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 ↓


Optical Instruments


Optical instruments are devices that process light waves to enhance the image for a clearer view or to collect light for measurement. These instruments are used in a wide range of applications such as photography, microscopy, and astronomy. The study of optical instruments falls under geometrical optics, where the behavior of light rays is used to understand how these instruments work.

Fundamentals of geometrical optics

Geometrical optics, also known as ray optics, is a branch of optics that describes light propagation in terms of rays. The basic principles of geometrical optics are reflection and refraction, which are governed by simple rules.

Reflection

The law of reflection states that when a ray of light reflects from a surface, the angle of incidence is equal to the angle of reflection. This can be demonstrated using a simple mirror. 

        Angle of incidence (i) = Angle of reflection (r)

Refraction

Refraction occurs when a ray of light passes from one medium to another, changing its speed and direction. Snell's law quantifies this behavior: 

        n1 * sin(θ1) = n2 * sin(θ2)

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

Types of optical instruments

Optical instruments can be broadly classified into two categories: instruments for viewing, such as microscopes and telescopes, and instruments for measurement, such as spectrometers and photometers.

Microscope

A microscope is used to look at objects that are too small to be seen with the naked eye. It uses a combination of lenses to magnify the image of a small object. The basic types of microscope include the simple microscope and the compound microscope.

Simple microscope

A simple microscope is basically a magnifying glass with a short focal length. It has a convex lens to magnify objects.

object Lens image

Compound microscope

A compound microscope uses two or more lenses to achieve high magnification. The objective lens, which is closest to the object, forms a real, inverted image. The eyepiece lens then magnifies this image.

object objective lens Eyepiece Lens

Telescope

Telescopes are used to view distant objects. They can be refracting telescopes or reflecting telescopes, depending on the method used to gather and focus the light.

Refracting telescope

Refracting telescopes use converging lenses to gather light and focus it to form an image. The first lens, called the objective, gathers light and forms a small image of the distant object, which is then magnified by the eyepiece lens.

Objective Eyepiece

Reflecting telescope

Reflecting telescopes use mirrors instead of lenses to focus light. A concave mirror is used to gather the light and reflect it to the focal point, where an image is formed. The image can then be magnified by the eyepiece.

primary mirror

Principles of lenses in optical instruments

Lenses are fundamental components in optical instruments. They bend light rays through refraction. There are two main types of lenses: convex (converging) lenses and concave (diverging) lenses.

Convex lens

Convex lenses are thicker at the center than at the edges. They converge parallel light rays to a focal point. The focal length of a convex lens is the distance from the center of the lens to the focal point.

convex lens Focal point

Concave lens

Concave lenses are thinner at the center than at the edges. They diverge parallel light rays. A virtual focal point is created behind the lens.

Concave Lens virtual focal point

Each type of lens has different effects on light rays, and their application in optical instruments varies according to the image formation or magnification required.

Practical applications and examples

Understanding how optical devices work helps in a variety of practical applications. Here are some examples:

Camera

The camera takes pictures by capturing light on a photosensitive surface. The lens focuses the light through refraction to form a sharp image on the film or sensor.

Glasses

Glasses correct vision by changing the path of light rays entering the eye. Convex lenses correct farsightedness and concave lenses correct nearsightedness.

Projector

The projector magnifies images by focusing and directing light using lenses. The lens system ensures that the image remains sharp and clear when projected onto the screen.

Binoculars

Binoculars use lenses and prisms to magnify distant scenes. The objective lens gathers light, and the eyepiece lens magnifies the image.

Conclusion

Optical instruments are vital in enhancing our understanding and observational capabilities, from the microscopic world to the vast universe. Geometrical optics provides a fundamental understanding of how these instruments control light, using the principles of reflection and refraction to aid in a variety of scientific and practical applications.


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Optical Instruments

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