident light rays)
  • Irregular reflection (reflected rays and parallel incident rays are not parallel with each other)
• Refraction


  The bending of a wave when it passes from one medium to another, caused by differences in density between the two substances
• Laws of Refraction


  • The incident ray, refracted ray, and the normal to the interface of two media at the point of incidence all lie on the same plane
  • The ratio of the sine of the angle of incidence to the sine of the angle of refraction is constant (Snell's law)
• Refraction of Light in Real Life

  • Mirage and looming
  • Swimming pool appearing shallower
  • Formation of a rainbow
  • White light splitting into colors in a prism
• The twinkling effect of stars is due to atmospheric refraction
• Ray diagram


  A representation of the possible paths light can take to get from one place to another
• Parts of a ray diagram

  • Object
  • Focal point
  • Incident rays
  • Reflective rays
  • Principal axis
• Real vs Virtual Images

  Real image (di = + (left))

  Virtual image (di = - (right))

  Upright is always positive (+), inverted is always negative (-)
• SALT method


  S - Size of the image with respect to the object

  A - Attitude of the image with respect to the object

  L - Location of the image with respect to the object

  T - Type of image
• Example ray diagram: Enlarged, inverted, in front of the mirror and far away from the focal point, real image
• Ray diagram


  • Enlarged in size
  • Inverted
  • In front of the mirror and far away from the focal point
  • Real image
• Electromagnetic Spectrum

  A) Electromagnetic Spectrum

  B) Radio

  C) Microwaves

  D) Infrared

  E) Visible Light

  F) Ultraviolet

  G) X-rays

  H) Gamma