Grade 11
  1. Mechanics  1.1. dynamics  1.1.1. Motion in one dimension  1.1.2. Motion in two and three dimensions  1.1.3. Displacement and Distance  1.1.4. Speed and Velocity  1.1.5. Acceleration and deceleration  1.1.6. Graphical analysis of motion  1.1.7. Equations of motion (advanced derivations)  1.1.8. Free fall and terminal velocity  1.1.9. Projectile motion  1.1.10. Relative velocity in one and two dimensions  1.1.11. Motion of a car on an inclined plane  1.2. Dynamics  1.2.1. Newton's laws of motion and their applications  1.2.2. Inertia and Newton's first law  1.2.3. Force and types of force  1.2.4. Static and kinetic friction  1.2.5. Circular motion and centripetal acceleration  1.2.6. Non-uniform circular motion  1.2.7. Banking of roads and curves  1.2.8. Momentum and Impulse  1.2.9. Conservation of momentum in one and two dimensions  1.2.10. Applications of Newton's Third Law  1.3. Work, Energy and Power  1.3.1. Work done by a constant and variable force  1.3.2. Work–energy theorem  1.3.3. Kinetic and potential energy  1.3.4. Gravitational and elastic potential energy  1.3.5. Conservation of mechanical energy  1.3.6. Power and instantaneous power  1.3.7. Efficiency of machines  1.3.8. Work done by conservative and non-conservative forces  1.4. Rotational motion  1.4.1. Torque and angular acceleration  1.4.2. Rotational equilibrium  1.4.3. Moment of inertia and its applications  1.4.4. Angular momentum and its conservation  1.4.5. Kinetic energy of rolling motion and rotation  1.4.6. Parallel and Perpendicular Axis Theorem  1.4.7. Dynamics of rotational motion
  2. Gravitational force  2.1. Universal gravitation  2.1.1. Newton's law of universal gravitation  2.1.2. Gravitational field and potential  2.1.3. Change in acceleration due to gravity  2.1.4. Kepler's laws of planetary motion  2.1.5. Orbital mechanics and satellites  2.1.6. Escape velocity and orbital velocity  2.1.7. Weightlessness and free fall  2.1.8. Gravitational potential energy and energy in orbits  2.1.9. Black holes and gravitational lensing
  3. Properties of matter  3.1. Fluid mechanics  3.1.1. Density and pressure in liquids  3.1.2. Pascal's theory and applications  3.1.3. Archimedes' Principle and Buoyancy  3.1.4. Bernoulli's equation and applications  3.1.5. Continuity equation and the Venturi effect  3.1.6. Surface tension and capillarity  3.1.7. Viscosity and Poiseuille's Law  3.1.8. Reynolds number and turbulence  3.2. Elasticity and deformation  3.2.1. Hooke's law and the stress-strain relation  3.2.2. Elastic modulus and applications  3.2.3. Deformation and yield strength of solids
  4. Thermal physics  4.1. Heat and temperature  4.1.1. Thermometric properties and temperature scale  4.1.2. Thermal expansion of solids, liquids and gases  4.1.3. Heat transfer system  4.1.4. Specific heat capacity and calorimetry  4.1.5. Latent heat and phase change  4.2. Kinetic theory of gases  4.2.1. Molecular model of gases  4.2.2. Kinetic explanation of temperature  4.2.3. Ideal Gas Equation and Deviations  4.2.4. Mean free path and Maxwell–Boltzmann distribution  4.3. Laws of Thermodynamics  4.3.1. Zeroth Law and Thermal Equilibrium  4.3.2. First Law and Internal Energy  4.3.3. The Second Law and Entropy  4.3.4. Carnot cycle and heat engines  4.3.5. Refrigerators and heat pumps
  5. Waves and oscillations  5.1. Simple Harmonic Motion  5.1.1. Equations of SHM  5.1.2. Energy in SHM  5.1.3. Damped and forced oscillations  5.1.4. Resonance and applications  5.1.5. Pendulum and spring-mass system  5.2. Wave motion  5.2.1. Types of mechanical waves  5.2.2. Wave motion and energy transport  5.2.3. Superposition Principle and Standing Waves  5.2.4. Reflection, Refraction and Diffraction  5.2.5. Doppler effect in sound and light  5.2.6. Pulsations and interference
  6. Electricity and Magnetism  6.1. Electrostatics  6.1.1. Electric charge and conservation  6.1.2. Coulomb's law and its applications  6.1.3. Electric field and electric flux  6.1.4. Electric potential and potential energy  6.1.5. Capacitance and Energy Stored in a Capacitor  6.2. Current Electricity  6.2.1. Ohm's law and electrical resistance  6.2.2. Resistivity and temperature dependence  6.2.3. Kirchhoff's Laws and Circuit Analysis  6.2.4. Electrical power and efficiency  6.2.5. Combination of resistors  6.3. Magnetism and Electromagnetism  6.3.1. Magnetic fields and their sources  6.3.2. Magnetic force on moving charges  6.3.3. Electromagnetic induction  6.3.4. Faraday's and Lenz's laws  6.3.5. Inductance and Transformer  6.3.6. Alternating current and its applications
  7. Optics  7.1. Reflection and Refraction  7.1.1. laws of reflection and refraction  7.1.2. Mirrors and lenses  7.1.3. Total internal reflection and optical fiber  7.2. Wave optics  7.2.1. Interference and Diffraction  7.2.2. Young's double-slit experiment  7.2.3. Polarization of light
  8. Modern Physics  8.1.1. Photoelectric effect and Einstein's theory  8.1.2. Wave–particle duality  8.1.3. Heisenberg's uncertainty principle  8.1.4. Compton Effect  8.2. Atomic and Nuclear Physics  8.2.1. Atomic model and energy levels  8.2.2. Radioactive decay and half-life  8.2.3. Nuclear Fission and Fusion
  9. Electronics and Communication  9.1. Semiconductors  9.1.1. pn junction and diode  9.1.2. Transistors and Logic Gates  9.1.3. Integrated Circuits and Applications  9.2. Communication Systems  9.2.1. Basics of Analog and Digital Communication  9.2.2. Wireless and Optical Communication  9.2.3. Modulation and Demodulation

Grade 11 → Optics → Reflection and Refraction ↓


Mirrors and lenses


In the study of optics, it is essential to understand how light interacts with different surfaces and materials. Mirrors and lenses are two types of surfaces that direct light in specific ways, providing the basis for many optical instruments such as telescopes and cameras. In this lesson, we will explore the properties and behaviors of mirrors and lenses, focusing on their roles in the reflection and refraction of light.

Reflections and mirrors

Reflection occurs when a ray of light strikes a surface. The law of reflection states that the angle of incidence is equal to the angle of reflection. Mirrors are perfect examples of surfaces that reflect light very precisely.

incident ray Reflected ray General Mirror Surface

In the diagram above, the red line represents the incident ray, and the blue line represents the reflected ray. The gray dashed line is the normal, a line drawn perpendicular to the mirror surface at the point of incidence.

Types of mirrors

There are mainly two types of mirrors: plane mirrors and curved mirrors (which include concave and convex mirrors).

Plane mirror

Plane mirrors are flat surfaces that reflect light in such a way that the virtual images formed are the same size as the object. When you look into a plane mirror, you see yourself as you are, but reversed from left to right. Plane mirrors are used in bathrooms, bedrooms, and other places where true images are needed.

Concave mirror

Concave mirrors are spherical mirrors that are curved inward like a cave. They focus light to a single point, known as the focal point. These mirrors are used to focus light in car headlights, flashlights, and telescopes.

F incident ray Reflected ray

In the diagram, the incident rays possibly reflect from the focal point F after hitting the surface and converge. This is an important feature of concave mirrors. The reflection of parallel rays from a concave mirror converges at the focal point.

Convex mirror

Convex mirrors are bulged outwards, causing the light rays to spread out or scatter. These mirrors are used as side mirrors of vehicles and in surveillance because they provide a wider field of view.

F incident ray Reflected ray

In this diagram, parallel rays appear to diverge and spread out upon reflection. It is because of this apparent divergence that images in convex mirrors appear smaller and provide a wider view.

Refraction and lenses

Refraction is the bending of light due to a change in its speed when it passes from one medium to another. Lenses use the property of refraction to focus or disperse light.

incident ray Refracted ray Lens

In the diagram, the light ray bends toward the normal as it enters the lens and away from the normal as it exits. The effect depends on the shape and type of lens, which leads us to types of lenses.

Types of lenses

Lenses are classified into two major types based on their shape: convex lenses and concave lenses.

Convex lens

Convex lenses are thicker in the middle than at the edges. They converge light rays to a focal point and are also known as converging lenses. These lenses are used in cameras, eyeglasses and magnifying glasses to focus light and magnify images.

incident ray Refracted ray Refracted ray Lens

The central red incident ray passes through the lens and bends inward at each refraction. The refracted rays (blue and green) converge at a focal point, demonstrating the property of a convex lens to focus light.

Concave lens

Concave lenses are thinner in the middle than at the edges. They spread light rays away from a point and are known as diverging lenses. They are used in devices such as peepholes and optics that require light to be dispersed.

incident ray Refracted ray Refracted ray Lens

In this diagram, the incident rays diverge as they pass through the lens, represented by the blue and green lines. This dispersion effect is a key feature of concave lenses, which causes them to diverge light rays.

Lens formula and magnification

Lenses have specific properties that are defined by the lens formula and magnification. The lens formula is represented as:

1/f = 1/v - 1/u

Where:

  • f is the focal length of the lens.
  • v is the distance of the image from the lens.
  • u is the distance of the object from the lens.

The magnification of a lens refers to the ratio of the height of the image to the height of the object and is expressed as:

M = H'/H = -V/U

Where:

  • h' is the height of the image.
  • h is the height of the object.
  • m is the magnification.

Positive magnification indicates an upright image, while negative magnification indicates an inverted image.

Applications and real-world examples

Understanding mirrors and lenses is important for the design of various optical instruments:

  • Telescopes: Use a concave mirror and a convex lens to make distant objects appear larger.
  • Camera: Use the lens to focus light and create a sharp picture.
  • Glasses: Use concave or convex lenses to correct vision by adjusting the focal length.
  • Microscopes: Use lenses to magnify small objects for detailed examination.

By mastering the properties of mirrors and lenses, we can create and adapt devices that improve our vision and understanding of the world around us.

In conclusion, mirrors and lenses play a vital role in the study of optics by using reflection and refraction principles to direct light. Knowing how light interacts with these elements enables us to develop important techniques in a variety of fields, including photography, astronomy, and vision correction. The rules and formulas associated with these interactions provide the basis for the design and enhancement of optical devices.


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Mirrors and lenses

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