Ray Optics

• Optics is the branch of physics studying light's behavior and properties, including its interactions with matter, and the construction of instruments that use or detect it.
• It explains optical phenomena like refraction, diffraction, interference, and polarization.
• Optics is typically described by the classical electromagnetic description of light.
• Complete electromagnetic descriptions of light are often difficult to apply practically, so simplified models are used.
• Rays are abstractions that travel in straight lines and bend when they meet an interface between different materials.
• Wave optics models light as a wave.
• Quantum optics deals with the quantum mechanical properties of light, where light is quantized in the form of photons.

Ray Optics

• Ray optics describes light as traveling in straight lines called rays.
• Rays bend at the interface between two materials.
• Reflection occurs when light bounces off a surface; the angle of incidence equals the angle of reflection.
• Refraction occurs when light passes through a surface between two transparent materials and changes direction; Snell's law relates the angles of incidence and refraction to the refractive indices of the materials.
• Refractive index of a material is the ratio of the speed of light in a vacuum to the speed of light in the material.
• Total internal reflection happens when light travels from a medium with a higher refractive index to one with a lower refractive index, striking the interface at an angle greater than the critical angle.
• Lenses use refraction to focus or defocus light and form images.
• Focal length of a lens is the distance from the lens to the point where parallel rays converge (converging lens) or appear to diverge from (diverging lens).
• Lensmaker's equation relates the focal length of a lens to its refractive index and the radii of curvature of its surfaces.
• Optical instruments like telescopes, microscopes, and cameras use combinations of lenses and mirrors to form images.

Wave Optics

• Wave optics treats light as a wave and explains phenomena like interference and diffraction.
• Interference occurs when two or more waves overlap in space and the resulting amplitude depends on the phase difference between the waves.
• Constructive interference occurs when the phase difference is a multiple of 2π, resulting in a larger amplitude.
• Destructive interference occurs when the phase difference is an odd multiple of π, resulting in a smaller amplitude.
• Young's double-slit experiment demonstrates interference by passing light through two narrow slits to create an interference pattern on a screen.
• Diffraction is the bending of waves around obstacles or through apertures.
• Huygens' principle states that every point on a wavefront can be considered a source of secondary spherical wavelets, and their envelope at a later time is the new wavefront.
• Diffraction grating consists of numerous equally spaced parallel slits, producing sharp interference maxima at specific angles based on the wavelength of light and the grating spacing.
• Polarization describes the direction of the electric field vector in a light wave.
• Unpolarized light has electric field vectors oscillating randomly.
• Polarized light has electric field vectors oscillating in a specific direction.
• Polarizers are materials that transmit light with a specific polarization and block light with the orthogonal polarization.
• Brewster's angle is the angle of incidence at which light with a particular polarization is perfectly transmitted through a transparent surface, with no reflection.

Quantum Optics

• Quantum optics studies the quantum mechanical properties of light and its interaction with matter.
• Light is quantized into packets of energy called photons.
• The energy of a photon is proportional to its frequency (E = hf), where h is Planck's constant.
• Photons exhibit both wave-like and particle-like behavior (wave-particle duality).
• Lasers (Light Amplification by Stimulated Emission of Radiation) produce coherent and monochromatic light through stimulated emission.
• Spontaneous emission occurs when an atom in an excited state randomly decays to a lower energy level, emitting a photon.
• Stimulated emission occurs when an incoming photon induces an excited atom to decay to a lower energy level, emitting a photon with the same phase, frequency, polarization, and direction as the incoming photon.
• Population inversion is a necessary condition for laser operation, where a majority of atoms are in an excited state.
• Optical cavities or resonators are used in lasers to provide feedback of the light and amplify the stimulated emission.
• Quantum entanglement occurs when two or more particles become linked together in such a way that the state of one particle instantaneously influences the state of the other, regardless of the distance between them.
• Quantum cryptography uses the principles of quantum mechanics to encrypt and transmit information securely.