Capillarity

Capillarity (or capillary action) is the ability of a liquid to flow in narrow spaces (such as inside a ca- pillary tube) without the assistance of external forces like gravity. This phenomenon occurs due to adhesive forces (attraction between the liquid and the solid surface) and cohesive forces (attraction between the liquid molecules).
Surface tension and capillarity: Higher surface tension leads to greater capillary rise.
E.g., plant water transport, wicking materials like towels, ink pens, and soil moisture.

Types of Capillarity

Capillary Rise: This occurs when the adhesive forces between the liquid and the tube are stronger than the cohesive forces between the liquid molecules. In this case, the liquid rises in the tube. E.g., water rising in a thin glass tube.
Capillary Fall: This happens when the cohesive forces between the liquid molecules are stronger than the adhesive forces between the liquid and the surface of the tube. In this case, the liquid falls in the tube. E.g., mercury in a glass tube.

Viscosity

Viscosity is a measureof a fluid's resistance toflow. It describes how much a fluid resists deformation under shear stress or tensile stress.
Viscosity arises from the internal friction between the layers of the fluid moving relative to each other. Therefore, viscosity reflects the "thickness" or "internal friction" of the fluid.
High viscosity fluids like honey or syrup flow slowly due to high resistance. Low viscosity fluids like water or alcohol flow easily due to low resistance.
Factors affecting viscosity are:
1. Temperature: For liquids, viscosity generally decreases with increasing temperature. For gases, vis- cosity generally increases with increasing temperature.
2. Intermolecular forces: Strong intermolecular forces between fluid molecules lead to higher viscosi- ty.
Types of fluids based on viscosity:

Newtonian fluids: Fluids with a constant viscosity regardless of the applied stress. E.g., water and air.
Non-Newtonian Fluids: Fluids whose viscosity changes with the applied stress or strain rate. E.g., blood and ketchup.

Types of viscosity are:

Dynamic Viscosity: It quantifies the internal resistance of a fluid to flow when an external force is applied.
1. Kinematic Viscosity: It relates dynamic viscosity to fluid density and measures how fast a fluid spreads under gravity.

Flow of Fluids

Laminar Flow or Steady Flow: In laminar flow, the fluid moves smoothly in parallel layers, with no mixing between the layers. This flow type is generally seen at lower velocities and in small, smooth pipes or channels. The velocity of the liquid at different points is uniform and predictable. E.g., a stream with gentle flow.
Turbulent Flow: In turbulent flow, the fluid moves chaotically and irregularly. This flow involves mix- ing, swirling, and eddies. This occurs at higher speeds and when the flow encounters obstacles or rough surfaces. E.g., water flowing rapidly in a river.
Reynolds number:The transition between laminar and turbulent flow is determined by this number.
ð Flow rate: It refers to the volume of fluid passing through a given point in a given time.
ð Critical velocity: The threshold velocity at which fluid flow transitions from laminar to turbulent flow.

Bernoulli's Theorem

Bernoulli's Theorem is a fundamental principle in fluid dynamics that describes the behaviour of a moving fluid. The theorem states, “For an incompressible, non-viscous fluid flowing steadily through a streamline, the total mechanical energy (sum of pressureenergy, kinetic energy, and potential energy) remains constant.” Thisisknown as the conservation of mechanical energy for fluids in motion.
- Implication: As the speed of a fluid increases, its pressure decreases because themechanical energy remains constant.
- Pressure Energy:The energy due to the pressure of the fluid.
- ð Kinetic Energy: The energy due to the motion of the fluid.
- ð Potential Energy: The energy due to the elevation of the fluid.
- - Assumptions in Bernoulli's Theorem:
    1. Incompressible fluid: The fluid's density remains constant throughout the flow.
    2. Non-viscous fluid: The fluid has no internal resistance to flow (no viscosity).
    3. Steady flow: The flow parameters (velocity, pressure, and density) do not change with time.
    4. Along a streamline: Bernoulli’s equation is valid for points along the same streamline of the fluid flow.
    - Applications of Bernoulli’s Theorem:
  1. Airplane wings: The curvedshape of an aeroplanewing creates a difference in airspeed above and below the wing, generating lift.
- Venturi meter: It is used to measure the flow rate of a fluid.

Torricelli's Law

Torricelli's Law states, “The speed of the fluid flowing out of an opening in a tank is proportional to the square root of the vertical distance (height) between the liquid surface and the centre of the opening.”
This law explains that the speed of a fluid exiting an opening depends on the height ofthe fluid above the opening. The greater the height, the faster the fluid will exit due to the influence of gravity.
This principle has applications in various fields, including hydraulics, fluid mechanics, and engineering design, such as in calculating the discharge rate from tanks, designing nozzles, etc.
Assumptions of Torricelli's Law:

Incompressible fluid: The fluid is incompressible, meaning its density remains constant.
Ideal fluid: The fluid is assumed to be an ideal fluid, meaning it has no viscosity (no internal fric- tion). In reality, all fluids have some viscosity.
Steady flow: The flow of the fluid is assumed to be steady, meaning the velocity and pressure at any given point in the fluid remain constant over time.
Small opening: The size of the opening in the tank is assumed to be small compared to the cross- sectional area of the tank itself.
Open tank: The tank is open to the atmosphere with no lid or covering.

Ideal Gas and Ideal Gas Law

Ideal Gas

An ideal gas is a theoretical gas that perfectly follows the ideal gas law, which is an equation describ- ing the behavior of gases under various conditions. The concept ofan ideal gas simplifies real gas be- havior.
Characteristics of an ideal gas are:

Negligible particle size: Gas molecules are point particles with no volume. The actual size of the molecules is negligible compared to the space they occupy.
No intermolecular forces: There are no attractive or repulsive forces between the gas particles, ex- cept during collisions.
Elastic collisions: Collisions between gas particles and with the walls of the container are perfectly elastic, meaning no energy is lost.
Random motion: Gas molecules are in constant, random motion.

Ideal Gas Law

The ideal gas law is expressed as: PV = nRT

Where, P is the pressure of the gas, V isthe volume of the gas, n is the number of moles of the gas, and R is the ideal gas constant (a universal constant).
The ideal gas law is a combination of Boyle's law, Charles's law, Gay-Lussac's law, and Avogadro's law.
Real gases do not perfectly follow the Ideal Gas Law, especially at high pressures and low tempera- tures.

Boyle's Law

Boyle’s law state that at constant temperature, the pressure of a given amount of gas is inversely proportional to itsvolume.

· Mathematically, 𝐏𝐏𝐄𝐄𝐊𝐊𝐌𝐌𝐌𝐌𝐝𝐝𝐄𝐄𝐊𝐊 𝐕𝐕𝐨𝐨 𝐊𝐊𝐇𝐇𝐊𝐊 𝐄𝐄𝐌𝐌𝐌𝐌 ∝ 𝟏𝟏

𝐕𝐕𝐕𝐕𝐕𝐕𝐝𝐝𝐦𝐦𝐊𝐊 𝐕𝐕𝐨𝐨 𝐊𝐊𝐇𝐇𝐊𝐊 𝐄𝐄𝐌𝐌𝐌𝐌

Examples

Breathing: During inhalation, the diaphragm moves down, increasing lung volume and decreasing pressure, allowing air to flow in. During exhalation, lung volume decreases, increasing pressure,and air is pushed out.
Syringes: Pulling the plunger increases volume inside the syringe, reducing pressure and drawing fluid in.

Charles's Law

Charles's law describes the relationship between the volume and temperature of a gas when the pres- sure and amount of gas remain constant.
Charles's law states that at constant pressure, the volume of a given amount of gas is directly propor- tional to its absolute temperature.

· Mathematically, 𝐕𝐕𝐕𝐕𝐕𝐕𝐝𝐝𝐦𝐦𝐊𝐊 𝐕𝐕𝐨𝐨 𝐊𝐊𝐇𝐇𝐊𝐊 𝐄𝐄𝐌𝐌𝐌𝐌 ∝ 𝐀𝐀𝐀𝐀𝐌𝐌𝐕𝐕𝐕𝐕𝐝𝐝𝐊𝐊𝐊𝐊 𝐊𝐊𝐊𝐊𝐦𝐦𝐓𝐓𝐊𝐊𝐄𝐄𝐌𝐌𝐊𝐊𝐝𝐝𝐄𝐄𝐊𝐊 𝐕𝐕𝐨𝐨 𝐊𝐊𝐇𝐇𝐊𝐊 𝐄𝐄𝐌𝐌𝐌𝐌

Examples

Hot air balloons: Heating the air inside the balloon increases its volume, causing the balloon to rise.
Deflating a ball in cold weather: As the temperature decreases, the air inside contracts, reducing the ball's volume.Hot air balloons: Heating the air inside the balloon increases its volume, causing the balloon to rise.
Deflating a ball in cold weather: As the temperature decreases, the air inside contracts, reducing the ball's volume.

Gay-Lussac's Law

Gay-Lussac's law describes the relationship between the pressure and temperature of a gas when the

volume and amount of gas remain constant.

Gay-Lussac's law states thatat constant volume, the pressure of a given amount of gas is directly pro- portional to its absolute temperature.

· Mathematically, 𝐏𝐏𝐄𝐄𝐊𝐊𝐌𝐌𝐌𝐌𝐝𝐝𝐄𝐄𝐊𝐊 𝐕𝐕𝐨𝐨 𝐊𝐊𝐇𝐇𝐊𝐊 𝐄𝐄𝐌𝐌𝐌𝐌 ∝ 𝐀𝐀𝐀𝐀𝐌𝐌𝐕𝐕𝐕𝐕𝐝𝐝𝐊𝐊𝐊𝐊 𝐊𝐊𝐊𝐊𝐦𝐦𝐓𝐓𝐊𝐊𝐄𝐄𝐌𝐌𝐊𝐊𝐝𝐝𝐄𝐄𝐊𝐊 𝐕𝐕𝐨𝐨 𝐊𝐊𝐇𝐇𝐊𝐊 𝐄𝐄𝐌𝐌

Examples

Pressure in a tire: On a hot day, the temperature of the air inside a car tire increases, causing the pressure to rise.
Pressure cookers: As the temperature inside a sealed pressure cooker increases, the pressure of the steam also increases.

Avogadro's Law

Avogadro's law describes the relationship between the volume and the amount (moles) of gas when the

pressure and temperature remains constant.

Avogadro's law states, “Equal volumesof all gases, at the same temperature and pressure, contain the same number of molecules.”This means that at constant temperature and pressure, the volume ofa gas is directly proportional to the number of moles (amount) of the gas.

· Mathematically, 𝐕𝐕𝐕𝐕𝐕𝐕𝐝𝐝𝐦𝐦𝐊𝐊 𝐕𝐕𝐨𝐨 𝐊𝐊𝐇𝐇𝐊𝐊 𝐄𝐄𝐌𝐌𝐌𝐌 ∝ 𝐍𝐍𝐝𝐝𝐦𝐦𝐀𝐀𝐊𝐊𝐄𝐄 𝐕𝐕𝐨𝐨 𝐦𝐦𝐕𝐕𝐕𝐕𝐊𝐊𝐌𝐌 𝐕𝐕𝐨𝐨 𝐊𝐊𝐇𝐇𝐊𝐊 𝐄𝐄𝐌𝐌𝐌𝐌

Examples

Inflating balloons: Adding more air (moles of gas) to a balloon increases its volume, assuming con- stant pressure and temperature.
Breathing: The volume of air in the lungs changes with the number of gas molecules inhaled or ex- haled.

---------- End of Chapter ----------

7. Waves: Mechanical and Electromagnetic

7.1. Waves

A wave is a disturbance or oscillation that travels through space and matter, transferring energy
from one point to another without the transport of matter.

Key Properties of Wave

Wavelength

Wavelength is the distance between two consecutive points in phase on a wave (e.g., crest to crest or trough to trough). It is measured in metres (m).

Amplitude

The maximum displacement of particles from their equilibrium position.
It is essentially the "height" of the wave.
It represents the energy carried by the wave; a larger amplitude indicates higher energy.

Frequency

The frequency of a wave is the number of waves that pass by each second. It is measured in Hertz (Hz).
The formulas for frequency are:

Frequency = Velocity / Wavelength
Frequency = 1 / Time Period

Time Period

The time period of a wave is the time taken for one complete oscillation or cycle. It is measured in
seconds (secs).
It is the inverse of frequency. The formula for the time period of a wave is: Time Period = 1 / Fre- quency

Wave Velocity

Wave velocity is the distance travelled by a wave per unit time. It is the speed at which a wave moves through a medium. It is measured in metres per second (m/s).
The formula for wave velocity is: Wave velocity = Wavelength x Frequency

7.2. Types of Waves

Mechanical Waves

Mechanical waves are disturbances that travel through a material medium (solid, liquid, or gas) by the oscillation of particles within the medium.
Characteristics of mechanical waves are:

Medium requirement: Mechanical waves cannot exist without a medium (e.g., air, water, steel).
Energy transfer: They transfer energy from one point to another without any net movement of particles inthemedium because the medium’s particles oscillate around their equilibrium position.
Restoring force: The disturbed particles of the medium return to equilibrium due to the elasticity of the medium.

E.g., sound waves and seismic waves.

Electromagnetic Waves

Electromagnetic waves are non-mechanical waves that do not require a medium for their propagation; they can travel through a vacuum. They are waves of energy consisting of oscillating electric and magnetic fields perpendicular to each other and to the direction of wave propagation.

Characteristics of electromagnetic waves are:

No medium required: They can travel through empty space, unlike mechanical waves.
Self-propagation: The oscillating electric field generates a magnetic field and vice versa, enabling the electromagnetic wave to propagate.
Constant speed in a vacuum: In a vacuum, electromagnetic waves travel at the speed of light
(3×108m/s).
Energy transfer: Electromagnetic waves carry energy and momentum, which can be transferred to objects upon interaction.

E.g., light waves and radio waves.

7.3. Types of Mechanical Waves

The types of mechanical waves include transverse waves and longitudinal waves.

Transverse Waves

In transverse waves, particles of the medium through which the wave propagates oscillate perpen- dicular to the direction of wave propagation.
The main features of transverse waves are:

Crest: The highest point of the wave.

Trough: The lowest point of the wave.

E.g., waves on a string and seismic S-waves (secondary waves).

Longitudinal Waves

In longitudinal waves, particles of the medium through which the wave propagates oscillate parallel to the direction of wave propagation.
The main features of longitudinal waves are:

Compressions: Regions in the wave where particles are close together.
Rarefactions: Regions in the wave where particles are spread apart.

E.g., sound waves in air and seismic P-waves (primary waves).

7.4. Types of Electromagnetic Waves

The types of electromagnetic waves include radio waves, microwaves, infrared waves, visible light, ultraviolet waves, X-rays, and gamma rays.

Radio Waves

Radio waves are the longest-wavelength (1 mm to 100 km) electromagnetic waves with the lowest frequencies (< 300 GHz) in the electromagnetic spectrum.
Radio waves have low energy compared to other electromagnetic waves.
Applications of radio waves are:

Communication: Radio and television broadcasting, cellular phones, Wi-Fi, Bluetooth, GPS, and satellite communication.
Radar: Used for navigation, weather tracking, and air traffic control.
Medical imaging: Magnetic Resonance Imaging (MRI) and radiotherapy.

Advantages of radio waves are:

Radio waves can travel long distances and penetrate through obstacles like buildings.
Radio waves are easy to produce and detect. They are generated by oscillating charges or currents in antennas.

Limitations of radio waves are:

Radio waves are subject to interference from other electronic devices.
They have limited bandwidth for data transmission compared to higher-frequency waves.

Microwaves

Microwaves are electromagnetic waves with shorter wavelengths (1 mm to 1 m) and higher frequencies (300 MHz to 300 GHz) than radio waves. They have higher energy compared to radio waves.
Applications of microwaves are:

Communication: Satellite communication, mobile phones and Wi-Fi, television broadcasting.
Cooking: Microwave ovens use microwaves to heat food by agitating water molecules.
Radar technology: Used for weather forecasting and air traffic control, detecting speed and loca- tion of objects (e.g., speed radars).
Medical applications: Microwave therapy for cancer treatment.

Advantages of microwaves are:

Microwaves can carry large amounts of data over long distances.
They are highly directional, allowing focused communication.
They are less susceptible to interference compared to radio waves.

Limitations of microwaves are:

Microwaves can be blocked by large obstacles.
They are affected by weather conditions, such as heavy rain.

Infrared

Infrared (IR) waves are electromagnetic waves with wavelengths (700 nm to 1 mm) longer than visible light but shorter than microwaves. The frequency range of infrared waves is 300 GHz to 430 THz. They have higher energy than microwaves but lower than visible light.
Infrared waves are primarily associated with heat and are emitted by all objects with temperatures

above absolute zero.

Applications of infrared waves are:

Thermal imaging: Used in night vision cameras and infrared thermography.
Remote controls: Many remote controls use infrared light to transmit signals.
Communication: Optical fibre communication utilises infrared light.
Heating: Infrared heaters and lamps are used for warmth in homes and industries.
Medical use: Infrared therapy for muscle relaxation and pain relief.
Food processing: Infrared waves are used for drying and cooking food.

Advantages of infrared waves are:

Infrared waves can penetrate smoke, fog, and thin layers of material.
They are efficient in energy transfer (e.g., heating applications).
They are non-invasive and safe for various uses, including medical applications.

Limitations of infrared waves are:

Infrared waves are limited to short-range communication (e.g., remote controls).
They are absorbed by water vapour, which can reduce effectiveness in certain conditions.

Visible Light

Visible light is the portion of the electromagnetic spectrum that the human eye can detect. It allows us to perceive colours and forms the basis of vision and illumination.
The wavelength range of visible light is 380 nm to 700 nm, and the frequency range is 430 THz to 770 THz. They have higher energy than infrared waves but lower than ultraviolet radiation.
Colours of visible light: The visible spectrum consists of seven colours: red, orange, yellow, green, blue, indigo, and violet. Red light has the longest wavelength and lowest energy, while violet light has the shortest wavelength and the highest energy.
Applications of visible light are:

Vision: Enables us to see the world around us.
Photosynthesis: Plants use visible light for photosynthesis.
Illumination: Visible light is used for lighting homes, streets, and workplaces.
Communication: Optical fibre communication uses visible light.
Photography and entertainment: Visible light is essential in cameras, projectors, and visual dis- plays.
Medical applications: Visible light is used in endoscopy, microscopy, and laser surgeries.

Advantages of visible light are:
1. Visible light is essential for life, enabling photosynthesis in plants and vision in humans.
2. It is safe for humans when exposure is moderate.
3. It is versatile with applications in science, art, and technology.
- Limitations of visible light are:
Visible light cannot penetrate through opaque objects.
It has a limited range in certain conditions, such as underwater or in fog.
[UPSC 2020] With reference to the “Visible Light Communication” technology, which of the following statements are correct?
VLC uses electromagnetic spectrum wavelengths 375 to 780 nm.
VLC is known as long-range optical wireless communication.
VLC can transmit large amounts of data faster than Bluetooth.
VLC has no electromagnetic interference.
Select the correct answer using the given code below:
1, 2 and 3 only
1, 2 and 4 only
1, 3 and 4 only
2, 3 and 4 only
Explanation
Visible light communication (VLC) is a wireless method that enables high-speed transmission of data with visible light. This data is transmitted by modulating the intensity of light given off by a light source. The signal is received by a photodiode device that transforms the data into forms that are readable and readily-consumed by end users.
- VLC operates in the visible light portion of the electromagnetic spectrum, which ranges from ap- proximately 375 nm to 780 nm for transmitting data through light signals.
- VLC is categorised as a short-range optical wireless communication technology. The reason for this is that visible light, unlike radio waves, cannot penetrate walls which limits its effective range.
- In VLC, the visible light spectrum offers a higher bandwidth when compared to other electromag- netic spectrums. As a result, it transmits larger volumes of data in a shorter time. In contrast, Blue- tooth typically offers lower speed.
- Since VLC uses visible light instead of radio waves, which has immunity to electromagnetic inter- ference (EMI).
Answer: (c) 1, 3 and 4 only

Ultraviolet Waves

Ultraviolet (UV) waves are electromagnetic waves with wavelengths (10 nm to 400 nm) shorter than vis- ible light but longer than X-rays. They have a frequency range of 7.5×1014 Hz to 3×1016 Hz.
UV waves are invisible to the human eye and are known for their high energy.
Applications of ultraviolet waves are:

Medical use: UV waves are used for sterilising medical equipment (UVC radiation kills bacteria and viruses). They are also used for the treatment of skin conditions like psoriasis.
Disinfection: They are used in water purification systems.
Forensics: They are used for detecting fingerprints and body fluids.
Industrial uses: They are used for curing inks, adhesives, and coatings.

Advantages of ultraviolet waves are:

UV waves are effective in sterilisation and disinfection.
They provide essential vitamin D synthesis when exposed to sunlight in moderation.

Limitations of ultraviolet waves are:

Overexposure to UV radiation can cause skin cancer, sunburns, eye damage (like cataracts), etc.
UV waves have limited penetration through opaque materials.

Types of UV Radiation

UVA (Longwave UV)

Wavelength range ofUVA nm to 00 nm.
Characteristics of UVA are:

UVA has the longest wavelength and lowest energy among UV rays.
It can penetrate deep into the skin's layers.
It is the least harmful among UV rays but contributes to skin ageing, indirect DNA damage and skin cancer.
95% of UV radiation reaching Earth from the Sun is UVA.

UVB (Midwave UV)

Wavelength range of UVB 80 nm to nm.
Characteristics of UVB are:

UVB has higher energy than UVA, but does not penetrate as deeply.
It causes direct DNA damage, sunburn, and skin cancer (including melanoma).
It is partially absorbed by the Earth's ozone layer.
It makes up about 5% of UV radiation reaching Earth from the Sun.
It is essential for vitamin D synthesis in the skin.

UVC (Shortwave UV)

Wavelength range of 89C 00 nm to 80 nm.
- Characteristics of UVC are:
- Shortest wavelength and highest energy among UV rays.
1. UVC is the most harmful form of UV radiation.
2. It is completely absorbed by Earth's atmosphere (ozone layer).
3. It can kill bacteria and viruses, making it useful for sterilisation.
4. It is dangerous for living tissues if exposure occurs (requires safety precautions).

Comparison of UV Radiation Types
Feature	UVA	UVB	UVC
Wavelength Range	315 nm – 400 nm	280 nm – 315 nm	100 nm – 280 nm
Energy Level	Lowest	Moderate	Highest
Penetration	Deep into skin layers	Outer skin layers	Absorbed by atmosphere
Effects on Skin	Ageing, wrinkles, indirect DNA damage	Sunburn, direct DNA damage, skin cancer	Highly harmful to human skin if exposed
Source	Sunlight (95% of UV reach- ing Earth), tanningbeds	Sunlight (5% of UV reach- ing Earth), UV lamps	Artificialsources like germi- cidal lamps, welding arcs
Ozone Ab- sorption	Not absorbed	Partially absorbed	Completely absorbed
Beneficial Ef- fects	Stimulates pigment produc- tion	Aids in vitamin D synthe- sis	Sterilisation and disinfection
Harmful Ef- fects	Premature ageing, skin damage	Skin cancer, sunburn	Harmful to living tissues
Protection	Broad-spectrum sunscreen, protective clothing	Sunscreen, hats, shade	Controlled environments only

X-Rays

X-rays are a type of electromagnetic radiation with wavelengths (0.01 nm to 10 nm) shorter than ultra- violet light and longer than gamma rays. They have high energy and are capable of penetrating most materials, making them invaluable in medical and industrial applications.
- Application of X-rays are:

Medical imaging: Diagnosing fractures, infections, and tumors through X-ray radiography. CT scans for detailed cross-sectional images of the body also use X-rays.
Industrial use: X-rays are used for inspecting welds, detecting flaws in materials, and security screening in airports.
Scientific research: It is used for studying atomic structures using X-ray crystallography.

Art restoration: X-rays detect underlying layers and authenticity in paintings.
- The advantage of X-rays is that they are non-invasive imaging of internal structures.
- The limitation of X-rays is that overexposure can cause damage to living tissues and increase cancer risk. Protective measures (e.g., lead aprons and shields) are required to minimise radiation exposure.

Gamma Rays

Gamma Raysare the most energetic form of electromagnetic radiation. They havethe shortest wave- lengths (<10-12 m) and the highest frequencies in the electromagnetic spectrum.
- The sources of gamma rays are:

Radioactive decay (e.g., gamma decay from isotopes like Cobalt-60)
Nuclear reactions (such as fusion and fission)
Cosmic phenomena (including supernovae and black holes)
- Applications of gamma rays are:
Medical uses: Gamma rays are used in radiation therapy to destroy cancer cells. They are also used for diagnostic imaging like PET scans.
Industrial uses: Gamma rays are used for non-destructive inspection of welds and structural integ- rity.
Sterilisation: Gamma rays are used for sterilising medical equipment and food.
Scientific research: Gamma rays are used for radioactive dating and analysis.
- The advantage of gamma rays is that they can penetrate most materials, including human tissue.
- The disadvantage of gamma rays is that they can cause cell mutations and increase cancer risk over time. High dose exposure can cause acute radiation sickness, severe tissue damage, and potential death.

Features	Radio Waves	Microwaves	Infrared Waves	Visible Light	Ultraviolet (UV) Rays	X-Rays	Gamma Rays
Wavelength range	1 mm to 100 km	1 mm to 1 cm	700 nm to 1 mm	400 nm to 700 nm	10nm to 400 nm	0.01 nm to 10 nm	< 0.01 nm
Frequency range	< 300 GHz	300MHz to 300GHz	300GHz to 430 THz	430 THz to 750 THz	750 THz to 30PHz	30PHz to 30EHz	> 30 EHz
Energy	Lowest	Low	Moderate	Moderate	High	Very high	Highest
Penetration	Verylow	Low	Low	Visible to the human eye	Moderate	High	Very high
Sources	Antennas,stars	Radar, ovens,	Sun,	Sun, artificial	Sun, UV	X-ray	Radioac-

		cosmic sources	heaters, warm objects	lightsources	lamps	ma- chines, stars	tive decay, cosmic events
Applica- tions	Communica- tion, broadcast- ing	Cooking, radar, communica- tion	Remote controls, night vi- sion	Illumination, photog- raphy	Sterilisa- tion, vita- min D syn- thesis	Medical imaging, security	Cancer treatment, research
Effects on Humans	Minimal	Heating of tis- sues	Skin warming, burns	Enables vi- sion	Sunburn, DNA dam- age	Cell damage, cancer risk	Severe tis- sue dam- age, radia- tion sick- ness
Protection	No shielding needed	Insulation, dis- tance	Insula- tion, shielding	None need- ed	Sunscreen, clothing	Lead shielding	Lead or thick con- crete shielding

---------- End of Chapter ----------

8. Light and Optics

Light is a form of energy which travels as an electromagnetic radiation that is visible to the human eye and is responsible for the sense of sight.

8.1. Characteristics of Light

Dual Nature (Wave-Particle Duality)

Dual nature (wave-particle duality): Light behaves as a wave, showing properties like reflection, re- fraction, diffraction, and interference. Light also behaves as a particle (photon) in phenomena like the photoelectric effect.
- Electromagnetic wave: Light is a transverse wave consisting of oscillating electric and magnetic fields perpendicular to each other and the direction of propagation.
- Speed of light: In a vacuum, light travels at a constant speed of 3×108 m/s. Light slows down in denser media, such as glass or water.

Wavelength and frequency relationship: The speed of light is related to its wavelength and frequency as: Speed of light = Wavelength x Frequency
Spectrum: The visible spectrum ranges from 400nm (violet) to 700nm (red).

8.2. Reflection of Light

Reflection of lightis the phenomenon where lightrays strike a surface and bounce back. This process is responsible for many optical effects, including the formation of images in mirrors and the appear- ance of objects.
Key terms of reflection of light are:

Incident ray: The incoming ray of light.
Reflected ray: The ray of light that bounces back from the surface.
Normal: An imaginary line perpendicular to the surface at the point where the light ray strikes.
Angle of incidence: The angle between the incident ray and the normal.
Angle of reflection: The angle between the reflected ray and the normal.

Laws of Reflection

First Law of Reflection: The angle of incidence is equal to the angle of reflection.
Second Law of Reflection: The incident ray, the reflected ray, and the normal to the surface all lie in the same plane.

Types of Reflection

Regular Reflection (Specular Reflection)

Regular reflection occurs when light reflects off a smooth, shiny surface, such as a mirror or still water.
The reflected rays are parallel, and a clear image is formed.
E.g., reflections in a plane mirror.

Irregular Reflection (Diffuse Reflection)

Irregular reflection occurs when light strikes a rough or uneven surface.
The reflected rays scatter in many directions, and no clear image is formed.
E.g., reflection from a wall or unpolished surface.

8.3. Mirrors

A mirror is a smooth surface that reflects light, forming an image of whatever is in front of it.
Key concepts associated with mirrors are:

Pole: The geometric centre of the reflecting surface of the mirror.
Centre of curvature: The centre of the sphere of which the mirror forms a part.

Radius of curvature: The distance between the pole and the centre of curvature.
Principal axis: A straight line passing through the pole and the centre of curvature.
Principal focus: The point on the principal axis where parallel rays of light incident on the mirror converge (concave mirror) or appear to diverge (convex mirror) after reflection.
Focal length: The distance between the pole and the principal focus.
Aperture: The effective diameter of the reflecting surface of the mirror.
- The mirror equation relates the focal length, the object distance (distance from the mirror to the ob- ject), and the image distance (distance from the mirror to the image):
𝟏𝟏
𝑭𝑭𝑭𝑭𝑭𝑭𝑭𝑭𝑭𝑭 𝑭𝑭𝑻𝑻𝒍𝒍𝒈𝒈𝒍𝒍𝒍𝒍

𝟏𝟏
= +
𝑰𝑰𝑻𝑻𝑭𝑭𝒈𝒈𝑻𝑻 𝒅𝒅𝒅𝒅𝒅𝒅𝒍𝒍𝑭𝑭𝒍𝒍𝑭𝑭𝑻𝑻

𝟏𝟏
𝑶𝑶𝑶𝑶𝑶𝑶𝑻𝑻𝑭𝑭𝒍𝒍 𝒅𝒅𝒅𝒅𝒅𝒅𝒍𝒍𝑭𝑭𝒍𝒍𝑭𝑭𝑻𝑻

8.4. Types of Mirrors

Plane Mirrors

Plane mirrors have a flat surface.
- Properties of an image formed by plane mirrors:

The image is virtual, upright, and laterally inverted (left-right reversal).
The image size is the same as the object size.
The image is formed behind the mirror.

The image distance is equal to the object distance.
- Uses: Everyday mirrors (bathroom, makeup, etc.), telescopes, and periscopes.

Concave Mirrors (Converging Mirror)

Concave mirrors are curved inward (like the inside of a spoon).
- Reflection: In concave mirrors, parallel rays of light converge after reflection.
- Image formation: They can form real or virtual images, depending on the object’s position relative to the focal point.
- Uses: Reflecting telescopes, flashlights, shaving mirrors, and satellite dishes.

Images Formed by a ConcaveMirror
Position of Object	Position of Image	Nature of Image	Orientation	Size
At infinity	At the focus	Real	Inverted	Highly dimin- ished
Beyond the centre of curva- ture	Between the centreof cur- vature and focus	Real	Inverted	Diminished
At the centre of curvature	At the centreof curvature	Real	Inverted	Same size
Between the centre of curva- ture and focus	Beyond the centreof cur- vature	Real	Inverted	Magnified
At the focus	At infinity	Real	Inverted	Highly magni- fied
Between the focus and the pole of the mirror	Behind the mirror	Virtual	Upright	Magnified

Convex Mirror (Diverging Mirror)

Convex mirrors are curved outward (like the back of a spoon).
- Reflection: In convex mirrors, parallel rays of light diverge after reflection.
- Image formation: They always form virtual, upright, and reduced images. The image is always small- er than the object.
- Uses: Vehicle side mirrors, security mirrors, and traffic mirrors for safety and wide coverage.

Magnification

The magnification produced by a mirror is given by the ratio of the image height to the object height or equivalently, the ratio of the image distance to the object distance:

M𝐌𝐌𝐄𝐄𝐊𝐊𝐊𝐊𝐨𝐨𝐊𝐊𝐊𝐊𝐌𝐌𝐊𝐊𝐊𝐊𝐕𝐕𝐊𝐊 =

If m>1, the image is magnified.

𝐈𝐈𝐦𝐦𝐌𝐌𝐄𝐄𝐊𝐊 𝐇𝐇𝐊𝐊𝐊𝐊𝐄𝐄𝐇𝐇𝐊𝐊

=

𝐎𝐎𝐀𝐀𝐎𝐎𝐊𝐊𝐊𝐊𝐊𝐊 𝐇𝐇𝐊𝐊𝐊𝐊𝐄𝐄𝐇𝐇𝐊𝐊

𝐈𝐈𝐦𝐦𝐌𝐌𝐄𝐄𝐊𝐊 𝐝𝐝𝐊𝐊𝐌𝐌𝐊𝐊𝐌𝐌𝐊𝐊𝐊𝐊𝐊𝐊

𝐎𝐎𝐀𝐀𝐎𝐎𝐊𝐊𝐊𝐊𝐊𝐊 𝐝𝐝𝐊𝐊𝐌𝐌𝐊𝐊𝐌𝐌𝐊𝐊𝐊𝐊𝐊𝐊

8.5. Types of Images

There are two primary types of images formed by mirrors: real images and virtual images.

Real Images

A real image is formed when light rays actually converge after reflecting from a mirror.
- Characteristics of a real image:

The image is inverted (upside down).
It is reduced or magnified in size, depending on the distance from the mirror.
It can be captured or projected on a screen.

Virtual Images

A virtual image is formed when light rays appear to diverge after reflecting from the mirror, but no actual convergence occurs. The image appears to be formed behind a mirror, but, in reality, the image is not present there.
- Characteristics of a virtual image:

The image is upright (right-side up).
It cannot be captured or projected on a screen; it can only be seen by looking into the mirror.

8.6. Refraction of Light

Refraction of light is the bending of light as it passes from one medium to another with a different refractive index. This bending occurs due to the change inthe speed of light in different media.
Key terms of refraction of light are:

Incident ray: The ray of light that strikes the surface of a medium. It is the incoming ray approach- ing the boundary between two media.
Refracted ray: The ray of light that passes into the second medium and bends at the boundary due to a change in speed.
Angle of incidence: The angle at which the light ray strikes the boundary between the two media.
Angle of refraction: The angle at which the light ray bends as it enters the second medium.
Normal: An imaginary line perpendicular to the surface at the point where the light ray strikes.

Applications of refraction:

Lenses: Used in eyeglasses, cameras, and microscopes.
Prism and Dispersion: Separation of white light into its spectrum.
Mirages: Optical phenomena caused by refraction in air layers of different densities.
Fiber Optics: Transmission of light signals through total internal reflection.

Characteristics of Refraction

Change in speed: Light travels fastest in a vacuum. Light slows down in a denser medium and speeds up in a rarer medium.
Direction of bending: Light bends towards the normal when it enters a denser medium. Light bends
away from the normal when it enters a rarer medium.
No refraction: If the light ray enters perpendicular to the surface (along the normal), it does not bend.
Wavelength and frequency: The wavelength of light changes during refraction, but the frequency re- mains constant.

Laws of Refraction

First Law of Refraction: The incident ray, refracted ray, and normal all lie in the same plane. • Second Law of Refraction (Snell's Law): The ratio of the sine of the angle of incidence (�) to the sine of the angle of refraction (�) is constant for a given pair of media. Here, constant is the refractive index of the second medium relative to the first medium. sin � sin � = ��

The refractive index of a medium quantifies how much light bends or changes direction when enter- ing that medium from another. It is defined as the ratio of the speed of light in a vacuum to the speed of light in a given medium.

The formula is: Refractive index = Speed of light in a vacuum / Speed of light in the medium

Refractive Index Values for Common Materials
Material	Refractive Index
Vacuum	1.000
Air	1.0003
Water	1.33
Glass (Typical)	1.5
Diamond	2.42

Types of Refractive Index

Absolute Refractive Index: It is the refractive index of a medium relative to a vacuum or air. The for- mula is: Refractive index = Speed of light in a vacuum / Speed of light in the medium
Relative Refractive Index: It is the refractive index of one medium relative to another. The formula is:

Relative refractive index = Refractive index of medium 2 / Refractive index of medium 1

Total Internal Reflection

Total internal reflection is a phenomenon that occurs when light waves are completely reflected back into a medium instead of refracting into another medium. It happens when light travels from a denser medium to a less dense medium at an angle greater than the critical angle.
Critical angle: It is theangle of incidence in the denser medium forwhich the angle of refraction in the
rarer medium is 0.

E.g., diamond sparkle, prism, mirages, and fibre optics.

Mirage

A mirage is an optical phenomenon caused by the refraction of light due to temperature gradi- ents in the atmosphere. It creates an illusion where distant objects appear displaced, inverted, or even as if they are floating, often resembling water on a hot surface.

Types of Mirages

Inferior Mirage

Inferior mirage is commonly seen on hot surfaces, such as roads or deserts.
The image appears below the actual object, often looking like a pool of water.

Superior Mirage

Superior mirage occurs in colder conditions, often over water.
The image appears above the actual object, caused by light bending due to cold air trapped be- neath warm air (temperature inversion).
Processes Involved in Mirage Formation
Temperature Gradient:
A mirage occurs when there is a significant difference in air temperature between layers close to the ground.
- Inferior Mirage: The ground is hotter than the air above it.
- Superior Mirage: The ground or surface is colder, and a layer of warm air lies above cooler air (temperature inversion).
Variation in Air Density
The air's refractive index changes with temperature:
Hot air is less dense and has a lower refractive index.
Cold air is denser and has a higher refractive index.
- This variation in density causes light rays to bend as they travel through the atmosphere.
Refraction of Light
Refraction occurs when light passes between two mediums with different refractive indices.
- In a mirage, light travels through layers of air with continuously changing densities. So, as light passes from denser (cool) air to less dense (hot) air or vice versa, its speed and direction change, causing the ray to bend.
Bending of Light Rays
The curvature of light rays depends on the temperature gradient:
Inferior Mirage: Light bends upwards as it moves from cooler, denser air to warmer, less dense air near the ground.
Superior Mirage: Light bends downwards as it moves from warmer, less dense air to cooler, denser air below.
Total Internal Reflection
In cases where the temperature gradient is steep, light rays can undergo total internal reflection
at the boundary between layers, creating a mirror-like effect.
Perception by the Observer:
The human brain assumes light travels in straight lines. When observing refracted light rays, the brain interprets the displaced rays as coming from a different location, creating an illusion:
1. Inferior Mirage: The object appears below its actual position, often as a reflection resembling water.
2. Superior Mirage: The object appears above its actual position, sometimes inverted or distorted.

8.7. Lens

A lens is a transparent optical device made of glass or other transparent materials, designed to re- fract (bend) light to focus or disperse it. Lenses are widely used in optical instruments such as eye- glasses, microscopes, telescopes, and cameras.
- Primary types of lenses are: concave lenses and convex lenses.

Key concepts associated with lenses:

Principal axis: The straight line passing through the centre of the lens and perpendicular to the sur- faces of the lens.
Optical Centre: The point at the centre of the lens where light rays passing through do not bend.
Focus: The point where light rays converge or appear to diverge after passing through the lens.
1. For convex lenses: The focal point is real and on the opposite side of the light source.
2. For concave lenses: The focal point is virtual and on the same side as the light source.
Focal length: The distance between the optical centre and the focus.
1. For convex lenses: The focal length is positive.
2. For concave lenses: The focal length is negative.
Lens type: Lenses can be convex (converging) or concave (diverging).

Concave Lens

Power of a Lens

The power of a lens refers to its ability to bend (refract) light and bring it to focus. It is measured as the reciprocal of the focal length of the lens in meters.
The formula is: Power of the lens = 1 / Focal length of the lens
The power of a lens is measured in dioptres (D).

Convex Lens

F1 and F2: Represent the two principal foci of the lens, located on opposite sides.

ð 2F1 and 2F2: Represent points twice the focal length from the lens centre.

F1 and F2: Represent the two principal foci of the lens, located on opposite sides.

ð 2F1 and 2F2: Represent points twice the focal length from the lens centre.

8.8. Dispersion of Light

Dispersion of light refers to the phenomenon where white light separates into its constituent colours (red, orange, yellow, green, blue, indigo, and violet) when it passes through a transparent medium with varying refractive indices for different wavelengths.

Examples

Prism: When white light passes through a glass prism, it splits into a spectrum of colours.
Rainbows: Water droplets in the atmosphere act as natural prisms, causing sunlight to disperse into a colourful arc.

Principles of Dispersion of Light

Dependence of refractive index on wavelength: The refractive index of a material varies with the

wavelength of light.

Shorter wavelengths (like violet) have a higher refractive index and bend more.
Longer wavelengths (like red) have a lower refractive index and bend less.

Separation of colours: White light, a mixture of all visible wavelengths, splits into its component col- ours (spectrum) when it passesthrough a medium such as a prism. This is because each wavelength re- fracts at a different angle, producing a continuous spectrum of colours.
Material dispersion power: The dispersion power of a material indicates its ability to separate light into its constituent colours. Materials with a high dispersion power, like flint glass, produce a more widely spread spectrum compared to materials with lower dispersion power, like crown glass.
Chromatic dispersion: Chromatic dispersion is the phenomenon where light waves of different wavelengths travel at different speeds within a medium, leading to varying degrees of bending.
Angle of deviation: The deviation of each colour depends on its wavelength. Violet light deviates the most, while red light deviates the least in a prism.

Rainbow

A rainbow is a natural optical phenomenon resulting from the interaction of sunlight with water droplets in the atmosphere. It is caused by refraction, internal reflection, and dispersion oflight within the droplets, producing a spectrum of collars in the form of a circular arc.
- The rainbow consists of seven colours arranged in the following order: red (outermost), orange, yel- low, green, blue, indigo and violet (innermost).

Formation of a Rainbow

Refraction: When sunlight enters a water droplet, it slows down and bends due to a change in medi- um (air to water).
1. Dispersion: The light separates into its constituent colours (spectrum) because each colour has a dif- ferent wavelength and refracts at a slightly different angle.
2. Internal Reflection: The light reflects off the inside surface of the water droplet.
3. Refraction Again: As the light exits the droplet, it refracts again, bending further and enhancing the separation of colours.
4. [UPSC 2014] Rainbow is produced when sunlight falls on drops of rain. Which of the following physical phenomena are responsible for this?
  1. Dispersion
    1. Refraction
      Internal reflection
  Select the correct answer using the codes given below.
  1. 1 and 2 only
  2. 2 and 3 only
  3. 1 and 3 only
  4. 1, 2 and 3
  Explanation
  - When sunlight passes through a raindrop, it undergoes refraction, dispersion, and internal reflec- tion. All three processes work together to produce a rainbow.
  Answer: (d) 1, 2 and 3
  [UPSC 2014] Consider the following phenomena:
  1. Size of the sun at dusk
  2. Colour of the sun at dawn
  3. Moon being visible at dawn
6. Twinkle of stars in the sky
7. Polestar being visible in the sky
9. Which of the above are optical illusions?
10. 1, 2 and 3
11. 3, 4 and 5
12. 1, 2 and 4
13. 2, 3 and 5
15. Explanation
17. Size of the sun at dusk: The sun appears larger near the horizon due to atmospheric refraction, an optical illusion.
  1. Colour of the sun at dawn: The sun appears red or orange at dawn because of the scattering of shorter wavelengths of light (blue and violet) by the atmosphere, creating an illusion of colour.
  2. Moon being visible at dawn: This is not an optical illusion; the moon is visible depending on its po- sition relative to the Earth and the Sun.
  3. Twinkle of stars in the sky: This is an optical illusion caused by the Earth's atmosphere, which causes the light from stars to refract and appear to twinkle.
  4. Polestar being visible in the sky: The polestar's visibility is not an illusion; it remains relatively fixed in the sky.
18. Answer: (c) 1, 2 and 4

8.9. Scattering of Light

Scattering of light refers to the process by which small particles in a medium cause light rays to de- viate from their straight path. This phenomenon occurs when light interacts with particles in the at- mosphere, such as dust, gas molecules, or water droplets, and gets dispersed in different directions.
- Types of scattering are: Rayleigh scattering, Mie scattering and non-selective scattering.

Rayleigh Scattering

Rayleigh scattering is the scattering of light by particles that are much smaller than the wavelength of the light. This type of scattering occurs in all directions and is highly dependent on the wavelength of the light.

Examples of Rayleigh Scattering

Blue Sky

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