12th Physics Full Syllabus

Overview of the Video

• The video is a comprehensive lecture covering the entire Class 12th Physics syllabus, from Chapter 1 to Chapter 14
• The video aims to provide a thorough understanding of the concepts and is recommended to be watched from start to finish to avoid missing any crucial information
• The presenter encourages viewers to like and share the video if they find it helpful

Additional Resources and Courses

• A PDF of the notes presented in the video is available for download on the Arvind Academy app
• The app's store section contains Class 12th free PDFs that are unlocked and available for download
• The presenter also introduces two courses: "Drona 2.0" and "12th Sampoorna"
• Drona 2.0 includes NCERT exercise video solutions, examples, past year question video solutions, chapter-wise assignments, MCQs, assertion reasoning, and case studies in video format
• "12th Sampoorna" focuses on numerical problems and includes past year questions, NCERT exercises, and example video solutions, totaling 771 videos
• Special offers of these courses are available via the Arvind Academy app

Electric Charge

• Electric charge is an intrinsic property of matter, such as electrons and protons
• Electrons are negatively charged, and protons are positively charged
• Electric charge is a scalar quantity

Fundamental Law of Electrostatics

• Like charges repel each other
• Unlike charges attract each other

Mass Change and Electric Charge

• A material that is negatively charged has gained electrons, increasing its mass
• A material that is positively charged has lost electrons, decreasing its mass

Basic Properties of Charges

• There are three important properties of charges:
  • Additivity
  • Quantization
  • Conservation

Additivity of Charge

• The total charge of a system is the algebraic sum of all the individual charges, considering their signs

Quantization of Charge

• Charge is transferred from one body to another in integral multiples of the elementary charge (electron)
• The amount of charge transferred is given by q = ne, where n is an integer (0, ±1, ±2, ...)
• It is impossible to transfer a fraction of an electron

Conservation of Charge

• In an isolated system, the total charge remains constant

Pair Production

• Pair production is the phenomenon where energy (gamma rays) is converted into an electron and a positron
• A positron has the same mass as an electron but carries a positive charge (+e)
• Net charge remains zero

Annihilation of Matter

• Annihilation of Matter states that when an electron and a positron collide, they annihilate each other and convert into radiation (energy)
• The net charge before and after is zero

Methods of Charging

• Charging can be done by:
  • Friction
  • Conduction

Charging by Friction

• Charging by friction involves rubbing two objects together, causing electrons to transfer from one to the other
• Example: Rubbing a comb through dry hair and then holding it near small pieces of paper will cause the paper to be attracted to the comb.

Charging by Conduction

• Charging by conduction happens when a charged object is placed in contact with an uncharged object, resulting in charge transfer until both objects have the same potential

Charging by Induction (Out of Syllabus)

• Charging by induction involves using a charged object to induce a charge distribution in another object without direct contact
• The process involves polarization and grounding, resulting in the initially neutral object acquiring a charge opposite to that of the charging object

Coulomb's Law

• Coulomb's law quantifies the force between two point charges
• The force is given by: f = (1 / 4πε₀) * (q1q2 / r²) were:
  • q1 and q2 are the magnitudes of the charges
  • r is the distance between the charges
  • ε₀ is the permittivity of free space
  • 1 / 4πε₀ ≈ 9 × 10⁹ Nm²/C²

Coulomb's Law Constants

• The constant 1 / 4πε₀ has a value of 9 × 10⁹ with appropriate SI units
• The permittivity of free space, ε₀, has a value of 8.85 × 10⁻¹² with appropriate units

Vector Form of Coulomb's Law

• The force between charges is a vector quantity with both magnitude and direction
• F₂₁ represents the force on charge 2 due to charge 1

Permittivity

• Permittivity (ε) is the property of a medium that affects the electric force between charges
• Relative permittivity (εᵣ) or dielectric constant (k) is the ratio of the electric force in vacuum to that in the medium
• f_medium = f_vacuum / k

Relative Permittivity/Dielectric Constant

• Relative permittivity (εᵣ) or dielectric constant (k) is a dimensionless quantity
• εᵣ = Force in vacuum / Force in medium
• The dielectric constant for vacuum is 1
• The dielectric constant for air is approximately 1
• The dielectric constant for water is approximately 80, meaning the electric force is reduced 80 times when charges are placed in water

Superposition Principle

• The net force on a charge due to multiple other charges is the vector sum of the individual forces

Electric Field

• An electric field exists in the space around a source charge
• A test charge placed in an electric field experiences a force
• Electric field (e) is defined as the force per unit charge: e = f / q₀
• For precision, q₀ should approach zero to minimize disturbance of electric field

Electric Field due to a Point Charge

• The electric field due to a point charge q at a distance r is given by: e = (1 / 4πε₀) * (q / r²)
• Important Points: Electric field ~ 1/r²

Electric Lines of Force

• Electric lines of force are imaginary lines representing the electric field
• The tangent to an electric field line at any point gives the direction of the electric field

Properties of Electric Field Lines

• Continuous and smooth curves
• Start from positive charges and end at negative charges
• Do not form closed loops
• Tangent at any point gives the direction of the electric field
• Never intersect
• Always perpendicular to the surface of a charged conductor
• Contract lengthwise (attraction)
• Expand laterally (repulsion)
• Electric field inside a conductor is always zero

Electric Field of a Plane Conductor

• Electric field points at 90 degree emerging away from the surface

Electric Field due to Charge Ring

• Electric field on the axis of charged ring:
  • e = (1 / 4πε₀) * (qr / (r² + r²) ^ (3/2))
  • Where r is the distance from the center of the ring
  • Where is R is the Radius of the radius

Electric Dipole

• An electric dipole consists of two equal and opposite charges (+q and -q) separated by a small distance (2l)
• Dipole moment (p) is a measure of the strength of the dipole: p = q * 2l
• Dipole moment is a vector quantity directed from -q to +q

Ideal Electric Dipole

• Length approaching 0, while dipole moment is non-zero

Electric Field vs Point Charge

• Ideal dipole field is inversely proportional to r³ (1/r³)
• Point change is inversely proportional to r² (1/r²)

Electric Field at Axial Point

• Electric field at an axial point due to a dipole: e = (1 / 4πε₀) * (2p / r³)
• Same direction to dipole moment

Electric Field at Equatorial Point

• Electric field at an equatorial point due to a dipole: e = (1 / 4πε₀) * (p / r³)
• Apposite direction to dipole moment

Torque on a Dipole in a Uniform Electric Field

• The torque (τ) on a dipole in a uniform electric field is given by: τ = pe sinθ
  • Where τ = p x e Torque is maximum when θ = 90° (perpendicular) Stable Equilibrium: θ = 0° (Dipole aligned with the field) Unstable Equilibrium: θ = 180° (Dipole anti-aligned with the field)

Electric Field Strength Indication

• In a region with electric field lines, stronger electric field is indicated by higher density of electric field lines

Area Vector

• Represents the direction of a surface Open surface: perpendicular to surface Closed surface: outward normal to the surface

Electric Flux

• The no. of electric field lines passing through a surface, defined as * Φ = E · S = ES cos θ
• Electric flux is a scalar quantity
• In non-uniform electric fields, flux is calculated by Φ = ∫E · dS### Gauss's Law
• The net flux through a closed surface is equal to the total charge inside the surface divided by ε₀ (permittivity of free space).
• Mathematically, this is expressed as ∮ E ⋅ ds = Q_inside / ε₀, where:
  • ∮ E ⋅ ds is the surface integral of the electric field over the closed surface.
  • Q_inside is the total net charge enclosed by the Gaussian surface.
  • ε₀ is the vacuum permittivity.
• This law is valid only for closed surfaces, regardless of their shape (e.g., irregular, straight).
• When calculating the electric field (E) in Gauss's law, all charges (both inside and outside the Gaussian surface) contribute to the field.
• When calculating the total charge (Q_inside), only the charges inside the Gaussian surface are considered.
  • Net charge might be represented as Q1 - Q2 + Q3.
• If the medium surrounding the charge changes, the permittivity (ε₀) in the formula is replaced with the absolute permittivity (ε), where ε = k * ε₀ (k is the dielectric constant of the medium).

Applications of Gauss's Law

• Infinitely Long Straight Wire:

  • Electric field (E) at a distance (r) from the wire: E = λ / (2π ε₀ r), where λ linear charge density (charge per unit length).
  • The formula is derived using a cylindrical Gaussian surface.
  • Remember the graph of E vs r.

• Infinitely Large Charged Sheet:

  • Electric field (E) from the sheet: E = σ / (2 ε₀), where σ is the surface charge density (charge per unit area).
  • E is independent of distance (r) from the sheet.
  • For a positively charged sheet, the electric field points away from the sheet.
  • For a negatively charged sheet, the electric field points towards the sheet.

Electric Field Between Two Charged Conducting Plates

• Consider two charged conducting plates with surface charge densities σ₁ and σ₂, where σ₁ > σ₂.
• The electric field between the plates: E = (σ₁ - σ₂) / (2 ε₀).
• The electric field in regions outside the plates is calculated by adding the electric fields due to each plate.

Uniformly Charged Thin Spherical Shell

• Considers a hollow, conducting sphere (like a copper football).
• Outside the shell (r > R):
  • Electric field: E = 1 / (4π ε₀) * Q / r², resembling a point charge at the center.
• At the surface (r = R):
  • Electric field: E = 1 / (4π ε₀) * Q / R² = σ / ε₀ (where σ is the surface charge density).
• Inside the shell (r < R):
  • Electric field: E = 0.
• Inside the shell, electric potential isn't zero and remains constant, equal to its value on the surface.
• Remember the graph of E vs r for inside the shell, the surface, and the outside.

Potential Difference

• The work done in moving a unit positive charge from one point to another against the electrostatic force, per unit charge.
• Mathematically: V_B - V_A = W / q₀.
• SI unit: Volt (V).
• Scalar quantity (no direction).

Electric Potential

• Similar to potential difference, but the reference point (A) is at infinity.
• Potential at infinity is considered zero.
• SI unit: Volt (V).

Electric Potential Due to a Point Charge

• Potential (V) at a distance (r) from a point charge (Q): V = 1 / (4π ε₀) * Q / r.
• Scalar quantity.
• Q's sign is important (positive or negative).

Electric Potential Due to an Electric Dipole

• Axial Position:
  • Potential (V) at a distance (r) from the center of the dipole: V = 1 / (4π ε₀) * p / (r² - a²).
  • For short dipoles, the formula simplifies to: V = 1 / (4π ε₀) * p / r².
  • p = dipole moment (2qa, where q is the magnitude of charge and 2a is the separation between charges).
• Equatorial Position:
  • Potential (V): V = 0.
  • The distances from -q and +q are the same to equatorial positions and are bisected 90° from the midpoint.

Differences Between Dipole Potential and Single Charge Potential

• Dipole potential depends on the angle between the point of observation and the dipole axis.
  • Change in distance or angle affects voltage.
• Single charge potential is cylindrically symmetric while dipole potential is spherically symmetric.
• Dipole potential varies proportional to 1/r², while single charge potential is proportional to 1/r.

Electric Potential Due to a System of Point Charges

• Total potential at point P due to multiple charges is the algebraic sum of potentials due to each charge: V_net = V₁ + V₂ + V₃ +....

Uniformly Charged Spherical Shell

• Outside the shell (r > R):
  • Potential (V): V = 1 / (4π ε₀) * Q / r (behaves like a point charge).
• At the surface (r = R):
  • Potential (V): V = 1 / (4π ε₀) * Q / R.
• Inside the shell (r < R):
  • Potential (V): V = 1 / (4π ε₀) * Q / R.

Relation Between Electric Field and Electric Potential

• E = -dV/dr.
• Electric field direction is in the direction of decreasing potential.

Equipotential Surfaces

• Surface with a constant potential at every point.
• No work is done in moving a charge along an Equipotential surface.
• Electric field is always perpendicular.
• Equipotential surfaces are closer together where the electric field is stronger.
• Equipotential surface never intersect.
• Remember diagrams of Equipotential surfaces.

Electric Potential Energy

• Work done assembling charges from infinity.
• Two-charge system: U = 1 / (4π ε₀) * Q₁Q₂ / r (where r is the distance between charges).

Electric Dipole in a Uniform Electric Field

• Work Done = Potential energy = pE (cos θ₁ - cos θ₂).
• Potential energy (U) = -p ⋅ E = -pE cos θ.
  • θ is considered as the angle for 90°.

Special Cases for Dipole in Electric Field

• Stable Equilibrium:
  • θ = 0° (dipole aligns with the electric field).
  • Minimum potential energy (U = -pE).
• Zero Potential Energy:
  • θ = 90°.
• Unstable Equilibrium:
  • θ = 180° (dipole opposes the electric field).
  • Maximum potential energy (U = +pE).

Free and Bound Charges in Metals

• Free charges (electrons) can move freely within the metal.
• Bound charges (ions) are fixed in the lattice and cannot move.

Behavior of Conductors in Electrostatic Fields

• Electric field inside a conductor is always zero.
• Electric field just outside the surface is perpendicular.
• Any charge given to a conductor resides entirely on its outer surface.
• The electric potential is constant throughout the volume of the conductor and on its surface.
• Electric field (E) at the surface of the conductor: E = σ / ε₀ * n, where n is a unit vector normal to the surface.
• Electric field inside a cavity within a conductor is zero.
• Electrostatic Shielding (Faraday Cage): Using a conductor to shield sensitive devices from external electric fields by creating a field-free region inside the conductor.

Dielectrics

• Dielectrics are insulators.
• Do not allow the flow of charge but permit electrostatic forces.
• Polar dielectrics: Molecules have permanent dipole movements (e.g., HCl, H₂O).
• Non-polar dielectrics: Molecules do not have permanent dipole moments (e.g., H₂, CO₂).
• Polarization: When an external electric field is applied to a dielectric, dipoles are induced or aligned, which is called polarization.
• The presence of a dielectric reduces the electric field inside by a factor of k: E_net = E₀ / k.

Electrical Susceptibility and Dielectric Constant

• Relationship: ε_r = K = 1 + χ_e.
• χ_e is the electric suspectibility, measures how easily.

Dielectric Strength

• Maximum electric field a dielectric can withstand before breaking down and becoming conductive.

Electric Capacitance of a Conductor

• The ratio of charge (Q) to potential (V) for a conductor: C = Q / V.
• C is independent of Q.
• SI unit: Farad (F).
• Capacitance depends on:
  • Size and shape of the conductor.
  • Permittivity of the surrounding medium.
  • Presence of other conductors nearby.

Spherical Conductor

• Capacitance (C) of a spherical conductor with radius (R): C = 4π ε₀ R.

Parallel Plate Capacitor

• C = ε₀ A / d, where A is the area, d is the separation between plates, ε₀ is the permittivity of free space.
• With dielectric: C = k ε₀ A / d with dielectric K.
• Series: 1/C = 1/C1 + 1/C2
• Parallel C = C1 + C2.
• Energy Stored (U): U = 1/2 CV² = 1/2 Q² / C = 1/2 QV.
• Series and Parallel: the energy is added.

Energy Density

• Energy per unit volume stored in the electric field: u = 1/2 ε₀ E².

Redistribution of Charges

• Charge distribution after connection depends on the ratio of capacitances.
• The final charge values are proportional to their capacitance values.
• Q1'/Q2' = C1/C2. Potential V= (C1V1+ C2V2)/( C1+C2).
  • C1, C2 are the capacitances of the two conductors
  • V1, V2 are the individual potentials prior to contact ΔU =1/2 (C1C2/C1+C2)((V1-V2)^2).

Partially Filled Dielectric

C = ε₀ A / (d - t + t/k). k = dielectric. t = thickness.

• For a conducting sheet, the value k = infinity.

Effect of Dielectric on Various Parameters

Remember chart of Effects of Dielectric With Battery Disconnected and With Battery Connected

Corona Discharge

• Occurs at sharp edges of charged conductors where the electric field is very high.
• High electric field ionizes the air molecules, creating a discharge or spark.
• Leads to loss of charge from the conductor.
• Employed in electrostatic shields.

Direction of conventional and electronic current

Always opposite of each other

Ohms Law

V =IR

Factors affecting the Resistance

R = p L /A R is directly proportional to L R is inversely proportional to A

Current Dentsity

J = I/ A J is a vector quantity

SI unite Amperes / meter2

Conductance

Reciprocal of resistance, which is R SI unite is mho

Conductivity

Reciprocal of resistivity Ohm/ m

Non ohmic conductors

V graph is nonlinear

Thermal speed

10^5 m/s

Relaxation time

Very small 10^-14 seconds.

Electric current and drift velocity

I: neAv n = electron density

Deduction of Ohms Law

R = ml / ne^2 TA

Mobility of electron

Mobility = VD / E SI unite is m^2 V-1 S-1

Temperture Dependace

Metals : Alpha is +

Semiconductors _ Alpha is negative - resistivity decreases as temperature increases

Joules Law

H is proportional to I^2 R T H = V I T = I^2 R T = V^2 /R T

Electric power

P= WV/t = V I = I^2 R Commercial unite is KW - Hr 1 hP is about 746 watts

Power ratings

Power/ Volt

Power Consumption with Resistances

In series 1/p = In parallel : P = P1+ P2+P3

Efficiency

Pout / Pin

Electromoative Force (EMF)

E.M.F is not a force .It is energy or work done E =w/q

Internal Resistance

In case of discharge V = E + IR

Factors of Internal resistences on battery

Temperature Distance b/w plates Area Emmerced inside batter Electrolyte

Characteristics carve from cell EMF verse IR verse power and verse current ,

Must need to be knowne

Combination of cells in series , Parallel and mixed Connection

Know their Respective Equations to do good.

kirchoffs Law

1st Low Is about Juntion low 2nd Low is about Loop Low Also know its alternate names as well and they each follow conservations of what : which can easily catch.

Whestones Bridge

P/Q = R/S

Conpect of magnetic field

Magnetisum is the force b/w charges in relative motion

Magnetic field lines

Shows the direction that a N pole would point in the magnetic field , they never cross ,.the strength is proportional to the area density.

Compums Law

F is proportion to Q1 Q 2 / r ^2

Magnetic dipole

M= q L m= magnetic moment direction is from S to N

bar magnet EQUIVALENTS.

Be able to write this equation out if needed:

Gausss low in electromagnetisum

.B .DA = o

Magnetic Term

intencite

Magnetic Feild Inside sample contri

Understanding Inconsistency in Ampere's Law

• Initially, when calculating the magnetic field, B, Ampere's Law faces an inconsistency.
• When 'i' is set to zero due to no current penetration, attempting to calculate B results in two different values: once B is present, and another time it is zero.
• This discrepancy arises because Ampere's Law doesn't restrict the choice of area for the loop.
• One could select a loop with an area that the current doesn't penetrate.
• This leads to a scenario where B exists according to one calculation method but is zero when the current is nil.

Maxwell's Introduction of Displacement Current

• James Clerk Maxwell introduced the concept of displacement current to resolve the inconsistencies in Ampere's Law.
• Displacement current is defined as epsilon-naught multiplied by the rate of change of electric flux (dΦE/dt).
• Displacement current occurs only when there is a change in the electric field or electric flux.
• If the electric flux is constant, the displacement current is zero.

Modified Ampere's Law

• Maxwell modified Ampere's Law by adding the displacement current to the original equation.
• The modified Ampere's Law includes both conduction current (I) and displacement current (ID): B = μ0(I + ID).
• The inclusion of displacement current makes the law consistent in scenarios where the original law was not.

Consistency Demonstrated

• When calculating B using the modified Ampere's Law, the initial inconsistency is resolved, and the same result is achieved.
• In a scenario where a capacitor is being charged, the conduction current (I) is zero.
• However, the displacement current (ID) is not zero because there is an electric field changing between the capacitor plates.
• The electric field changes during capacitor charging, leading to a non-zero electric flux and, therefore, a displacement current.
• The electric field (E) between the capacitor plates can be expressed as σ/ε0, where σ is the charge density.
• Substituting σ = Q/A, the electric field becomes E = Q/(Aε0), where Q is the charge on the plates and A is the area.
• Electric flux (Φ) is E multiplied by A
• This leads to ID = ε0(dQ/dt), which accounts for the changing charge on the capacitor plates.
• In terms of calculation B around or inside a capacitor: B = (μ0/2πr) * ID = (μ0/2πr) * ε0(dΦE/dt)
• Using the modified law, it becomes consistent.

Properties of Displacement Current

• Displacement current exists only when there is a change in the electric field.
• If the electric field is static (no change), the displacement current is zero.
• This is particularly important in scenarios with steady currents, where the absence of change in the electric field means no displacement current.

Maxwell's Equations

• Maxwell summarized electromagnetism with four equations.
• Maxwell did not create these, but compiled them.
• The first of these is Gauss's Law.

Maxwell's Equations

• Electromagnetism is governed by four equations.
• Gauss's Law for Electricity: Closed integral of E · dS = q/ε₀
• Gauss's Law for Magnetism: Closed integral of B · dS = 0, where B represents the magnetic field.
• Faraday's Law: e = -dΦ/dt, e represents electromotive force, and Φ represents magnetic flux.
• Modified Ampere's Law: A slightly changed equation.
• These four equations collectively explain the principles of electromagnetism.

Electromagnetic Waves

• Electromagnetic waves are formed by accelerated charges.
• They contain electric and magnetic field vectors oscillating perpendicular to each other.
• The electric and magnetic fields oscillate at 90 degrees relative to the direction of wave propagation.
• The direction of electromagnetic wave movement is determined by E cross B.
• Electric field vector 'E' and magnetic field vector 'B' are perpendicular.
• 'E' and 'B' are also perpendicular to the direction of wave propagation.

Properties of Electromagnetic Waves

• Accelerated charges are the source of electromagnetic waves.
• The direction of propagation is found using E cross B.
• They are transverse waves because electric and magnetic field vectors oscillate at 90 degrees to the direction of propagation.
• Electromagnetic waves carry energy and momentum.
• Energy density (energy per unit volume) is denoted by 'u'.
• The energy due to the electric field is given by 1/2 επ E squared RMS.
• The energy due to the magnetic field is given by 1/2 B squared RMS/μ₀
• Electric and magnetic fields contribute equally to the energy.
• Total energy density is double either the electric field's contribution or the magnetic field's contribution.

Intensity and Momentum

• Intensity: Energy per unit time per unit area in the normal direction of wave propagation.
• Intensity is calculated as επ E squared RMS * c.
• Momentum: Total energy (U) divided by the speed of light in a vacuum (c), so U/c.
• Electromagnetic waves exert pressure, i.e., radiation pressure.
• Radiation pressure equals intensity (I) over the speed of light (c), I/c.

Further Properties

• They don't require a material medium to travel.
• They travel in a vacuum.
• They are transverse in nature due to electric and magnetic field vectors.
• They are in the same phase - Electric field and magnetic field reach peak and zero values at the same time
• All electromagnetic waves have the same speed in a vacuum: 3 * 10^8 meters per second.
• In a medium, the speed is v = 1/√(μ * ε) = c/n, where 'n' is the refractive index.
• Electric field vectors and magnetic field vectors ratio is equal to 'c'.
• They are not deflected by electric or magnetic fields.
• They follow the principle of superposition.
• They show reflection, refraction, interference, diffraction, and polarization.
• Electric field vector amplitude is much greater than the magnetic field vector amplitude.

Electromagnetic Spectrum

• It is an orderly arrangement of electromagnetic waves, ordered by frequency or wavelength.
• Properties of electromagnetic fields change as frequency or wavelength changes.
• As the frequency goes up, the wavelength goes down.

Radio Waves

• They Have Longest wavelength and minimum frequency.
• Radio waves used in radio, television communication systems and radio astronomy
• Wavelength range: should be memorized
• Frequency range: should be memorized
• Source: Accelerated motion of charges in conducting wires and oscillating circuits.

Microwaves

• Smaller Wavelength than Radio waves
• Used in radar systems, aircraft navigation & microwave oven.
• Wavelength range: should be memorized
• Frequency range: should be memorized
• Source: Oscillating currents in vacuum tubes like klystrons, magnetrons, and gunn diodes.

Infrared Waves

• Also known as Heat waves, have heating effects.
• Used in remote controls for TVs and VCRs.
• Wavelength range: memorized
• Frequency range: memorized
• Source: Hot bodies and molecules.

Visible Light

• Sensitive to the Human Retina
• Involved with how we see things i.e. sight, and chemical reactions
• Wavelength range: should be memorized
• Frequency range: should be memorized
• Source: Radiated by excited atoms in ionized gas and incandescent bodies.

Ultraviolet (UV) Rays

• Present in Sunlight
• Used for food preservation to kill bacteria. Also used to kill viruses, and bacteria in water in water purifiers
• Too much exposure not good for our skin
• Wavelength range: should be memorized
• Frequency range: should be memorized
• Source: High-voltage gas discharge tubes, arcs of iron mercury, or the sun.

X-Rays

• Used in medical treatments to find fractures. Also used in Radio Therapy.
• Wavelength range: should be memorized
• Frequency range: should be memorized
• Source: Sudden deceleration of fast-moving electrons on a metal target.

Gamma Rays

• Used in Radio Therapy (Cancer Treatment to kill bad tissue)
• High penetrating Power
• Wavelength range: should be memorized
• Frequency range: should be memorized
• Source: Radioactive nuclei and nuclear reactions with Cobalt 60.

Reflection of Light

• Incident light returns to original medium after hitting reflective surface.
• Angle of incidence equals angle of reflection.
• Incident ray, reflected ray, & normal are all in same plane.

Spherical Mirrors

• Created by cutting a hollow sphere and polishing one side
• Polishing outside yields concave mirror, polishing inside yields convex mirror.
• Center of Curvature: Center of the sphere from which the mirror was cut.
• Radius of Curvature: Radius of the sphere from which the mirror was cut.
• Aperture: Diameter of the cut part.
• Principal Axis: Line joining focus and center of curvature.

Focus

• Parallel rays converge or appear to diverge from the focus.
• Concave mirrors have a real focus, convex mirrors have a virtual focus.
• Concave mirror's focal length is negative, convex mirror's focal length is positive.

Sign Convention

• Distances in the direction of the incident ray are positive, opposite are negative.
• Distances above the principal axis are positive, below are negative.

Relation between f & r

• r = 2f for both convex and concave mirrors, but only with small apertures

Rules for Image Formation

• Ray parallel to principal axis passes through/appears to pass through the focus.
• Ray passing through the focus becomes/appears to pass through parallel to the principal axis
• Ray passing through center of curvature retraces its path.
• Incident ray on the pole results in i = r.

Image Formation Summary

• Concave Mirror: Real, inverted images beyond C; virtual, erect images between F and P.
• Convex Mirror: Always virtual, erect, smaller images.

Equations

• Mirror Formula: 1/v + 1/u = 1/f.
• Linear Magnification from Optical Instruments: Height of image over height of objects equals -v/u. Note It is different than Angular Magnification.

Linear Magnification (m)

• |m| > 1: Image is magnified.
• |m| < 1: Image is diminished.
• |m| = 1: Same size.
• m > 0: Virtual and erect.
• m < 0: Real and inverted.

Refraction of Light

• Bending of light when it travels from one medium to another.
• Snell's Law: sin i / sin r = refractive index (μ).
• Incident ray, refracted ray, & normal all in the same plane.

Refractive Index

• Refractive Index has no units, is dimensionless.
• Refractive Index of medium 2 with respect to 1 : μ2/μ1 = v1/v2 = λ1/λ2

Combination of Media

• Sequential Refraction through multiple media formulas can be simplified.

Real and Apparent Depth

• Object appears shifted due to refraction.
• Refractive index (μ) = real depth / apparent depth.
• Normal shift (d) = t(1 - 1/μ); t = real depth.

Total Internal Reflection (TIR)

• Light ray in denser medium reflects internally when incidence angle exceeds critical angle
• Necessary conditions:
  • Ray must travel from denser to rarer medium
  • Incidence angle must be greater than the critical angle.

Refractive Index Relationship

• Refractive index of denser medium (μ) = 1 / sin i(critical).

TIR Application

• Optical Fibers based in TIR
• Fiber consists of a core with high refractive index, and cladding with lower one
• Light undergoes multiple TIRs as it travels through the fiber.

Lenses

• Transparent medium with at least one curved surface.
• Convex Lenses: Thicker in the middle.
• Concave Lenses: Thinner in the middle.
• Each has two centers of curvature (C1, C2) & two radii of curvature.
• Principal Axis joins the two centers of curvature.
• Optical Center is point where a ray passes undeviated.

Focus

• Lenses have two focal points.
• Focus 1: Rays passing through/towards F1 become parallel after refraction.
• Focus 2: Parallel rays converge/appear to converge to F2.

Convention

• Secondary focus (F2) is taken as reference point for analysis and formulas
• Convex lenses have positive focal length, concave lenses have negative.

Refraction at Spherical Surfaces, convex

• Convex: Four Cases (Object in rarer/denser, image real or virtual) & concave : only cases where the images is virtual.
• Formula: u2/v - u1/u = (u2 - u1)/radius
• If ray moves rarer to denser.
• Object in denser medium (ray from denser to rarer): Interchange μ1 and μ2.

Lens Maker Formula

• Relates focal length to radii of curvature and medium: 1/f = (u2 - u1)/u1 (1/radius1 - 1/radius2)
• If lens is in Air : Formula is simplified

Rules for Drawing Images

• Ray parallel to principal axis refracts through the focus.
• Ray through focus becomes parallel after refraction.
• Ray through optical center passes without deviation.

Image Formation in Lenses

• Convex: Real/inverted or virtual/erect depending on object position.
• Concave: Always give virtual/erect images, smaller than the object..

Lens Formula

• Thin lens: Formula 1/v - 1/u = 1/f.
• Linear Magnification: Height of image over height of objects = v/

Comprehensive lecture covering the entire Class 12th Physics syllabus. Aimed to provide a thorough understanding of the concepts. Encourages viewers to like and share the video. PDF notes are available for download on the Arvind Academy app.