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 ↓


Mirrors and lenses


Geometrical optics is a field of physics that deals with the reflection and refraction of light using mirrors and lenses. It follows the principles of light propagation and uses them to explain phenomena related to mirrors and lenses. The fundamental concepts are important to understand how light interacts with these objects, one of the cornerstones in physics education. This article will help you understand these concepts in a simple but detailed manner.

Reflection and types of mirrors

Before learning about mirrors, it is important to understand the law of reflection, according to which when light reflects from a surface, the angle of incidence is equal to the angle of reflection. Mathematically, it is expressed as:

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

Mirrors use this principle to form an image. Mirrors are mainly of two types: plane mirrors and curved mirrors. Curved mirrors are further classified into concave and convex mirrors.

Plane mirror

A plane mirror has a flat reflecting surface. When light rays strike a plane mirror, they return back with an angle of incidence equal to the angle of reflection. The image formed by a plane mirror is virtual, which means it cannot be projected on a screen. The image is also erect and is the same size as the object.

Concave mirror

Concave mirrors have a reflecting surface that curves inward. They can converge light rays to a point, making them useful in devices such as telescopes and headlights.

Consider a concave mirror having principal axis, focal point (F) and centre of curvature (C). Here is the ray diagram representing it:

In the diagram, light rays coming parallel to the axis converge at the focal point after reflection. The type of image formed (real or virtual) depends on the position of the object relative to the mirror. Concave mirrors can form both real and inverted image or virtual and erect image.

Convex mirror

Convex mirrors bulge outward and spread out light rays, giving a wider field of view. This property makes them suitable for safety and security applications, such as side-view mirrors in vehicles.

Ray diagrams help explain how convex mirrors work. Below is an illustration:

All images formed by convex mirrors are virtual, small and erect. The focal point is behind the mirror because the rays diverge when they meet the reflecting surface.

Refraction and lenses

Refraction is the bending of light as it passes through different media. Its main principle is expressed by Snell's law:

n 1 * sin(θ 1 ) = n 2 * sin(θ 2 )

n 1 and n 2 are the refractive indices of the two media, while θ 1 and θ 2 are the angles of incidence and refraction, respectively. Refraction helps bend light through a lens, making image formation possible.

Types of lenses

Lenses are classified into two main types: convex lenses and concave lenses. Each type handles light differently, producing different effects useful in optical instruments.

Convex lens

Convex lenses are thicker at the center than at the edges and converge light rays passing through them to a focal point. This property makes them suitable for applications requiring magnified or focused light. Convex lenses are used in magnifying glasses, cameras, and corrective eyeglasses.

Explain with the help of the following diagram how light passes through a convex lens:

In the illustration, parallel incoming rays refract through the lens and converge at its focal point. As with concave mirrors, the type of image depends on the distance of the object from the lens. Convex lenses can form real and inverted images or virtual and erect images.

Concave lens

Concave lenses are thin at the center and thick at the edges, causing light rays to diverge as they pass through. They are typically used for applications requiring a reduced or diffused light pattern, such as in peepholes or to correct nearsightedness.

The ray diagram for a concave lens will look like this:

The virtual focal point is used to extend the diverging rays outwards. Images formed by a concave lens are always virtual, erect and diminished.

Image formation by mirrors and lenses

The study of image formation involves specific rules and setups for each mirror and lens type. Applying the mirror formula and lens formula helps calculate image properties and is important for any optical analysis.

Mirror formula

The mirror formula relates the object distance (u), image distance (v), and focal length (f). It is given as:

1/f = 1/u + 1/v

The sign convention is important here. For concave mirrors, the focal length and image distance are negative, while for convex mirrors, they are positive.

Lens formulas

Similar to mirrors, the lens formula connects object distance, image distance, and focal length:

1/f = 1/v - 1/u

The signs in the lens formula differ: for a convex lens, the focal length is positive, while for a concave lens, it is negative. Understanding these conventions helps predict whether the image will be real or virtual, upright or inverted, and what its size will be.

Magnification

Magnification tells us how big or small the image is compared to the object. It is expressed differently for mirrors and lenses.

Magnification for mirrors

Defined as the ratio of image height (h i) and object height (h o), in which:

M = H I / H O = -V/U

While positive magnitude indicates upright image, negative magnitude indicates inverted image.

Magnification for lens

In terms of lenses, magnification takes the same form:

M = H I / H O = V/U

Here, the sign convention is essential: positive magnification suggests an erect image for both the lens and the mirror.

Applications and practical examples

Understanding mirrors and lenses in geometrical optics has countless applications in daily life and advanced technology.

  • Telescopes and Microscopes: Use both concave mirrors and convex lenses to magnify distant or small objects for observation.
  • Camera: Use a lens to focus light onto photographic film or sensor to take still and video pictures.
  • Glasses and contact lenses: correct vision by converging or diverging light rays, adjusting the focus of light on the retina.
  • Projectors: Use a combination of lenses to focus and magnify a display or magnify images projected onto a surface.

These practical examples make it clear how understanding the principles of mirrors and lenses has a profound impact on technological advancement and everyday conveniences.

Conclusion

Mirrors and lenses are fundamental to the study of optics in undergraduate physics. This detailed overview will provide you with a foundational understanding of how light interacts with mirrors and lenses. From forming images to enabling technology applications, the underlying physics provides the basis for continued innovation and understanding. Mastery of ray diagrams, formulas, and theories ensures accuracy in the prediction and manipulation of light, which is essential for optical physicists and engineers.


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Mirrors and lenses

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