Physics Short Notes PDF

ELECTROSTATICS  1 Q N dV...

ELECTROSTATICS  1 Q N dV 1 Q J Electric Field Intensity:- E = vector unit:- E=− Electric Potential V = scalar unit:- V = − E.dr 40 r 2 C dr 40 r C Electric Dipole:- Equal and Opposite charge separated by small distance, Dipole moment P = 2ql vector(direction from negative to positive charge unit:- C m E & V on Equitorial line:- Torque on Dipole:- Net force = +qE – qE = 0 E & V on Axial Line:- E at pt. P on axial line Torque = Force × ⊥ distance E = EA cos  + EB cos  = qE × BC [BC = 2l × sin θ since = qE 2l sin θ = E (2ql) sin θ is E = E B + ( −E A ) EA = EB τ = PE sin θ = P  E 1 q 1 q E = 2EA cos  τmax = PE for θ = 90o E= − 40 ( r − l )2 40 ( r + l )2 work done in Rotating Dipole 1 q l l E= q  1  − 1   40  ( r − l )2 ( r + l )2  E = 2 2ql   40 x2  x  P cos  = x W=   d = (1 − cos ) PE   E= = Energy of Dipole: U = –PE cos θ 40x3 ( ) 3 Stable equilibrium θ = 0, U= –PE 2  2qrl 2pr 40 x2 + l2 E= = Unstable equilibrium 40 ( r2 − l2 ) 40 ( r2 − l  ) 2 2 P Θ = 180o ⇒ U = PE. E= 3 40 ( r2 + l2 ) 2 2P Gauss Theorem:- Total electric flux (total no. of lines E= For short dipole r >> l (direction (-) 3 40r of forces) emerges from closed surface is 1 times the P 0 to (+)) E= For short dipole r >> l 40 ( r3 )  E.dS =  qin 1 −q 1 q Direction (+) to (-) charge enclosed V = VA + VB = + 40 ( r + l ) 40 ( r − l ) 1 ( −q ) 0 1 q V = VA + VB = + =0 P 40 x 40 x 1 P = V= 40 ( r2 − l2 ) 4 r2 0 E due to long charged wire: E due to charged plane sheet: E due to charged Hallow Sphere: q q q Linear charge density  = Surface charge density  = Volume charge density  = l A V  E.dS =  qin For non conducting plate charge is on both side  E.dS =  qin  q 0 2 E.dS = 0 0 E.dS +  E.dS +  E.dS =  qin  q 1 2 3 E dS = q 0 0 2EA = For dS2 and dS3 θ = 90 o 0 E( 4r2 ) = q For curved surface dS1 θ = 0 q  E= E= 0  q q E dS = ⇒ E ( 2rl ) = 20 A 20 0 0 E= 1 q On surface  40 R 2 2q For conducting sheet E = 0 q 1 2 1 q E= = l ⇒E= * E is independent of distance from the sheet. E= Outside & E = 0 as q = 0 inside 2rl0 40r 40 r 40 r2 Capacitor:- Q = CV unit:- Farad, * C depends on dimensions Capacitance for parallel plate Surface charge Density Energy of Capacitor capacitor Q  = Q = A Energy = work done in bringing charge Consider || plate capacitor with A at potential V area of plate A, capacitance C and Electric field q dW = V  dq =.dq dist. b/w plates d E = Eair + Edielectric C Q Q Q C= Q = Q   1  q2  1 Q2 = +   1 V Ed 0 k0 U = dW = q  dq =   = C C  2 0 2 C  0 0 E= for charged sheet Potential V = E × d 0 1Q 1 2 1 (  U= = CV 2 = QV V = a + b) + t 2 C 2 2 = Q for surface charge density 0 k0 A Energy Density (energy per unit volume)  t A  A V= a + b +  1 2 1 0 A ( E  d) 2 C= = 0 0  k CV  1 d d = 2 =2 d = 0E2 0  t volume Ad 2 V= d − t +  0  k Unit of energy density:- J/m3 If dielectric with dielectric Q A constant k is filled b/w the plates. Now C= = V  t C’ = kC d − t +  0  k  CURRENT ELECTRICITY q A – Area Electric Current: i = , unit - Ampere n – number of free electrons in unit volume t nAle RA m * Scalar quantity i =q/t = resistivity ρ = ρ = Drift velocity:- v = u + a t l ne2 if u = 0  − relaxation time (10 –14 s) Also J =  E Vd = a Current I = neAVd J= I = current density (vector) eE eV I ne 2 A A Also ma = eE = f  a = I = neA = m ml V ml V = IR eE Vd = (10–5 m/s) as V = Exl V ml m R= = I ne2 A eV Vd = V ml Mobility  = d (m2/sV) E Temperature dependence of resistivity Electric Energy & power Colour Coding of Resistor with increase in temperature Power = Energy / Time = Work done / Time conductors :  decrease.   inc. It is a scalar quantity  V2 semiconductors; n increase   dec E = V.I.t = I 2 Rt = t R V2 P = V.I = I 2 R = R 1 unit = 1 KWh Series combination of resistance:- R = R1 + R2. Current same E = V + ir charging KIRCHOFF’S LAW Parallel combination of resistance:- 1/R = 1/R1 + 1/R2 Voltage same E = V – ir discharging i. i = 0 Junction law ii. iR = E = 0 Voltage law Cell in series I = nE /nr + R Meter Bridge: nE Let Unknown Resistance = X Cell in parallel i= r + nR R l = Wheatstone Bridge: X 100 − l Balance condition P/Q=R/S R(100 − R) X= Potential at A & B same at null pt. l RA Position of Galvanometer & Resistivity  = L battery can be interchanged at null pt. Meter bridge in most sensitive when null pt. in middle. Potentiometer: Principle:- If constant current flows through wire of uniform cross section, then drop in directly proportional to length of that portion E Advantage of Potentiometer over voltmeter:- K = = Potential gradient 1. Preferred over voltmeter as it give exact reading draw no L current When K1 inserted then E1 = K × L1 2. Sensitivity increase with increase in length When K2 inserted then E2 = K × L2 3. A small P. D can be measured accurately with the help of E1 L1 potentiometer. The resistance of voltmeter is high but not = E 2 L2 infinity to work as an ideal voltmeter. 4. The internal resistance of a cell can be measured with the help of potentiometer. When only K1 is inserted then E = K × L1 When K1 and K2 both are inserted then V = K × L2 = E – r l  r = R  1 − 1  l2   MOVING CHARGES & MAGNETISM Magnetic Field:- Produced by magnet, moving charge, Vector quantity. Unit:- Tesla (weber/m2), gauss (maxwell/cm2) IT = 104 G Oested Experiment:- Current carrying conductor produces magnetic field.  Bio Savart Law:- It gives M.F. at a point around Ampere’s Circuital Law:- B.dl = 0i The line integral of magnetic field B for current carrying conductor.  idl sin  any closed circuit is equal to μ0 times current i threading through this closed loop dB = 0 4 r 2 and this closed loop is called Amperian loop. 0 B. Due to Infinitely Long Wire:- = 10−7 TmA−1 Magnetic field at P due to wire 4 μ0 – Permeability of free space Direction of B:- Perpendicular to dl and r.  B.dl = 0i  B = 0 if sin θ = 0 B dl = 0i B = max sin θ = 1 θ = 90o  idl  r B(2πr) = μ0i Vector Form dB = 0 4 r 3  2l B= 0 4 r Mag. Field At Centre of Coil:- Direction:- Right Hand Thumb Rule curly finger gives field direction if thumb of  idl sin 90o right hand points current outside dB = 0 4 r2 B. due to Solenoid:- B =   i dB = 0 2 4 r  dl  Bdl = B.dl cos   i N – Total Turns = 0 2 (2r ) d 4 r  i B = 0 or B = 0  Ni a  B.dl = 0i 2r 2r b c d a Direction:- Right Hand Thumb Rule. On Axis of Coil:- 0 idl sin 90o  a  b  c  B.dl + B.dl + B.dl + B.dl = 0 ( Ni ) d dB = 4 x2 b B =  dB sin   B.dl + 0 + 0 + 0 =  ( Ni ) a 0 0i ( 2a ) a =. b 4x2  x N B. dl = 0 Ni B.L = 0 ni ⇒ ∴ B = μ0ni n= (Turns per unit Length) 2 L 0 Nia B= a 2 ( a2 + r 2 ) 3/ 2 Force on charge in Electric field:- Magnetic Field:- B. Due to Toroid:- (Closed solenoid) F = qE (both for rest & motion) F = qV Bsin θ (only for moving charge)  B.dl =  Ni0 B (2r ) = 0 Ni 0 Ni  N  B= n =  2 r  2r  B = 0 ni [at P] Lorentz Force:- F = qE + qvB sin θ = q (E + vB sin θ) Cyclotron:- Used to accelerate charge Particles. Force b/w 2 parallel current carrying wire:- Force acting on a due to b. Principle:- The repeated motion of charged particles under mag. & ele.   2i  field accelerates it. E.F. provides energy while M.F. changes direction. F =  0 1  i2l sin 90o  4 r  Construction:- Dees, Sources, M.F., R.F. Oscillator 1 2    2i i Working:- Max KE = mvmax F =  0  1 2 (For unit Length) 2  4  r 2 By Flemings LHR force is of attraction for same 1  qBr  = m  direction of current and force of repulsion for opposite 2  m  direction of current. 2 2 2 1q B r if i1 = i2 = 1 A, r = 1m. K.E. = 2 m then F = 2 × 10–7 N. Current Sensitivity:- Deflection per unit current Moving Coil Galvanometer:- Device Torque Experienced By a  BAN Radian Is = = to detect & measure electric current. Current loop in uniform i C Ampere Principle:- Current loop experience Magnetic Field:- Voltage Sensitivity:- Deflection per unit voltage torque in uniform M.F. τ = F × ⊥ distance I   BAN  Radian  Construction:- Light Coil, concave = Bil × bsin θ Vs = s = = =   magnetic Poles → radial field. τ = Bi A sin θ R V iR CR  Volt  Theory:- Deflecting torque For N Turns:- Limitation:- Only charged particles can be acceleration Application:- = Restring force (torque) τ = BiNa sin θ For circular path:- For nuclear B × i × N × A × sin θ = CØ mv2 mv reaction & other (θ = 90o) as field is radial = qvB ⇒ r = ⇒r∝v research purpose. C r qB ∴ B AiN = CØ ⇒ i = ABN 1 q 2 B2r 2 K.E. = 2 m Time period = Distance / Velocity = 2πr / v ⇒ T = 2πm / qB Frequency of Revolution:- f = 1/T = qB/2πm Conversion of Galvanometer into Ammeter:- Conversion Into Voltmeter:- By connecting high resistance in series (i – ig)S = ig.G {For Ideal voltmeter, R = ∞} ig.G V = ig ( R + G ) S = i − ig V ( = R + G) {For Ideal Ammeter R = 0} ig ELECTROMAGNETIC INDUCTION (E.M.I) The phenomena of producing induced current due to change in magnetic flux is called electromagnetic induction. Faraday Law:- (i) Change in magnetic flux induces current which last till there is change. −d  (ii) e = dt Lenz’s Law:- Induce current opposes the factor due to which it is produced. Method of producing emf:- acc. to law of conservation of energy. − d  − dBAcos  e= = dt dt Induced current / charge:- −d  e −d  dq −d  e= ,i = = , = dt R Rdt dt Rdt −d  dq = R Motional emf:- The emf induced due to motion of a conductor in M. field. −d  −d  Eddy Current:- The circulating induced Motional emf:- e = Rotating rod:- e = current in a oscillating metallic block kept in dt dt magnetic field. In can be reduced by using − dB.A − dBA = e= laminated core, or cutting slots in block. dt dt Application:- − BdA − Bldx BdA (i) Magnetic brakes = = e= (ii) Induction furnace dt dt dt (iii) Dead beat galvanometer e = − Bvl BL2 e= Direction = Anticlockwise 2 Force:- i = Bvl  R 1 1 e = BL2 or e = BR2  Bvl  2 2 F = Bil = − B  l  R  No. of spokes is increased emf remain same. − B2vl 2 F= R Power:- P = Fv − B2v2l 2 P= R Self – Induction:- Change in current in a coil, induced Mutual – Induction:- when the change in current *No. of turns is double than inductance current is produced which opposes the change in same coil. in primary coil induces current in secondary coil. become four times ( L ∝ n2). Electrical Resonance:- Unit:- L = 1 Henry (H) ϕ∝i 1 1 Dimension Formula:- [ML2T–2A–2] ϕ = Mi F= 2 LC Solenoid:- Unit – Henry ϕ = Li ∈0 = Farad/m Power in A.C. circuit:- ϕ = BAN = (μ0niA) × N μ0 = Henry/m 1 P = V0i0 cos  Li = μ0n2 × i × A × l (n = N/l) Solenoid:- B2 = μ0n2i2 2 L = μ0n2Al ϕ = B2AN1 V i ϕ = (μ0n2i2)AN1 P = 0 0 cos  ϕ = Mi2 2 2 Mi2 = μ0n1n2Ali2  P = VRMS iRMS Cos  M = μ0n1n2Al  R Cos  = Z   MAGNETISM & MATTER Properties of Magnet: Permanent Magnets are made up of steel: Magnetic Material: 1. Magnets have north pole and south pole. Hysteresis Loop / curve: The graph plotted b/w 2. Likes poles repel & unlike attract each other. external field (H) & mag. induction (B) is called “BH Paramagnetic Diamagnetic Ferromagnetic 3. Freely suspended magnet rests in N – S direction. curve ‘or hysteresis Loop. 1. odd no of e– 1. Even no of 1. 4. Monopole do not exist. Energy Loss: Work done (energy loss) in in outer most e– and Ferromagnetic 5. Mag. Length is eq to 0.84 times of their geometric magnetization and demagnetization is eq. to area of orbit & possess net materials length. BH curve. possess net dipole have some Elements of Earth’s magnetic field: dipole moment is 0. unpaired Magnetic Dipole Moment: N  2l → S 1. Angle of Dip: Angle b/w horizontal line & mag. moment. electrons so M = m2l unit: Am2 their atoms meridian as a freely suspended magnet. m → pole Strength. have a net 2. Angle of Declination: Angle b/w geographical M → Magnetic Dipole Moment magnetic meridian & mag. meridian is called Angle of Declination moment. They M. Due to Current Loop: When current is passed get their strong 3. Horizontal Intensity of Earth Mag. through a loop it, behaves like a magnet. (M = iA) = magnetic The horizontal component of to. Earth’s field at any current × Area, M = NiA properties due point is called horizontal intensity q evr to the presence ⸫ M= ( r) 2 = {for e-, v = 2r/t} BV Bsin  = tan  , B2 = (BH ) 2 + ( BV ) 2 t 2 = of magnetic BH Bcos  domains. Magnetic Dipole Moment of a revolving: B = BH 2 + BV 2 M = iA = ( r 2 ) = q evr 2. Aligns || to 2. Align ⊥ 2. When {for e-, v = 2r/t} field & get a magnetizing t 2 to ext. field. weakly force magnetized is applied, the Magnetic Field of Earth: along ext. domains Magnetic Field Intensity due to magnetic Dipole: field. become aligned 0 2M to produce a 1. On Axial line: B = 4 r 3 strong magnetic  M field 2. On Equatorial line: B = 0 3 within the part. 4 r Torque Acting on dipole in Mag. field: 3. Mag. field 3. Mag. field 3. Temp. at  = f  dis. = mB2 l sin = m2 lBsin pass through repelled by which substance substance. ferromagnetic = MBsin substance ⸫  = MBsin  becomes →Torque is ⊥ to mag. field and mag. dipole paramagnetic moment (M) called curie Temperature. →  max = MB (sin = 1),  = 90° {Due to torque 4. Increase rotation motion or liner. } 4.Increase with increase →  min = 0 = (sin = 0) ,  = 0 with decrease in temp in temp. Work done in Rotating the Dipole: W = MB [cos1 – cos2] Electromagnets: Are prepended by passing electric current in a solenoid. The magnet lasts till the current is passed. It can be increased by: 1. Increasing number of turns. 2. Increasing current. 3. using soft iron core.  ALTERNATING CURRENT (A.C) TRANSFORMER: - It is a device use the A.C. Generator :- It is a device which convert mechanical Alternating Current: - change AC voltage. energy into electrical energy. D.C – Direction & magnitude are fixed. Principle: It is based on principle of mutual Principle: It is based on principle of electromagnetic A.C – Change in both magnitude and direction. induction. induction. Construction: two coil primary & secondary Construciton:  V Step up: Increase voltage (k>1) and decrease (i) Arumature coil. HALF– CYCLE: Vavg. =  current. (ii) Field magnet 0 Step down: decrease voltage (k < 1) and (iii) Slip ring 1 increase current. (iv) Brushes. Vavg. =   V sin  d 0 V N ip  − d 0 Theory:  s = S = = K  e= 1  −V0 cos 0  Vp N p is  dt Vav = – dBA cos t   output  e= −V0  =  100%  dt Vav = cos  − cos 0  input  e = BA(–ωsinωt)  e = BAN ωsin ωt emax = e0 = BANω 2V0 2I0 Vav = or Iav = e = e0sinωt   2 1 Full Cycle: Vav = 2  V d 0 2 1 Vavg = 2  V sin  d 0 0 V0 ( − cos )0 2 Vavg = 2 A.C. Circuit: - V V Pure Resistive Circuit: (Circuit containing Pure capacitor circuit (circuit containing capacitor only) Vavg = 0 ( − cos 2 + cos ) = 0 ( −1 + 1) 2 2 resistance) Q = CV Vavg =0 or Iavg = 0 d dV d d V V0 =C , i=C (V0 sinωt) i = CV0 sin  t Root mean Square: = sin  t dt dt dt dt 2 R R 1 VRMS = V 2 2 i = i0 sin t  V = V0 sin t  0 2 2 1 1 V 2 RMS = V = V sin 2  d 2 2 2 2 0 V 0 0 I ωCV0 cosωt V0 V02 V2  2 1 − cos 2  Resistance is independent frequency of A.C. i= sin( t +  / 2) V 2 RMS = ( ) = 0 sin  =  1 2 2  2  C V0 I0 VRMS = or IRMS = V i= 0 2 2 1 C Pure inductive circuit: Series LCR circuit: - V = V0 sin ωt Ldi v2 = VR2 + (Vc − Vc)2 V= dt (IZ)2 = (IR) 2 + (IX L − IXC ) 2 +Vdt di = Z = R 2 + (XL − XC )2 L V0 sin  tdt 2 di =  1  L Z = R 2 +  L −   C  V0 V  di = L  sin t dt = L0 ( − cos t )  L − 1   C  ⇒  tan  = XL − XC   tan  =    R   R     RAY OPTICS I −v Reflection of Light: i = r, Magnitization m = = − real inverted. + virtual erect. o u → Convex Mirror +f, m < 1 and negative m > 1 (enlarged) m < 1(small) → Concave Mirror −f , m > 1, < 1, = 1 both +& − sin i μ2 v1 λ1 1 Refraction of Light: μ = , 1μ2 = = = = = 2μ1 sin r μ1 v2 λ2 1μ2 1 Total Internal Reflection (i) Denser → Rarer (ii) i > ic sin ic = ( ) μd Mirror formula: Thin lens formula: Refraction through Spherical Surface: ASSUMPTION: Object AB image A′ B ′ △ ABP ≈△ A′ B ′ P △ AFB ≈△ PFN AB PB u AB AB FB u − f = = − (i) = = = − (i) A′ B ′ PB ′ v PN A′ B ′ PF f △ MPF ≈△ A′ B ′ F (Since i & r are very small) ΔA′ B ′ F ≈ ΔMFP PM PF f 1. Small Aperture MP AB PF f = ′= − = ′ ′= ′= − (ii) AB′ ′ FB v−f 2. Point size object AB′ ′ AB FB v−f AB v By snell's law from eq − (i) and (ii). ′ ′ = − (ii) AB v−f sin i i u−f f From eq (i) and (ii) μ= = = sin r r f v−f f u i = μr By sing convention u, v, f are -ve. = v−f v △ COM f 2 = (u − f)(v − f) Since u = −ve sign convention α=i+γ ∴ i=α−γ f 2 = uv − uf − fv + f 2 vf = (−u)v − (−u)f △ CIM uv = uf + vf. vf = −uv + uf β=r+γ ∴ r = β − γ. Dividing by uvf uv = uf − vf α − γ = μ(β − γ) uv uf vf Dividing by uvf = + PM PM (PM PM) uvf uvf uvf 1 1 1 − =μ − 1 1 1 = − −u −R −v −R = + f v u 1 1 μ μ μ 1 μ 1 f v u − = − ⇒ − = − u R v R v u R R m = I/0 = −v/u μ 1 (μ − 1) − = v u R Lens maker formula: 1 μ 1−μ Combined focal length: - − = − (ii) v v′ R2 adding eq (i) & (ii). 1 1 1 1 − = (μ − 1) ( − ) v u R1 R 2 By Refraction through first surface 1 1 1 First lens forms image I ′ of 0 μ 1 μ−1 = (μ − 1) ( − ) − = ⋯ (1) f R1 R 2 1 1 1 v′ u R1 = − − (i) Power of Lens: f1 v′ u I ′ acts as an object for second surface so 1 100 I' acts as object for second lens and that final image is formed at I, so for P= = Diopter. f( m) f( cm) final image is formed at I, so for second second surface. leans. 1/μ 1 1/μ − 1 − = 1 1 1 v v′ R2 = − − (ii) f2 v v ′ Adding eq (i) & (ii) 1 1 1 1 − = + v u f1 f2 Refraction through a Prism: In quadrilateral AMPN. By snell’s Low ∠A + 90∘ + ∠P + 90∘ = 360∘ sin i μ= N A + 90∘ + 180 − (r1 + r2 ) + 90 = 360 sin r A = (r1 + r2 ) − − − (2) A + δm sin ( ) μ= 2 i+e = A+δ A At minimum deviation δm sin ( ) 2 i = r1 + x ie, r1 = r2 = r For then prism } vertically e = r2 + y A + δm 2i = A + δm opposite Angles. (A + δm ) 2 μ= i + e = (r1 + r2 ) + (x + y) –-----(1) ∴i= − − − − − (3) A/2 2 δ=x+y A δm = (μ − 1)A exterior angle is equal A = 2r ∴ r = ( ) − − − −(4) A-Prism Angle 2 to sum of interior angles μ = Refractive Index. ∠P = 180 − (r1 + r2 ). Angular Dispersion: θ = δV − δR = (μV − μR )A θ δv −δR (μv −μR )A (μv −μR ) Dispersive Power: ω = = = ⟹ ω= δy δy (μy −1)A (μy −1) 1 Scattering of light: δ ∝ (Rayleigh) Danger signals Red. λ4 (RAYLEIGH LAW) sky appears blue. Reddish appearance of sun-rise, sunset. OPTICAL INSTRUMENTS: Simple Microscope: Convex lens of low focal length and high power. i) Image at D.: Object placed blow Focus and tens. ii) Image at ∞ Object placed on focus. Magnifying Power. D magnifying Power m = D f m= 1+ fe β Angle made by image m= = α angle made by object when kept in position of image. Compound Microscope: Objective - (convex lens of low focal length and small aperture). Eyelens - (convex lens of high focal length and large aperture). i) Image at D.: Final virtual inverted Image. ii) Image at infinity ∞ Final Image at Infinity. v0 D 1 D m = m0 × me = (1 + ) ≈ (1 + ) −u0 fe fe fe v0 D L D ( )≈ ⋅ m=− u0 fe f0 fe Length of tube L = v0 + fe Astronomical Telescope: Objective - (convex lens of high focal length & large aperture.) Eyelens - (Convex tens of low focal length & small aperture.) i) Image at Infinity ii) Image at D f0 m= f0 fe fe m= (1 + ) fe D L = f0 + fe (Length of tube) D Length of the Tube L = f0 + ue R. P = 1.22λ D-Diameter of objective Reflecting Telescope: Concave mirror acts as an objective. ADVANTAGES: 1) Bright Image is formed. 2) Image free from chromatic aberration. Resolving Power:- The ability of optical instrument to form distinct image of two object situated close to eachother. Resolving Power of Microscope Telescope 2μ sinθ D [(R ⋅ P)m = ] [(R ⋅ P)T = ] λ 1.22λ 1 (R ⋅ P) ∝ limit of resolution E0 Polarisation: C= Brewsters law tan ip = μ B0 Malus law: Iθ = I0 cos 2 θ  WAVE OPTICS A wavelet is the point of disturbance due to propagation of light. A wavefront(w.f.) is the locus of points having the same phase of oscillation. A line perpendicular to a wavefront is called a 'ray'. HUYGEN'S PRINCIPLE:- Find the shape of wavefront at any particular instance. The two postulate are- (i) Each paint on primary w. f. acts as a source of secondary w.f. which travel in all direction with speed of light. (ii) The forward envelope or common tangent of secondary w. f. give shape of new wavefronts. Reflection by Huygen’s Principle Refraction by Huygen’s Principle S′1 S′2 (M-1) i MPN and MQN , MN = MN common side P = Q = 90o ,PN = MQ (dist. covered by light in same time) PN = V1t MPN  MQN (by SAS) MQ = V2t 90 − i = 90 − r sini PN / MN PN μ0 = = = i=r sinr MQ / MN PQ v1 t v1 μ0 = = v 2t v t INTERFERENCE OF LIGHT: - Variation of intensity of light due to overlapping of two light waves. Constructive: - Resultant increase and bright light is formed. λ 3λ λ Path diff.:- Δx = 0, λ, 2λ,..... ,3λ Destructive:- Path diff.:- x = , ,....., (2n − 1) 2 2 2 Phase diff.:- Δϕ = 0,2π, 4π, 6π,..... ,2nπ Phase diff.:- Δϕ = π, 3π, 5π ⋯ (2n − 1)π 2π Δϕ = × Δx λ Destructive:- Resultant is minimum. Young's double slit Experiment (YDS):- A monochromatic light beam is incident in double slit the pattern obtain on screen consist alternate bright and dark bands called fringes. Expression for Interference Pattern: Expression for fringe width: Let, two interference wave y1 = a,sinωt y 2 = a2(sin(ωt + ))   = phase diff. by Principle of Superposition- y = y1 + y 2 y = a1sinωt +a2sin(ωt + ) y = a1sinωt +a2sinωt cos  +a2cosωt sin  y = sinωt (a1 +a2cos)+a2cosωt sin S2M = S2P-S1P from S2PC a1 + a2cos = Rcosθ S2P2 = D2 +(x + d / 2)2   a2sin = Rsinθ  from S1BP1 y = R sinωt cosθ+cosωt R sinθ S1P2 = D2 +(x - d / 2)2 y = R sin(ωt +θ)  a1 +a2cos +a2 sin = Rcosθ+Rsinθ Square both side S2P2 - S1P2 = 2xd a12 + a22cos2 + a22sin2 = R 2cos2θ+ R 2sin2θ (S2P-S1P)(S2P+S1P)= 2xd a + a (cos  + sin ) = R (sin θ+ cos θ)- 2a1a2 cos  2 1 2 2 2 2 2 2 2 (S2P-S1P)(D+D)= 2xd a + a + 2a1a2cos  = R 2 1 2 2 2 (S2P-S1P)(D+D)= 2xd R = a12 + a22 +2a1a2cos  2xd S2P - S1P = 2D R max =(a1 +a2 )  = 0º From bright fringe for path difference, R min = (a1 − a2 )  = 180º S2P-S1P = n λ β = xn+1 − xn I ∝ a2 ∝ ω xd = nλ β= (n+1)λD − nλD D d d nD λ λD xn = β= d d Dλ x= d For destructive interference: xd λ = (2n -1) β = x n +1 − x n D 2 λD λD (2n − 1)λ D x n = (2n − 1) β = (2(n + 1) − 1) − 2d 2d 2d λD β= d Interference pattern the intensity of all bright band is equal. Coherent Source - The two light source behave like coherent source if they belong to same parent source. Diffraction - It is bending of light at sharp corners or edges. Fresnel’s distance - df = d2 /λ Single slit diffraction – Intensity distribution curve: dark band or minima - d sin θ = n λ (2n+1) maxima - dsinθ = λ 2 Linear width of central maxima:  arc  angle = raclius , β0 = θ  D   λD β0 = d  DUAL NATURE Of MATTER AND RADIATION Photoelectric emission: The emission of electron due to action of light of suitable energy is called photoelectric emission. The e− emitted are called photoelectrons. Properties of Photon- (a) Photon is a bundle of energy- E = n0 ⇒ E = hc/λ (b) Photon travel with speed of light. (c) Rest mass of photon is zero. (d) momentum of photon is p = E/C. Photoelectric effect → The of e− from a metal surface when light of suitable frequency is incident on it is called photoelectric effect. Alkali metals like Li, Na, K show photoelectric effect with visible light metal like Zn, mg, Ca respond to ultraviolet light, Laws of Photoelectric emission - (a) minimum energy required called threshold energy or work function. The freq. corresponding to threshold energy called threshold freq. E = f = hν0 ν0 = threshold frequency Work function(E = f) (b) Every photon interact with a single electron. (c) increasing the energy of incident photon the Kinetic energy of e− emitted increase. Effect of Intensity:- I1 > I2 (Freq. = constant) Voltage Effect of frequency: Determination of Plank's constant:- frequency From Einstein Photoelectric equation – hν = hν0 + K ⋅ E eν0 = K ⋅ E hν = hν0 + ev0 Einstein Phataelectric Equation: Photoelectric effect was explained using quantum theory by Einstein. E=ϕ+K⋅E In terms of wavelength:- 1 hν = hν0 + mv 2 c c 1 2 h ( − ) = mv 2 1 λ λ0 2 hν − hν0 = mv 2 2 1 1 1 1 hc ( − ) = mv 2 h(ν − ν0 ) = mv 2 λ λ0 2 2 Dual Nature of Matter: De-broglie Hypothesis – Acc. to De-Broglie a wave is associated with every moving particle. This wave is called matter wave and its wavelength is known as de-Broglie wavelength. Expression for 𝛌 : In term of Energy: In term of charge & potential: By particle nature, E = mc 2 P = mv 2 E = qV By wave nature E = hν 1 h E = mv 2 λ= equate both the energy 2 √2qVm 2E = mv 2 mc 2 = hν For electron:- hc 2mE = m2 v 2 h m = 2 2mE = p2 λ= λc √2meV o h P = √2mE 12⋅3 A m = Therefore λ= λc √V h h h Temp:- λ = h λ = λ= = √3mKT mc P √2mE 3 h ( P = momentum) E= kT λ = 2 p K = Boltzmann constant Davisson & Germer Experiment:- Theory/ working:- A high energy e− beam is incident on a (i) Electron gun - producers a fine beam of e− of high nickel crystal which diffracts this e− beam. The intensity of speed. diffracted beam in various direction is measured with help of (ii) Nickel crystal - It is used to diffract the e− beam. detector mounted on circular scale. (iii) Detector - It is used to find the intensity of diffracted At 54 volt a clear hump (maxima) at angle of 50∘ , then by e− beam. bragg's law for diffraction by crystal. 2dsin θ = nλ 0.91 × sin 65∘ = 1 × λ ∴ λ = 1.65Å by de-Broglie hypothesis h λ = = 1.66Å p  ATOM & NUCLEI Rutherford 𝛂-particle scattering Exp:  o n 2 h2 Exp. Setup: Radius of Bohr orbit: rn = me2z for hydrogen z = 1 ENERGY OF BOHR ORBITS:- 1 ze(−e) E = KE + PE = mv 2 + 2 4πεo r OBSERVATIONS: 1 ze2 ze2 mv 2 1 2e2 = − ( = ) (i) Most of the α-particle passed underiated. 2 4πεo r 4πεo r r 4πεo r (ii) Few α-particle scattered at angle θ −Ze2 En = 8πεo rn 1 N∝ −e2 −13.6 θ For H Atom En = = eV sin4 ( ) 8πεo rn n2 2 HYDROGEN SPECTRUM:- (iii) Very few retraces their path. Hydrogen spectrum consist of group of radiation emitted by RUTHERFORD’S MODEL OF ATOM: (1909) a h-atom whose wavelength is given as i) Most of the part of atom is hollow. ii) The central core is (+) very charged called nucleus (10-15m) 1 1 1 = Rz2  2 – 2  Rydberg constant R =1.09  107. m–1 e− revolves around the nucleus & radius of orbit decreases   n1 n2  due to decrease in energy (dement). Distance of closest approach: −e2 En = 1 1 (2e)(ze) 8πεo rn mv 2 = 2 4πεo r0 2ze2 ∴ r0 = 1 4πεo ( mv 2 ) 2 Impact parameter: It is perpendicular distance of the velocity vector when α −particle from centre of nucleus when α particle is far away from atom. 1 2ze2 θ b= 2 cot 4πεo mv 2 smaller is b’ larger is angle of scattering θ Lyman Series: θ 2b Electron jump from higher orbit to first orbit. cot = 2 r0 n = L, n2 = 2, 3, 4........ for θ = 180∘ (rebounds) b = 0 BOHR’S MODEL: (1913) 1 1  3  1. The e− can exist in certain orbit without radiating energy. v1 = R,  2 – 2  = R   n1 n 2  4  mv 2 1 ze2  Ultra Voilet Region = 1 1  8  r 4πεo r 2 v2 = R  2 – 2  = R  2. Only those orbit are allowed for which the angular  n1 n 2  9  momentum (mvr) is integral multiple of h/2π. BALMER: Visible Region nh Paschen, Brackett, P Fund :- Far Infrared mvr = n = 1, 2, 3…. Quantum No. 2π 3. Electrons Reboring in their stationary orbit do not radiate energy (non-radiative orbits or BOHR’S orbits) 4. If the e– goes from orbit of energy E1 to other orbit of energy E2 then a photon of energy hv is radiated such that hv = E2 – E1 Nucleons = Protons + Neutrons Nuclear volume ∝ Mass No. 1 1 amu = A = Z + N. 4 3 12( 12 6 C) πR ∝ A Mass = Atomic + No. of 3 = 1.66 × 10 −22 kg No. Neutrons. OR R = R O A1/3 Electron volt (ev) – unit of energy R 0 = 1.4 × 10−15 m 1 eV = 1.6 × 10−19 J. 1 Fermi = 10−15 m. 1 amu = 931MeV NUCLEAR DENSITY: 1017 kg/m3 Nuclear force Independent of mass no. and same For strong all elements short range m⋅A 3m e= 3 = spin dependent 4/3πR 0 A 4πR30 charge independent Isotopes: Same protons (Z) but different(A) Ex ∶ 1H 1 , 1H2, 1H3; 2H3 , 2H4, 2 H6 No. of Neutron. Isobars: Same (A) but different (2) Ex ∶ 11 Na22 ; 10 Ne22 ; 20 Ca40 ; 18 Ar 40 Isotones: Same no. of neutrons. Ex: 1 H 3 ; 2 He4 ; 8 O16 ; 6 C14 Mass Energy Relation: Variation in B.E/Nucleon with mass no. E = Δmc 2 1. B. E/A is very less for A = 8 and then increases up to A = 60∘ Energy & mass are 2. Decreases after A = 120∘ interconvertible. 3. Maximum 10.8mev for Mass Defect: Difference in masses. of Range A = 30∘ to A = nucleons & nucleus. 120∘ Δm = [ZMp + (A − Z)Mn ] 4. Peak for 2 He4 , 6 C12 , 8 O16