Physics (Theory) Class 12 ISC (Arts) CISCE Topics and Syllabus

• Electric Charges 
  • Point charge
  • Test charge
• Basic Properties of Electric Charge 
  • Additive Nature of Charge
  • Quantization of Charge
  • Conservation of Charge
  • Forces between Charges
• Quantisation of Charge 
• Coulomb’s Law - Force Between Two Point Charges 
  • Coulomb's law
  • Electric permittivity
  • Dielectric constant (Kor E_r)
• Force Between Two Point Charges 
• Superposition Principle - Forces Between Multiple Charges 
  • Superposition principle
  • Forces between multiple charges
• Superposition Principle of Forces 
• Electric Field 
  • Introduction of Electric Field 
• Electric Field Due to a Point Charge 
• Electric Field Lines 
• Electric Dipole 
  • The field of an electric dipole
  • The physical significance of dipoles
  • Couple Acting on an Electric Dipole in a Uniform Electric Field
  • Electric Intensity at a Point due to an Electric Dipole
  • Electric dipole moment (p)
  • Electric field intensity·due to an electric dipole at a point on its axial line
  • Electric field intensity due to an electric dipole at a point on the equatorial line
  • Electric field intensity at a general point due to short electric dipole
• Dipole in a Uniform External Field 
  • Torque on a Dipole in Uniform Electric Fleld
  • Work of an electric dipole
• Electric Flux 
  • Electric Flux
  • Tube of force
  • Tube of induction
  • Normal Electric Induction (NEI)
  • Total Normal Electric Induction (TNEI)
• Uniformly Charged Infinite Plane Sheet and Uniformly Charged Thin Spherical Shell (Field Inside and Outside) 
• Applications of Gauss’s Law 
  • Statement of Gauss'S Theorem and Its Applications to Find Field Due to Infinitely Long Straight Wire
  • Field due to an infinitely long straight uniformly charged wire
  • Field due to a uniformly charged infinite plane sheet
  • Field due to a uniformly charged thin spherical shell - Field outside the shell, Field inside the shell

Electric charges; conservation and quantisation of charge, Coulomb's law; superposition principle and continuous charge distribution.

Electric field, electric field due to a point charge, electric field lines, electric dipole, electric field due to a dipole, torque on a dipole in uniform electric field.

Electric flux, Gauss’s theorem in Electrostatics and its applications to find field due to infinitely long straight wire, uniformly charged infinite plane sheet and uniformly charged thin spherical shell

• Coulomb's law, S.I. unit of charge; permittivity of free space and of dielectric medium. Frictional electricity, electric charges (two types); repulsion and attraction; simple atomic structure - electrons and ions; conductors and insulators; quantization and conservation of electric charge; Coulomb's law in vector form; (position coordinates r_1, r₂ not necessary). Comparison with Newton’s law of gravitation; Superposition principle (vecF_1=vecF_12+vecF_13+vecF_14+ ....)
• Concept of electric field and its intensity; examples of different fields;gravitational, electric and magnetic; Electric field due to a point charge vecE =
• Electric charges; conservation and quantisation of charge, Coulomb's law; superposition principle and continuous charge distribution.
• Electric field, electric field due to a point charge, electric field lines, electric dipole, electric field due to a dipole, torque on a dipole in uniform electric field.
• Electric flux, Gauss’s theorem in Electrostatics and its applications to find field due to infinitely long straight wire, uniformly charged infinite plane sheet and uniformly charged thin spherical shell
• Coulomb's law, S.I. unit of charge; permittivity of free space and of dielectric medium. Frictional electricity, electric charges
  (two types); repulsion and attraction; simple atomic structure - electrons and ions; conductors and insulators; quantization and conservation of electric charge; Coulomb's law in vector form; (position coordinates r_1, r₂ not necessary). Comparison with Newton’s law of gravitation; Superposition principle (vecF_1=vecF_12+vecF_13+vecF_14+ ....)
• Concept of electric field and its intensity; examples of different fields;gravitational, electric and magnetic; Electric field due to a point charge vecE = vecF/qo (q0 is a test charge) vecE for
  a group of charges (superposition principle); a point charge q in an electric field E experiences an electric force vecF_E = qvecE. Intensity due to a
  continuous distribution of charge i.e. linear, surface and volume.
• Electric lines of force: A convenient way to visualize the electric field; properties of lines of force; examples of the lines of force due to (i) an
  isolated point charge (+ve and - ve); (ii) dipole, (iii) two similar charges at a small distance;(iv) uniform field between two oppositely charged parallel plates
• Electric dipole and dipole moment; derivation of the vecE at a point, (1) on the axis (end on position) (2) on the perpendicular bisector (equatorial i.e. broad side on position) of a dipole,
  also for r>> 2l (short dipole); dipole in a uniform electric field; net force zero, torque on an electric dipole: vect = vecpxxvecE and its derivation.
• Gauss’ theorem: the flux of a vector field; Q=vA for velocity vector vecv||vecA, vecA is area vector. Similarly for electric field vecE , electric flux Φ_E = EA for vecE||vecA and phi_EvecE.vecA for uniform vecE. For non-uniform field phi_E = intdphi = intvecE.dvecA. Special cases for  = 0º, 90º and 180º. Gauss’ theorem, statement: ΦE =q/∈₀ or phi_E = intvecE.dvecA = q/epsilon_0 where  Φ_E is for a closed surface; q is the net charge enclosed, ∈_o is the permittivity of free space. Essential properties of a Gaussian surface.
• Applications: Obtain expression for vecE due to 1. an infinite line of charge, 2. a uniformly charged infinite plane thin sheet, 3. a thin hollow spherical shell (inside, on the surface and outside). Graphical variation of E vs r for a thin spherical shell

• Electric Potential 
• Electric Potential Difference 
• Potential Due to a Point Charge 
  • Electric Potential Due to Point Charge
• Potential Due to a System of Charges 
  • system of charges
• Equipotential Surfaces 
  • Equipotential surface
  • Properties of equipotential surface
  • Shapes of equipotential surface due to various charge distributions
• Electrical Potential Energy of a System of Two Point Charges and of Electric Dipole in an Electrostatic Field 
  • Electric potential energy
  • Electric potential energy of a system of two point charges
  • Electric potential energy of an electric dipole in uniform electric field
  • Dipole-dipole interaction
  • Equilibrium of charges
  • Types of equilibrium
    1) Stable equilibrium
    2) Unstable equilibrium
    3) Neutral equilibrium
  • Different cases of equilibrium of charge
• Conductors and Insulators Related to Electric Field 
• Free Charges and Bound Charges Inside a Conductor 
• Capacitors and Capacitance 
  • Capacitance
  • Redistribution of charges and concept of common potential
  • Capacitance of an isolated spherical conductor
  • Capacitor
  • Principle of a capacitor
  • Types of capacitor
    1) Parallel plate capacitor
    2) Spherical capacitor
    3) Cylindrical capacitor
  • Applications of capacitors
• Combination of Capacitors 
  • Combination of Capacitors in Series and in Parallel
  • Wheatstone's bridge of capacitors
• Capacitance of a Parallel Plate Capacitor with and Without Dielectric Medium Between the Plates 
  • Capacitance of parallel plate capacitor without dielectric medium
  • Capacitance of parallel plate capacitor with dielectric slab between the plates
• Energy Stored in a Capacitor 

Electric potential, potential difference, electric potential due to a point charge, a dipole and system of charges; equipotential surfaces, electrical potential energy of a system of two point charges and of electric dipole in an electrostatic field.

Conductors and insulators, free charges and bound charges inside a conductor. Dielectrics and electric polarisation, capacitors and capacitance, combination of capacitors in series and in parallel. Capacitance of a parallel plate capacitor, energy stored in a capacitor

Concept of potential, potential difference and potential energy. Equipotential surface and its properties. Obtain an expression for
electric potential at a point due to a point charge; graphical variation of E and V vs r, VP=W/q0; hence V_A -V_B =
W_BA/ q₀ (taking q₀ from B to A) = (q/40)(1/rA - 1/rB); derive this equation; also VA = q/40 .1/rA ; for
q>0, VA>0 and for q<0, VA < 0. For a collection of charges V = algebraic sum of the potentials due to each charge; potential due to a dipole on its axial line and equatorial line; also at any point for r>>2l (short dipole). Potential energy of a point charge (q)
in an electric field E , placed at a point P where potential is V, is given by U =qV and U =q (VA-VB). The
electrostatic potential energy of a system of two charges = work done W21=W12 in assembling the system; U12
or U21 = (1/4piepsilon_0 ) q1q2/r12. For a system of 3 charges U₁₂₃ = U₁₂ + U₁₃ + U_{23 =} 1/4pielipson_0((q_1q_2)/r_12+(q_1q_3)/r_13+(q_2q_3)/r_23).

For a dipole in a uniform electric field, derive an expression of the electric potential energy U_E = -vecp .vecE , special cases for Φ=0º, 90º and 180º.

Capacitance of a conductor C = Q/V; obtain the capacitance of a parallelplate capacitor (C = ∈₀A/d) and equivalent capacitance for capacitors in series and parallel combinations. Obtain an expression for energy stored (U = 1/2CV^2=1/2QV=1/2Q^2/C^2) and enery density.

Dielectric constant K = C'/C; this is also called relative permittivity K = ∈_r = ∈/∈_o; elementary ideas of polarization of matter in a uniform electric field qualitative discussion; induced surface charges weaken the original field; results in reduction in E and hence, in pd, (V);
for charge remaining the same Q = CV = C' V' = K. CV'; V' = V/K; and E' =  E/K; if the Capacitor is kept connected with the source of emf, V is kept constant V = Q/C = Q'/C' ; Q'=C'V = K. CV= K. Q increases; For a parallel plate capacitor with a dielectric in between, C' = KC = K.∈_o . A/d = ∈_r .∈_o .A/d. Then C' = (∈_0A)/(d/∈_r). for a capacitor partially filled dielectric, capacitance C'= ∈_0A/(d-t+t/∈_r)

• Magnetic Force 
  • Sources and fields
  • Magnetic Field, Lorentz Force
  • Magnetic force on a current-carrying conductor
• Oersted’s Experiment 
• Magnetic Field Due to a Current Element, Biot-Savart Law 
  • Biot Savart’s Law
  • Some important features of Biot Savart's law
  • Its application to the current carrying circular loop
• Ampere’s Circuital Law 
  • Ampere's Law and Its Applications to Infinitely Long Straight Wire
  • Magnetic field due to the current carrying wire of infinite length using Ampère’s law 
  • Magnetic field due to a long current carrying solenoid
  • Toroid
• Straight and Toroidal Solenoids (Only Qualitative Treatment) 
• Force on a Moving Charge in Uniform Magnetic and Electric Fields 
• Motion in Combined Electric and Magnetic Fields 
  • Cyclotron 
    • Cyclotron
    • Principle
    • Construction
    • Working
    • Limitations
    • Uses
• Force on a Current - Carrying Conductor in a Uniform Magnetic Field 
• Force Between Two Parallel Currents, the Ampere 
  • Definition of Ampere
  • Force Between Two Parallel Current-carrying Conductors
  • Roget's Spiral For Attraction Between parallel currents
• Torque on a Current Loop in Magnetic Field 
  • Torque on a rectangular current loop in a uniform
    magnetic field
  • Circular current loop as a magnetic dipole
  • The magnetic dipole moment of a revolving electron
• Moving Coil Galvanometer 
  • Moving Coil Galvanometer
  • Moving Coil Galvanometer Conversion to Voltmeter and Ammeter
  • Moving Coil Galvanometer Current Sensitivity
  • Types of Moving Coil Galvanometer

  1. Suspended type MCG: Principle, Construction
  2. Pivoted type MCG

  • Sensitivity of MCG
  • Current sensitivity (S_i)
  • Voltage Sensitivity (S_v)
  • Factors affecting the sensitivity of MCG
  • Accuracy of MCG
  • Conversion of MCG into ammeter
  • Conversion of MCG into voltmeter

Concept of magnetic field, Oersted's experiment. Biot - Savart law and its application. Ampere's Circuital law and its applications to infinitely long straight wire, straight and toroidal solenoids (only qualitative treatment). Force on a moving charge in uniform magnetic and electric fields, cyclotron. Force on a currentcarrying conductor in a uniform magnetic field, force between two parallel current-carrying conductors-definition of ampere, torque experienced by a current loop in uniform magnetic field; moving coil galvanometer - its sensitivity. Conversion of galvanometer into an ammeter and a voltmeter.

• Current Loop as a Magnetic Dipole and Its Magnetic Dipole Moment 
• Magnetic Dipole Moment of a Revolving Electron 
• Magnetic Field Intensity Due to a Magnetic Dipole (Bar Magnet) Along Its Axis 
• Magnetic Field Intensity Due to a Magnetic Dipole (Bar Magnet) Perpendicular to Its Axis 
• Torque on a Magnetic Dipole (Bar Magnet) in a Uniform Magnetic Field 
• The Bar Magnet 
  • The magnetic field lines
  • Bar magnet as an equivalent solenoid
  • The dipole in a uniform magnetic field
  • The electrostatic analog
  • Magnetic potential
• The Earth’s Magnetism 
  • Earth's magnetic field
  • Important terms
    1) Geographic axis
    2) Geographic meridian
    3) Geographic equator
    4) Magnetic axis
    5) Magnetic meridian
    6) Magnetic equator
  • Effects of Earth's magnetic field
• Magnetic Properties of Materials 
  • Classification of magnetic material: Diamagnetic, Paramagnetic, Ferromagnetic
  • Atomic theory of magnetism
  • Magnetism on the basis of electron theory
    1) Diamagnetism
    2) Paramagnetism
    3) Ferromagnetism
• Permanent Magnet and Electromagnet 
  • Permanent magnet
  • Electromagnets and factors affecting their strengths
  • Difference between Permanent magnet and electromagnet
  • Advantage of an electromagnet over a permanent magnet
• Magnetic Force 
  • Sources and fields
  • Magnetic Field, Lorentz Force
  • Magnetic force on a current-carrying conductor
• Magnetisation and Magnetic Intensity 
  • Magnetisation
  • Magnetic Intensity
  • Relation between permeability and susceptibility

A current loop as a magnetic dipole, its magnetic dipole moment, magnetic dipole moment of a revolving electron, magnetic field intensity due to a magnetic dipole (bar magnet) on the axial line and equatorial line, torque on a magnetic dipole (bar magnet) in a uniform magnetic field; bar magnet as an equivalent solenoid, magnetic field lines; earth's magnetic field and magnetic elements. Diamagnetic, paramagnetic, and ferromagnetic substances, with examples. Electromagnets and factors affecting their strengths, permanent magnets.

Only historical introduction through Oersted’s experiment. [Ampere’s swimming rule not included]. Biot-Savart law and its vector form; application; derive the expression for B (i) at the centre of a circular loop carrying current; (ii) at any point on its axis. Current carrying loop as a magnetic dipole. Ampere’s Circuital law: statement and brief explanation. Apply it to obtain vecB near a long wire carrying current and for a solenoid (straight as well as torroidal). Only formula of vecB due to a finitely long conductor.

Force on a moving charged particle in magnetic field vecF_B = q(vecv xx vecB); special cases, modify this equation substituting dl / dt for v and I for q/dt to yield vecF  = I dvecl xx vecB for the force acting on a current carrying conductor placed in a magnetic field. Derive the expression for force between two long and parallel wires carrying current, hence, define ampere (the base SI unit of current)
and hence, coulomb; from Q = It. Lorentz force, Simple ideas about principle, working, and limitations of a cyclotron.

Derive the expression for torque on a current carrying loop placed in a uniform vecB, using vecF = Ivecl XX vecB and vect = vec r xx vecF
;t = NIAB sinΦ for N turns =vecm × vecB where the dipole moment vec m = NI vecA , unit: A.m². A current carrying loop is a magnetic dipole;directions of current and vecB and vecm using right hand rule only; no other rule necessary. Mention orbital magnetic moment of an electron in Bohr model of H atom. Concept of radial magnetic field. Moving coil galvanometer; construction, principle, working, theory I= kΦ , current and voltage sensitivity. Shunt. Conversion of galvanometer into ammeter and voltmeter of given range.

Magnetic field represented by the symbol vecB is now defined by the equation vecF =qo(vecv xx vecB); vecB is not to be
defined in terms of force acting on a unit pole, etc.; note the distinction of vecB  from vecE is that vecB forms closed loops as there are no magnetic monopoles, whereas vecE lines start from +ve charge and end on -ve charge. Magnetic field lines due to a magnetic
dipole (bar magnet). Magnetic field in end-on and broadside-on positions (No derivations). Magnetic flux Φ =vecB.vecA = BA for B uniform and vecB||vecA ; i.e. area held perpendicular to For Φ = BA(VecB||vecA), B=Φ/A is the flux density [SI unit of flux is weber (Wb)]; but note that this is not correct as a defining equation as B is vector and  and /A are scalars, unit of B is tesla (T) equal
to 10^-4 gauss. For non-uniform vecB field, Φ= ∫dΦ=∫B. dA . Earth's magnetic field vecB_E is uniform over a limited area like that of a lab; the component of this field in the horizontal direction BH is the one effectively acting on a magnet suspended or pivoted horizontally.
Elements of earth’s magnetic field, i.e. BH, δ and Θ - their definitions and relations.

Properties of diamagnetic, paramagnetic and ferromagnetic substances; their susceptibility and relative permeability. It is better to explain the main distinction, the cause of magnetization (M) is due to magnetic dipole moment (m) of atoms, ions or molecules being 0 for dia, >0 but very small for para and > 0 and large for ferromagnetic materials; few examples; placed in external B , very small (induced) magnetization in a direction opposite to B in dia, small magnetization parallel to B for para, and large magnetization parallel to B for ferromagnetic materials; this leads to lines of B becoming less dense, more dense and much more dense in dia, para and ferro, respectively; hence, a weak repulsion for dia, weak attraction for para and strong attraction for ferro magnetic material. Also, a small bar suspended in the horizontal plane becomes perpendicular to the B field for dia and parallel to B for para and ferro. Defining equation H = (B/0)-M; the magnetic properties, susceptibility m = (M/H) < 0 for dia (as M is opposite H) and >0 for para, both very
small, but very large for ferro; hence relative permeability μ_r =(1+ χ_m) < 1 for dia, > 1 for para and >>1 (very large) for ferro; further, χ_m1/T (Curie’s law) for para, independent of temperature (T) for dia and depends on T in a complicated manner for
ferro; on heating ferro becomes para at Curie temperature. Electromagnet: its definition, properties and factors affecting the strength of electromagnet; selection of magnetic material for temporary and permanent magnets and core of the transformer on the basis of
retentivity and coercive force (B-H loop and its significance, retentivity and coercive force not to be evaluated

• Electromagnetic Induction 
  • Electromagnetic Induction
  • Demonstration of the phenomenon of electromagnetic induction
  • Faraday's explanation of Electromagnetic Induction
• Faraday’s Law of Induction 
  • Laws of Electromagnetic Induction or Faraday's Laws of Induction
    1) First law
    2) Second Law
• Induced e.m.f. and Induced Current 
• Lenz’s Law and Conservation of Energy 
  • Lenz's Law
• Eddy Currents 
  • Eddy Current
  • Drawbacks
  • Applications 
    1) Dead-beat galvanometer
    2) Electric-brakes
    3) Induction furnace
    4) Speedometer
    5) Energy meter
    6) Induction motor
• Inductance 
  • Mutual Inductance 
    • Mutual Induction
    • Factors affecting mutual inductance (M)
    • Relation between M, L₁, and L₂.
    • Two coils in series
    • Two coils in parallel
• Magnetic Flux 

Fraday's laws, induced emf and current; Lenz's Law, eddy currents. Self-induction and mutual induction. Transformer

• Electromagnetic induction, Magnetic flux, change in flux, rate of change of flux and induced emf; Faraday’s laws. Lenz's law, conservation of energy; motional emf ε = Blv, and power P = (Blv)²/R; eddy currents (qualitative);
• Self-Induction, coefficient of selfinductance, Φ= LI and L = ε/(dI/dt); henry = volt. Second/ampere, expression for coefficient ofselfinductance of a solenoid L = (mu_0N^2A)/l = mu_0n^2Axxl
• Mutual induction and mutual inductance (M), flux linked Φ₂ = MI₁; induced emf ε_{2 =} (dphi_2)/dt = (MdI_1)/dt_. Definition of M as M = epsilon_2/(dI_1)/dt or M = (phi_2)/I_1. SI unit henry. Expression for coefficient of mutual inductance of two coaxial solenoids M = (mu_0N_1N_2A)/l=mu_0n_1N_2A Induced emf opposes changes, back emf is set up, eddy currents.
• Transformer (ideal coupling): principle, working and uses; step up and step down; efficiency and applications including transmission of power, energy losses and their minimisation. 

• Alternating Currents 
  • Alternating current
  • Terms Related to alternating current

  1. Instantaneous value
  2. Peak value
  3. Mean value or average value
  4. Mean square value
  5. Root mean square (r.m.s) value
  6. Peak to peak value
  7. Form factor and peak factor
  8. Impedance (Z)
  9. Reactance (X): Inductive and Capacitive reactance
  10. Admittance (Y)
  11. Susceptance (S): Inductive and Capacitive susceptance
  12. Conductance
• Peak and Rms Value of Alternating Current Or Voltage 
• Reactance and Impedance 
• LC Oscillations 
• AC Voltage Applied to a Series LCR Circuit 
  • LCR Series Circuit
  • Phasor-diagram solution
  • Analytical solution
  • Resonance  - Sharpness of resonance
• Forced Oscillations and Resonance 
  • Free, Forced and Damped Oscillations
  • resonance
  • Small Damping, Driving Frequency far from Natural Frequency
  • Driving Frequency Close to Natural Frequency
• Power in AC Circuit: the Power Factor 
  • Power in A.C. Circuits
  • Power Factor
  • Wattless Current
  • Instantaneous power
  • Average power
  • Virtual power
  • Choke Coil
• Transformers 
  • Transformer
  • Principle of transformer
  • Efficiency of transformer (η)
  • Losses in transformer
    1) Cu loss (I²R)
    2) Eddy current loss
    3) Hysteresis loss
    4) Magnetic flux leakage
    5) Humming losses

Peak value, mean value and RMS value of alternating current/voltage; their relation in sinusoidal case; reactance and impedance; LC oscillations (qualitative treatment only), LCR series circuit, resonance; power in AC circuits, wattless current. AC generator.

Sinusoidal variation of V and I with time, for the output from an ac generator; time period, frequency and phase changes; obtain mean values of current and voltage, obtain relation between RMS value of V and I with peak values in sinusoidal cases only.

Variation of voltage and current in a.c. circuits consisting of only a resistor, only an inductor and only a capacitor (phasor representation), phase lag and phase lead. May apply Kirchhoff’s law and obtain simple differential equation (SHM type), V = Vo sin t, solution I = I0 sinωt, I0sin (ωt + π/2) and I0 sin (ωt - π/2) for pure R, C and L circuits respectively. Draw phase (or phasor)
diagrams showing voltage and current and phase lag or lead, also showingresistance R, inductive reactance XL;(XL=L) and capacitive reactance X_C, (X_C = 1/ωC). Graph of X_L and X_C vs f.

The LCR series circuit: Use phasor diagram method to obtain expression for I and V, the pd across R, L and C; and the net phase lag/lead; use the results of 4(e), V lags I by π/2 in a capacitor, V leads I by π/2 in an inductor, V and I are in phase in a resistor, I is the same in all three; hence draw phase diagram, combine VL and Vc (in opposite phase; phasors add like vectors) to give V=VR+VL+VC (phasor addition) and the max. values are related by V2 m=V2 Rm+(VLm-VCm)2 when VL>VC Substituting pd=current x
resistance or reactance, we get Z2 = R2+(XL-Xc) 2 and tan = (VL m -V_Cm)/VRm = (X_L-X_c)/R giving I = I m sin (wt-Φ) where I m =Vm/Z etc. Special cases for RL and RC circuits. [May use Kirchoff’s law and obtain the differential equation]Graph of Z vs f and I vs f.

Power P associated with LCR circuit = 1/2V_oI_o cos =V_rmsI_rms cosΦ = Irms 2 R; power absorbed and power dissipated; electrical resonance; bandwidth of signals and Q factor (no derivation); oscillations in an LC circuit (0 = 1 sqrt(LC) ). Average power consumed
averaged over a full cycle P = (1/2) V_oI_o cosΦ, Power factor cos = R/Z. Special case for pure R, L and C; choke coil (analytical only), XL controls current but cos = 0, hence P =0, wattless current; LC circuit; at resonance with XL=Xc , Z=Z_min= R, power delivered to circuit by the source is maximum, resonant frequency f_0= 1/(2pisqrt(LC))

Simple a.c. generators: Principle, description, theory, working and use. Variation in current and voltage with time for a.c. and d.c. Basic differences between a.c. and d.c.

• Reflection of Light by Spherical Mirrors 
  • Sign convention
  • Focal length of spherical mirrors
  • The mirror equation
• Ray Optics - Mirror Formula 
• Refraction 
• Total Internal Reflection 
  • Total Internal Reflection
  • Essential conditions for the total internal reflection
  • Total internal reflection in nature - optical fibres
  • Rainbow production
  • Refraction and total internal reflection of light rays at different angles of incidence
  • Consequences of total internal refraction
  • Applications of total internal reflection
• Refraction at Spherical Surfaces and Lenses 
  • Refraction at Spherical Surfaces 
    • Refraction at spherical surfaces

    1. Refraction from rarer to denser medium
    2. Refraction from denser medium to rarer medium
  • Combination of Thin Lenses in Contact 
    • Equivalent lens (Two thin lenses placed in contact)
    • Combination of a lens and a mirror:
      ⇒ Effect of silvering, one of the refracting surfaces of a lens
    • Defects in lenses
      1) Chromatic aberration
      2) Spherical aberration
      ⇒ Methods to reduce spherical aberrations in lenses
      3) Coma
      4) Curvature
• Lenses 
• Thin Lens Formula 
• Lensmaker's Formula 
• Magnification 
• Power of a Lens 
• Dispersion by a Prism 
• Some Natural Phenomena Due to Sunlight 
  • Mirage
  • Rainbow
• Optical Instruments 
  • The Microscope 

    Microscopes (Reflecting and Refracting) and Their Magnifying Powers

  • Telescope 
    • Astronomical Telescopes (Reflecting and Refracting) and Their Magnifying Powers
• Snell’s Law 

Ray Optics: Reflection of light by spherical mirrors, mirror formula, refraction of light at plane surfaces, total internal reflection and its applications, optical fibres, refraction at spherical surfaces, lenses, thin lens formula, lens maker's formula, magnification, power
of a lens, combination of thin lenses in contact, combination of a lens and a mirror, refraction and dispersion of light through a prism. Scattering of light.

Optical instruments: Microscopes and astronomical telescopes (reflecting and refracting) and their magnifying powers and their resolving powers.

• Reflection of light by spherical mirrors. Mirror formula: its derivation; R=2f for spherical mirrors. Magnification.
• Refraction of light at a plane interface,Snell's law; total internal reflectionand critical angle; total reflecting prisms and optical fibers. Total reflecting prisms: application to triangular prisms with angle of the prism 300, 450, 600 and 900 respectively; ray diagrams for Refraction through a combination of media, ₁n₂ X ₂n₃ X ₃n₁ = 1 , real depth and apparent depth. Simple applications.
• Refraction through a prism, minimum deviation and derivation of relation between n, A and δ_min. Include explanation of i-δ graph, i₁ = i₂ = i (say) for δ_m; from symmetry r₁ = r₂; refracted ray inside the prism is parallel to the base of the equilateral prism. Thin prism. Dispersion; Angular dispersion; dispersive power, rainbow - ray diagram (no derivation). Simple explanation. Rayleigh’s theory of scattering of light: blue colour of sky and reddish appearance of the sun at sunrise and sunset clouds appear white.
• Refraction at a single spherical surface; detailed discussion of one case only - convex towards rarer medium, for spherical surface and real image. Derive the relation between n1, n2, u, v and R. Refraction through thin lenses: derive lens maker's formula and lens formula; derivation of combined focal length of two thin lenses in contact. Combination of lenses and mirrors (silvering of lens excluded) and
  magnification for lens, derivation for biconvex lens only; extend the results to biconcave lens, plano convex lens and lens immersed in a liquid; power of a lens P=1/f with SI unit dioptre. For lenses in contact 1/F= 1/f₁+1/f₂ and P=P₁+P₂. Lens formula, formation of image with combination of thin lenses and mirrors.
• [Any one sign convention may be used in solving numericals].
• Ray diagram and derivation of magnifying power of a simple microscope with image at D (least distance of distinct vision) and infinity;
  Ray diagram and derivation of magnifying power of a compound microscope with image at D. Only expression for magnifying power of
  compound microscope for final image at infinity.
• Ray diagrams of refracting telescope with image at infinity as well as at D; simple explanation; derivation of magnifying power; Ray diagram of reflecting telescope with image at infinity. Advantages, disadvantages and uses. Resolving power of compound microscope and telescope.

• Huygens' Principle 
  • Wavefront
  • Wave normal
  • Wave surface
  • Huygens' Principle
  • Spherical Wavefront
  • Plane Wavefront
  • Cylindrical wavefront
• Proof of Laws of Reflection and Refraction Using Huygens' Principle 
  • Proof of laws of reflection by using Huygens' principle
  • Proof of laws of refraction using Huygens' Principle
• Interference 
• Interference of Light Waves and Young’s Experiment 
  • Young's Double Slit Experiment and Expression for Fringe Width or Young’s Experiment
  • Young's double-slit experiment: set up, diagram, geometrical deduction of path difference ∆x = dsinθ, between waves from the two slits
  • Using ∆x = nλ for bright fringe and ∆x = (n + ½)λ for dark fringe and sin θ = tan θ = yn/D as y and θ are small, obtain yn = (D/d)nλ and fringe width β = (D/d)λ.
  • Graph of distribution of intensity with angular distance.
• Coherent and Incoherent Sources and Sustained Interference of Light 
  • Coherent sources
  • Incoherent sources
  • Sustained interference pattern
  • Conditions necessary to obtain sustained (steady) interference pattern
• Fraunhofer Diffraction Due to a Single Slit 
  • Single slit Fraunhofer diffraction (elementary explanation only)
  • Formulae based comparison between secondary maxima and minima
  • Diffraction at a single slit: experimental setup, diagram, diffraction pattern, obtain an expression for the position of minima, a sinθn = nλ, where n = 1, 2, 3 … and conditions for secondary maxima, asinθn = (n + ½)λ.
  • Distribution of intensity with angular distance
  • Diffraction at plane grating
  • Diffraction due to circular aperture
  • Comparison between interference and diffraction
  • Fresnel distance
• Width of Central Maximum 
• Polarisation 
  • Method of producing polarised light

  1. Polarisation by reflection
  2. By Dichroism
  3. By double refraction
  4. Nicol prism
  5. By scattering

  • Uses of plane polarised light and Polaroids
• Plane Polarised Light 
• Brewster's Law 
• Law of Malus 
• Refraction of Monochromatic Light 

Wave front and Huygen's principle. Proof of laws of reflection and refraction using Huygen's principle. Interference, Young's double slit experiment and expression for fringe width(β), coherent sources and sustained interference of light, Fraunhofer diffraction due to a single slit, width of central maximum; polarisation, plane polarised light, Brewster's law, uses of plane polarised light and Polaroids.

• Huygen’s principle: wavefronts - different types/shapes of wavefronts;proof of laws of reflection and refraction using Huygen’s theory.
  [Refraction through a prism and lens on the basis of Huygen’s theory not required].
• Interference of light, interference of monochromatic light by double slit. Phase of wave motion; superposition of identical waves at a point, path difference and phase difference; coherent and incoherent sources; interference: constructive and destructive, conditions for sustained interference of light waves [mathematical deduction of interference from the equations of two progressive waves with a phase
  difference is not required]. Young's double slit experiment: set up, diagram, geometrical deduction of path difference Δx = dsinΘ, between waves from the two slits; using Δx=nλ for bright fringe and Δx= (n+½) for dark fringe and sin Θ = tan Θ =y_n /D as y and Θ are small, obtain yn=(D/d)n and fringe width β=(D/d). Graph of distribution of intensity with angular distance.
• Single slit Fraunhofer diffraction (elementary explanation only). Diffraction at a single slit: experimental setup, diagram, diffraction pattern, obtain expression for position of minima, a sinn= n, where n = 1,2,3… and conditions for secondary maxima, asinn =(n+½)λ.; distribution of intensity with angular distance; angular width of central bright fringe.
• Polarisation of light, plane polarised electromagnetic wave (elementary idea only), methods of polarisation of light. Brewster's law; polaroids. Description of an electromagnetic wave as
• transmission of energy by periodic changes in vecE  and vecB  along the path; transverse nature as vecE  and vecB are perpendicular to vecc. These three vectors form a right handed system, so that vecE x vecB is along vecc , they are mutually perpendicular to each other.For ordinary light, vecE and vecB are in all directions in a plane perpendicular to the vecc vector - unpolarised waves. If
  vec E and (hence vecB  also) is confined to a single plane only (vecc , we have linearly polarized light. The plane containing vecE  (or B) and vecc  remains fixed. Hence, a linearly polarised light is also called plane polarised light. Plane of polarisation (contains vecE and vecc); polarisation by reflection; Brewster’s law: tan ip=n; refracted ray is perpendicular to reflected ray for i= i_p; i_p+r_p = 90° ; polaroids; use in the production and detection/analysis of polarised light, other uses. Law of Malus.

• Alpha-particle Scattering and Rutherford’s Nuclear Model of Atom 
  • Alpha-particle Scattering Experiment and Rutherford's Model of Atom
  • Alpha-particle trajectory
  • Electron orbits
  • Rutherford’s nuclear model of atom (mathematical theory of scattering excluded), based on Geiger - Marsden experiment on α-scattering; nuclear radius r in terms of closest approach of α particle to the nucleus,
    obtained by equating ∆K = ½ mv² of the α particle to the change in electrostatic potential energy ∆U of the system `"U" = (2e xx "Ze")/(4πε_0r_0) r_0 ∼ 10^(-15) "m" = 1` fermi; atomic structure; only general qualitative ideas, including atomic number Z, Neutron number N and mass number A.
• Bohr’s Model for Hydrogen Atom 
  • Explanation of the line spectrum of hydrogen using Bohr theory
  • Bohr's theory and atomic spectrum of hydrogen
  • Ionization energy
• Energy Levels 
• Hydrogen Spectrum 

Alpha-particle scattering experiment; Rutherford's atomic model; Bohr’s atomic model, energy levels, hydrogen spectrum

• Rutherford’s nuclear model of atom (mathematical theory of scattering excluded), based on Geiger - Marsden experiment on α-scattering; nuclear radius r in terms of closest approach of α particle to the nucleus, obtained by equating ΔK=½ mv² of the α particle to the change in electrostatic potential energy ΔU of the system [U = (2exxZe)/4piepsilon_0r_0 r_0~10^(-15)m =1 fermi atomic structure; only general qualitative ideas including atomic number Z, Neutron number N and mass number A. A brief account of historical background leading to Bohr’s theory of hydrogen spectrum; formulae for wavelength in Lyman, Balmer, Paschen, Brackett and Pfund series. Rydberg constant. Bohr’s model of H atom, postulates (Z=1); expressions for orbital velocity, kinetic energy, potential energy, radius of orbit and total energy of electron. Energy level diagram, calculation of ΔE, frequency and wavelength of different lines of emission spectra;
  agreement with experimentally observed values. [Use nm and not Å for unit of λ].

• Atomic Masses and Composition of Nucleus 
  • Composition and Size of Nucleus
• Radioactivity 
  • Introduction of Radioactivity 
  • Alpha Decay 

    Alpha Particles Or Rays and Their Properties

• Law of Radioactive Decay 
• Atomic Mass, Mass - Energy Relation and Mass Defect 
  • Atomic Mass
  • Mass-Energy Relation
  • Mass Defect
  • Packing fraction
• Mass-energy and Nuclear Binding Energy 
  • Nuclear Binding Energy 
    • Binding Energy per Nucleon and Its Variation with Mass Number
• Nuclear Reactions 
  • Transmutation
  • Induced or artificial radioactivity
  • Nuclear fission
  • Nuclear fusion
  • Theoretical (qualitative) prediction of exothermic (with the release of energy) nuclear reaction, in fusing together two light nuclei to form a heavier nucleus and in splitting heavy nucleus to form middle order (lower mass number) nuclei, is evident from the shape of BE per nucleon versus mass number graph. Also, calculate the disintegration energy Q for a heavy nucleus (A = 240) with BE/A ∼ 7.6 MeV per nucleon split into two equal halves with A = 120 each and BE/A ∼ 8.5 MeV/nucleon; Q ∼ 200 MeV.
• Nuclear Energy 

Composition and size of nucleus, Radioactivity, alpha, beta and gamma particles/rays and their properties; radioactive decay law. Mass-energy relation, mass defect; binding energy per nucleon and its variation with mass number; Nuclear reactions, nuclear fission and nuclear fusion.

• Atomic masses and nuclear density; Isotopes, Isobars and Isotones – definitions with examples of each. Unified atomic mass unit, symbol u, 1u=1/12 of the mass of ¹²C atom = 1.66x10^-27kg). Composition of nucleus; mass defect and binding energy, BE= (Δm) c². Graph of BE/nucleon versus mass number A, special features - less BE/nucleon for light as well as heavy elements. Middle order more stable [see fission and fusion] Einstein’s equation E=mc2. Calculations related to this equation; mass defect/binding
  energy, mutual annihilation and pair production as examples
• Radioactivity: discovery; spontaneous disintegration of an atomic nucleus with the emission of α or β particles and γ radiation, unaffected by physical and chemical changes. Radioactive decay law; derivation of N = N_oe^-λt; half-life period T; graph of N versus t, with T marked on the X axis. Relation between half-life (T) and disintegration constant (λ); mean life ( τ) and its relation with λ. Value of T of some common radioactive elements. Examples of a few nuclear reactions with conservation of mass number and charge, concept of a neutrino.
• Changes taking place within the nucleus included. [Mathematical theory of α and β decay not included].
• Nuclear Energy: Theoretical (qualitative) prediction of exothermic (with release of energy) nuclear reaction, in fusing together two
  light nuclei to form a heavier nucleus and in splitting heavy nucleus to form middle order (lower mass number) nuclei, is evident from the shape of BE per nucleon versus mass number graph. Also calculate the disintegration energy Q for a heavy nucleus (A=240) with BE/A ~ 7.6 MeV per nucleon split into two equal halves with A=120 each and BE/A~ 8.5 MeV/nucleon; Q ~ 200 MeV. Nuclear fission: Any one equation of fission reaction. Chain reaction- controlled and uncontrolled; nuclear reactor and nuclear bomb. Main parts of a nuclear reactor including their functions - fuel elements, moderator, control rods, coolant, casing; criticality; utilization of energy output - all qualitative only. Fusion, simple example of 4 ¹H→⁴He and its nuclear reaction equation; requires very high temperature ~ 10⁶ degrees; difficult to achieve; hydrogen bomb; thermonuclear energy production in the sun and stars. [Details of chain reaction not required].