Grade 10
  1. Mechanics  1.1. Dynamics  1.1.1. Motion in one dimension  1.1.2. Motion in two dimensions  1.1.3. Displacement and Distance  1.1.4. Speed and Velocity  1.1.5. Acceleration  1.1.6. Graphical representation of motion  1.1.7. Equations of motion  1.1.8. Free fall and acceleration due to gravity  1.1.9. Projectile motion  1.1.10. Relative speed  1.2. Dynamics  1.2.1. Newton's Laws of Motion  1.2.2. Inertia and mass  1.2.3. Force and its types  1.2.4. action and reaction force  1.2.5. Friction and its effects  1.2.6. Coefficient of friction  1.2.7. Circular motion  1.2.8. Centripetal force and centripetal acceleration  1.2.9. Momentum and Impulse  1.2.10. Conservation of momentum  1.2.11. Newton's third law and applications  1.3. Work, Energy and Power  1.3.1. Work done by the force  1.3.2. Work–energy theorem  1.3.3. Kinetic energy  1.3.4. Potential energy  1.3.5. Mechanical energy  1.3.6. Energy Conservation  1.3.7. Power and efficiency  1.3.8. Renewable and non-renewable energy sources  1.4. Gravitational force  1.4.1. Newton's law of universal gravitation  1.4.2. Gravitational field and field strength  1.4.3. Acceleration due to gravity on different planets  1.4.4. Kepler's laws of planetary motion  1.4.5. Orbits and satellites  1.4.6. Weight and apparent weight  1.4.7. Gravitational potential energy
  2. Properties of matter  2.1. States of matter  2.1.1. Solid, liquid and gas  2.1.2. Molecular structure of matter  2.1.3. Intermolecular forces  2.1.4. Plasma and Bose–Einstein condensate  2.2. Pressure  2.2.1. Definition of Pressure  2.2.2. Pressure in liquids  2.2.3. Atmospheric pressure  2.2.4. Pascal's principle  2.2.5. Archimedes' Principle and Buoyancy  2.2.6. Surface tension and capillarity  2.3. Elasticity  2.3.1. Hooke's law  2.3.2. Stress and strain  2.3.3. Elastic Limit and Modulus of Elasticity  2.3.4. Applications of Elasticity
  3. Thermal physics  3.1. heat and temperature  3.1.1. Difference Between Heat and Temperature  3.1.2. Temperature scale  3.1.3. Thermal expansion  3.1.4. Thermal equilibrium  3.2. Heat transfer  3.2.1. Conductivity  3.2.2. Convection  3.2.3. Radiation  3.2.4. Insulation and its applications  3.3. Thermal properties of matter  3.3.1. Specific heat capacity  3.3.2. Latent heat and phase change  3.3.3. Boiling and Melting Point  3.3.4. Heat engines and refrigeration  3.4. Laws of Thermodynamics  3.4.1. Zeroth law of thermodynamics  3.4.2. First law of thermodynamics  3.4.3. Second law of thermodynamics  3.4.4. Carnot cycle
  4. Waves and optics  4.1. Nature and properties of waves  4.1.1. Types of waves in nature and properties of waves  4.1.2. Transverse and longitudinal waves  4.1.3. Wave parameters  4.1.4. Reflection and refraction of waves  4.1.5. Superposition and Interference  4.1.6. Standing Waves and Resonance  4.1.7. Doppler effect  4.2. Sound waves  4.2.1. Characteristics of sound waves  4.2.2. Speed of sound in different mediums  4.2.3. Applications of sound waves  4.2.4. Ultrasound and its uses  4.3. Light Waves and Optics  4.3.1. Nature of light  4.3.2. Reflection of light  4.3.3. Laws of reflection  4.3.4. Mirrors and Image Formation  4.3.5. Refraction of light  4.3.6. Snell's Law  4.3.7. Lenses and Image Formation  4.3.8. Total internal reflection and critical angle  4.3.9. Optical fibre  4.4. Optical Instruments  4.4.1. Microscope  4.4.2. Telescope  4.4.3. Human eye and vision defects  4.4.4. Camera and its working principle
  5. Electricity and Magnetism  5.1. Electrostatics  5.1.1. Electric charge and its properties  5.1.2. Conductors and Insulators  5.1.3. Coulomb's law  5.1.4. Electric field and field lines  5.1.5. Electric potential and potential difference  5.1.6. Capacitors and Capacitance  5.2. Current Electricity  5.2.1. Electric current and its measurement  5.2.2. Ohm's law  5.2.3. Resistance and resistivity  5.2.4. Series and Parallel Circuits  5.2.5. Electric power and energy  5.2.6. Kirchhoff's Laws  5.3. Magnetism and Electromagnetism  5.3.1. Magnetic field and field lines  5.3.2. Magnetic effects of electric current  5.3.3. Electromagnetic induction  5.3.4. Faraday's laws of electromagnetic induction  5.3.5. Transformers and Applications  5.3.6. AC and DC current
  6. Modern Physics  6.1. Nuclear physics  6.1.1. Structure of the atom  6.1.2. Bohr's atomic model  6.1.3. Electron Energy Levels  6.1.4. X-rays and applications  6.2. Radioactivity  6.2.1. Types of radiation  6.2.2. Half-life and radioactive decay  6.2.3. Nuclear reactions and applications  6.2.4. Fission and Fusion  6.3. Quantum physics  6.3.1. Wave–particle duality  6.3.2. Photoelectric effect  6.3.3. Energy quantization  6.3.4. Heisenberg's uncertainty principle
  7. Electronics and Communication  7.1. Semiconductors  7.1.1. Conductors, Insulators and Semiconductors  7.1.2. Diodes and their applications  7.1.3. Transistors and Logic Gates  7.1.4. LEDs and photodiodes  7.2. Communication Systems  7.2.1. Basics of communication  7.2.2. Analog and digital signals  7.2.3. Wireless and optical fibre communication  7.2.4. Radio Waves and Modulation

Grade 10 → Waves and optics → Light Waves and Optics ↓


Total internal reflection and critical angle


Light is an essential part of our daily lives. It helps us see the world around us, and its behavior can be described by the branch of physics known as optics. Two interesting phenomena related to the behavior of light are total internal reflection (TIR) and critical angle.

Understanding refraction

Before delving deeper into total internal reflection and critical angle, it is essential to understand refraction. Refraction is the bending of light as it passes from one medium to another with different densities, such as from air to water. When light enters the denser medium, it slows down and bends toward the normal (an imaginary line perpendicular to the boundary of the two media). When it passes from a denser medium to a less dense medium, it speeds up and bends away from the normal.

Snell's law

The refraction of light is governed by a principle called Snell's law. Snell's law can be expressed mathematically as follows:

n1 * sin(θ1) = n2 * sin(θ2)

Where:

  • n1 is the refractive index of the first medium.
  • θ1 is the angle of incidence (the angle between the incident ray and the normal).
  • n2 is the refractive index of the second medium.
  • θ2 is the angle of refraction (angle between the refracted ray and the normal).

Visualization of refraction

To understand how light bends during refraction, imagine a beam of light entering water from air. The refractive index of air is about 1, while the refractive index of water is about 1.33. As the light hits the surface of the water, it slows down and bends toward the normal. This effect can be demonstrated by the following example:

Water Air incident ray Refracted ray

Total internal reflection

Total internal reflection occurs when light attempts to pass from a denser medium to a less dense medium at a high angle of incidence. Instead of refraction, the light is completely reflected back into the denser medium. This phenomenon can only occur when light passes from a medium with a higher refractive index to a medium with a lower refractive index, such as from water to air.

Critical angle

The critical angle is the angle of incidence in the denser medium at which the angle of refraction in the less dense medium becomes 90 degrees. At this angle, the refracted ray travels along the boundary, just touching the interface between the two media. The formula for the critical angle θc can be obtained from Snell's law:

θc = arcsin(n2 / n1)

where n1 is the refractive index of the denser medium and n2 is the refractive index of the less dense medium.

Practical examples of total internal reflection and critical angle

One of the best-known practical examples of total internal reflection is fiber optic cable. These cables are used extensively in communications technology. In these cables the light is kept within the cable by TIR, allowing it to travel long distances without leaving the cable.

Mirages are another example. When light passes through layers of air with different temperatures, it can bend (due to different refractive indices) and create the illusion. On hot days, the ground heats the air above it, creating a temperature gradient. Light rays coming from the sky bend in such a way that they appear to come from the surface, creating a mirage, an example of TIR in a natural setting.

Visualization of total internal reflection

Consider a ray of light inside a glass prism. As it approaches the boundary between glass and air at an acute angle of incidence (greater than the critical angle), it is totally reflected back into the glass instead of being refracted. This situation can be represented visually as follows:

incident ray Reflected ray glass Air

Formulas and calculations

While a qualitative understanding of TIR and critical angle is essential, sometimes calculations help clarify these concepts. For example, suppose we know that the refractive index of water is approximately 1.33 and that of air is 1. Using the formula for critical angle:

θc = arcsin(1 / 1.33) ≈ 48.75°

This calculation shows that if light in water falls on the surface at an angle greater than 48.75 degrees, it will be completely reflected back into the water rather than refracted into the air.

Applications in real life

Fiber optics: These are used in telecommunications and internet connections. By bouncing light within a glass or plastic core, they can transfer information efficiently over long distances.

Endoscopes: Medical instruments that use TIR to allow doctors to see inside the human body without invasive surgery.

Periscopes: Devices that use angled mirrors to reflect a light path, allowing you to see objects above or around obstacles.

Conclusion

Total internal reflection and critical angle are fascinating topics that highlight the unique properties of light in different mediums. They have practical applications in the real world and are essential concepts in the study of optics. Understanding these phenomena not only helps us appreciate the science behind technology but also deepens our insight into the natural world.


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Total internal reflection and critical angle

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