Grade 9
  1. Mechanics  1.1. Motion  1.1.1. Types of motion  1.1.2. Distance and displacement  1.1.3. Speed and Velocity  1.1.4. Acceleration  1.1.5. Graphical representation of motion  1.1.6. Equations of motion  1.1.7. Uniform and non-uniform motion  1.1.8. Free fall and acceleration due to gravity  1.1.9. Relative speed  1.1.10. Circular motion  1.2. Laws of force and motion  1.2.1. The concept of force  1.2.2. newton's first law of motion  1.2.3. Newton's second law of motion  1.2.4. Newton's third law of motion  1.2.5. Inertia and types of inertia  1.2.6. Motion  1.2.7. Conservation of momentum  1.2.8. Application of Newton's laws in daily life  1.2.9. Types of Forces (Contact and Non-Contact)  1.2.10. Friction and its effects  1.3. Gravitational force  1.3.1. Newton's law of universal gravitation  1.3.2. Importance of Gravitational Force  1.3.3. Acceleration due to gravity  1.3.4. Free fall and weightlessness  1.3.5. Mass and weight  1.3.6. Variation of g with height and depth  1.3.7. Kepler's laws of planetary motion  1.3.8. Satellites and their orbits  1.4. Work, Energy and Power  1.4.1. Concept of work  1.4.2. Positive and negative actions  1.4.3. Work done by constant and variable force  1.4.4. Energy and its forms  1.4.5. Kinetic energy and potential energy  1.4.6. Law of conservation of energy  1.4.8. Commercial unit of energy  1.4.9. Work–energy theorem  1.5. Simple machines  1.5.1. Types of simple machines  1.5.2. Mechanical advantage  1.5.3. Machine efficiency  1.5.4. Levers and their types  1.5.5. Pulleys and Inclined Planes  1.5.6. Gears and their uses
  2. Properties of matter  2.1. States of matter  2.1.1. Solids, liquids and gases  2.1.2. Properties of different states of matter  2.1.3. Change in state of matter  2.1.4. Plasma and Bose–Einstein condensate  2.2. Density and pressure  2.2.1. Concept of density and relative density  2.2.2. Pressure in solids, liquids and gases  2.2.3. Pascal's law and its applications  2.2.4. Atmospheric pressure and its variations  2.2.5. Surface tension and capillarity  2.3. Buoyancy and Archimedes' principle  2.3.1. Buoyant force  2.3.2. Archimedes principle  2.3.3. Applications of Archimedes' Principle  2.3.4. floating and sinking objects  2.3.5. Theory of Flotation and Archimedes' Principle
  3. Heat and Thermodynamics  3.1. Temperature and heat  3.1.1. Concept of heat and temperature  3.1.2. Temperature measurement  3.1.3. Temperature scales  3.2. Heat transfer  3.2.1. Conduction of heat  3.2.2. Convection of heat  3.2.3. heat radiation  3.2.4. Applications of heat transfer  3.2.5. Thermal conductivity  3.3. Thermal expansion  3.3.1. Expansion of solids, liquids and gases  3.3.2. Abnormal expansion of water  3.3.3. Applications of Thermal Expansion  3.4. Specific heat capacity and latent heat  3.4.1. Concept of specific heat capacity  3.4.2. Measurement and applications of specific heat  3.4.3. Latent heat of fusion and vaporization  3.4.4. Heat Engines and Efficiency
  4. Waves and sound  4.1. Waves and their types  4.1.1. Mechanical and electromagnetic waves  4.1.2. Longitudinal and Transverse Waves  4.1.3. Properties of Waves  4.1.4. Wavelength, frequency and speed of the wave  4.1.5. Superimposition of waves  4.2. Sound waves  4.2.1. Nature and transmission of sound  4.2.2. Speed of sound in different mediums  4.2.3. Reflection of sound and echo  4.2.4. Sonar and ultrasound  4.2.5. Resonance and pulsation  4.3. Sound characteristics  4.3.1. Intensity, loudness and quality of sound  4.3.2. Doppler effect in sound
  5. Lighting and Optics  5.1. Reflection of light  5.1.1. Laws of reflection  5.1.2. Reflection from a plane mirror  5.1.3. Reflection from a spherical mirror  5.1.4. Image formation by concave and convex mirrors  5.1.5. Applications of Reflection  5.2. Refraction of light  5.2.1. Laws of refraction  5.2.2. Refractive index  5.2.3. Refraction through a glass slab  5.2.4. Refraction in water and air  5.2.5. Lenses and their types  5.2.6. Image formation by convex and concave lenses  5.2.7. Total internal reflection and its applications  5.3. Dispersion and scattering of light  5.3.1. Spectrum of white light  5.3.2. Prisms and Dispersion  5.3.3. Tyndall effect and blue sky
  6. Electricity and Magnetism  6.1. Electric charge and static electricity  6.1.1. The concept of electric charge  6.1.2. Charging by friction, contact and induction  6.1.3. Electroscope and its working  6.2. Current Electricity  6.2.1. The concept of electric current  6.2.2. Ohm's Law and Resistance  6.2.3. Factors affecting resistance  6.2.4. Series and Parallel Circuits  6.2.5. Heating effect of electric current  6.2.6. Electric power and energy  6.3. Magnetism  6.3.1. Natural and artificial magnets  6.3.2. Properties of magnets  6.3.3. Earth's magnetism  6.3.4. Magnetic field and field lines  6.3.5. Electromagnets and their applications
  7. Modern Physics  7.1. structure of the atom  7.1.1. Atomic Structure and Subatomic Particles  7.1.2. Electrons, Protons, and Neutrons  7.1.3. Rutherford and Bohr model  7.2. Radioactivity  7.2.1. Types of radioactive emissions  7.2.2. Half-life and radioactive decay  7.2.3. Uses and Hazards of Radioactivity
  8. Space science and astronomy  8.1. The universe and its components  8.1.1. Stars and galaxies  8.1.2. Planets and Solar System  8.2. Satellites  8.2.1. Natural and artificial satellites  8.2.2. Use of satellites

Grade 9 → Lighting and Optics → Refraction of light ↓


Laws of refraction


The phenomenon of refraction occurs when light passes from one medium to another and changes its speed. This change in speed causes the direction of the light to change. Understanding refraction involves looking at the two main "laws of refraction" described below.

Introduction to refraction

Refraction is a common optical phenomenon that can be observed in many everyday situations. It is what causes a straw in a glass of water to appear to bend at the surface of the water. Refraction occurs because light travels at different speeds in different mediums. For example, light travels faster in air than in water.

Two laws of refraction

The laws governing the refraction of light are the fundamental principles in optics. These are:

First law of refraction

The first law of refraction states that the incident ray, the refracted ray, and the normal to the interface of two media all lie in the same plane.

To see this, imagine a flat boundary between two substances, such as air and water. A ray of light falling on the surface will bend, but the incoming (incident) ray and the outgoing (refracted) ray, as well as the perpendicular to the surface (the normal), will all lie in one geometric plane.

Second law of refraction (Snell's law)

The second law of refraction, also called Snell's law, relates the angle of incidence and refraction to the refractive index of the two media. It is expressed mathematically as follows:

    n1 * sin(θ1) = n2 * sin(θ2)

Where:

  • n1 is the refractive index of the first medium.
  • n2 is the refractive index of the second medium.
  • θ1 is the angle of incidence.
  • θ2 is the angle of refraction.
θ1 θ2

In this diagram, the horizontal line represents the boundary between two media. The vertical line is the normal to the surface. The incident ray strikes the boundary at an angle θ1, and the refracted ray bends toward or away from the normal depending on the values of n1 and n2, making an angle θ2.

Examples and applications

Example 1: Refraction of light in water

Consider a ray of light traveling from air into water. Air has a lower refractive index than water, so the speed of light slows down as it enters the water. The bending of the ray can be calculated using Snell's law.

    n_air = 1.00
    n_water = 1.33
    θ_air = 45°

Use Snell's law to find θ_water:

    1.00 * sin(45°) = 1.33 * sin(θ_water)

Solving for θ_water will give the angle of refraction in water.

Example 2: Optical lens

Lenses are based on the principle of refraction. They are used to focus light at specific points. Convex lenses, often used in eyeglasses, cameras, and microscopes, use curved surfaces to bend light and focus it at a specific point.

Derivation of Snell's law

Snell's law can be derived from the wave theory of light, which takes into account the change in wavelength during the transition from one medium to another while maintaining the frequency of light. Let light travel from one medium with velocity v1 to another with velocity v2.

    n1 * sin(θ1) = n2 * sin(θ2)

The derivation assumes stationarity of the wavefronts at the interface, and continuity across the boundary.

incident ray Refracted ray

The angle of refraction represents the decrease in the speed of light as light travels from a less dense medium to a more dense medium. Conversely, the speed of light from water to air will increase, and the refracted ray will bend away from the normal.

Real-world applications

Mirage

Mirages are optical phenomena caused by the refraction of light in the atmosphere. When layers of air at different temperatures have different refractive indices, light bends when passing through these layers, creating the illusion of water on the roads.

Prism

A prism is a transparent optical element with a flat, polished surface that refracts light. The angle and direction of refraction are determined by the refractive index of the prism material and the angle of incidence.

Prisms are used to separate light into its spectral colours due to the difference in refractive index for different wavelengths.

Fiber optics

Fiber optic cables transmit light signals over long distances using the principle of total internal reflection, which is a special case of refraction. By ensuring that light is continuously refracted within the core, fiber optics allows for extremely efficient transmission of data.

Practice problems

  1. A light ray enters glass from air at an angle of incidence of 30°. If the refractive index of glass is 1.5, calculate the angle of refraction.
  2. Why do fish in a pond appear closer to the surface than they actually are? Explain using the principles of refraction.
  3. A ray of light enters water from a diamond. If the refractive index of diamond is 2.42 and that of water is 1.33, calculate the critical angle for this ray from diamond to water.

Understanding and using the laws of refraction is vital to explaining and designing many modern optical systems, leading to advances in technology and our understanding of the natural world.


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Laws of refraction

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