ENGINEERING PHYSICS 2 – For First Year Degree Course in Engineering – Semester 2 – As Per University of Mumbai (MU) Syllabus

Chapter 1: Diffraction
Chapter 2: Laser and Fibre Optics
Chapter 3: Electrodynamics
Chapter 4: Relativity
Chapter 5: Nanotechnology
Chapter 6: Physics of Sensors

Chapter – 1 : Diffraction

1.1 Introduction ……………………………………………………………………………………………………………………………….

1.2 Fraunhoffer’s Diffraction at Single Slit …………………………………………………………………………………..

1.3 Fraunhoffer Diffraction at a Double Slit ………………………………………………………………………………

1.4 Fraunhoffer Diffraction due to N-Slits (Diffraction Grating) …………………………………………… 1.14

1.5 Resolving Power ……………………………………………………………………………………………………………………… 1.20

1.5.1 Resolving Power of a Grating …………………………………………………………………………………….. 1.20

1.6 Applications of Diffraction Grating ……………………………………………………………………………………… 1.22

1.7 Determination of Wavelength of Light using Plane Transmission Grating ………………….. 1.23

• Summary ………………………………………………………………………………………………………………………………….. 1.24

• Important Formulae ……………………………………………………………………………………………………………….. 1.25

• Solved Problems …………………………………………………………………………………………………………………….. 1.26

• University Questions ………………………………………………………………………………………………………………. 1.42

• Practice Problems …………………………………………………………………………………………………………………… 1.43

Chapter – 2 : Laser and Fibre Optics

2.1 Introduction of Laser ……………………………………………………………………………………………………………….. 2.1

2.1.1 Interaction of Light with Matter (Quantum Processes) …………………………………………… 2.1

2.2 Einstein Coefficients and Their Relationship ……………………………………………………………………….. 2.5

2.3 Light Amplification …………………………………………………………………………………………………………………… 2.6

2.3.1 Population Inversion ……………………………………………………………………………………………………… 2.7

2.3.2 Metastable States ………………………………………………………………………………………………………….. 2.8

2.3.3 Active Medium ……………………………………………………………………………………………………………….. 2.8

2.3.4 Pumping ………………………………………………………………………………………………………………………….. 2.8

2.3.5 Optical Resonant Cavity ……………………………………………………………………………………………….. 2.9

2.3.6 Lasing Steps ……………………………………………………………………………………………………………………. 2.9

2.3.7 Properties of Laser ……………………………………………………………………………………………………….. 2.10

2.3.8 Various Levels of Laser System ………………………………………………………………………………….. 2.10

2.4 Helium-neon Laser …………………………………………………………………………………………………………………. 2.12

2.5 Nd : YAG Laser ………………………………………………………………………………………………………………………… 2.14

2.6 Semiconductor Diode Laser …………………………………………………………………………………………………. 2.15

2.7 Applications of Laser ……………………………………………………………………………………………………………… 2.18

2.7.1 Holography …………………………………………………………………………………………………………………… 2.19

2.8 Fibre Optics (Optical Fibre) …………………………………………………………………………………………………… 2.21

2.8.1 Propagation of Light through an Optical Fibre ………………………………………………………. 2.23

2.9 Types of Optical Fibre ……………………………………………………………………………………………………………. 2.25

2.9.1 V-Number ……………………………………………………………………………………………………………………… 2.28

• Summary ………………………………………………………………………………………………………………………………….. 2.28

• Important Formulae ……………………………………………………………………………………………………………….. 2.30

• Solved Problems …………………………………………………………………………………………………………………….. 2.31

• University Questions ………………………………………………………………………………………………………………. 2.37

Chapter – 3 : Electrodynamics

3.1 Introduction ………………………………………………………………………………………………………………………………. 3.1

3.2 Electrodynamics ……………………………………………………………………………………………………………………….. 3.1

3.3 Coordinate System …………………………………………………………………………………………………………………… 3.4

3.4 Vector Integration ……………………………………………………………………………………………………………………. 3.8

3.5 Del Operator ……………………………………………………………………………………………………………………………… 3.9

3.5.1 Gradient …………………………………………………………………………………………………………………………… 3.9

3.5.2 Divergence …………………………………………………………………………………………………………………….. 3.10

3.5.3 Curl …………………………………………………………………………………………………………………………………. 3.11

3.6 Gauss Law of Magnetism ………………………………………………………………………………………………………. 3.14

3.7 Stoke’s Theorem …………………………………………………………………………………………………………………….. 3.15

3.8 Faraday’s Law of Electromagnetic Induction …………………………………………………………………….. 3.16

3.9 Maxwell’s Equation ………………………………………………………………………………………………………………… 3.16

3.9.1 Derivation of Maxwell’s First Equation …………………………………………………………………….. 3.18

3.9.2 Maxwell’s Second Equation ……………………………………………………………………………………….. 3.19

3.9.3 Derivation of Maxwell’s Third Equation …………………………………………………………………… 3.19

3.9.4 Maxwell’s Fourth Equation …………………………………………………………………………………………. 3.20

• Summary ………………………………………………………………………………………………………………………………….. 3.22

• Solved Problems …………………………………………………………………………………………………………………….. 3.23

• University Questions ………………………………………………………………………………………………………………. 3.28

• Practice Problems …………………………………………………………………………………………………………………… 3.29

Chapter – 4 : Relativity

4.1 Introduction ………………………………………………………………………………………………………………………………. 4.1

4.2 Frames of References ………………………………………………………………………………………………………………. 4.2

4.3 Galilean Transformation ………………………………………………………………………………………………………….. 4.3

4.3.1 Galilean Coordinate Transformation ………………………………………………………………………….. 4.4

4.3.2 Galilean Velocity Transformation ………………………………………………………………………………… 4.4

4.3.3 Galilean Acceleration Transformation ………………………………………………………………………… 4.4

4.3.4 Invariance of an Equation …………………………………………………………………………………………….. 4.5

4.4 Einstein’s Special Theory of Relativity …………………………………………………………………………………… 4.5

4.5 Lorentz Transformation of Space and Time ………………………………………………………………………… 4.6

4.6 Length Contraction ………………………………………………………………………………………………………………… 4.10

4.7 Time Dilation …………………………………………………………………………………………………………………………… 4.11

4.8 Mass-Energy Relation ……………………………………………………………………………………………………………. 4.13

• Summary ………………………………………………………………………………………………………………………………….. 4.15

• Solved Problems …………………………………………………………………………………………………………………….. 4.16

• Questions …………………………………………………………………………………………………………………………………. 4.23

• Practice Problems …………………………………………………………………………………………………………………… 4.24

Chapter – 5 : Nanotechnology

5.1 Introduction ………………………………………………………………………………………………………………………………. 5.1

5.2 Properties of Nanoparticles ……………………………………………………………………………………………………. 5.2

5.2.1 Optical ……………………………………………………………………………………………………………………………… 5.2

5.2.2 Electrical…………………………………………………………………………………………………………………………… 5.4

5.2.3 Magnetic …………………………………………………………………………………………………………………………. 5.4

5.2.4 Structural …………………………………………………………………………………………………………………………. 5.5

5.2.5 Mechanical ……………………………………………………………………………………………………………………… 5.6

5.3 Surface to Volume Ratio …………………………………………………………………………………………………………. 5.6

5.4 Two Main Approaches in Nanotechnology …………………………………………………………………………. 5.7

5.4.1 Ball Milling ………………………………………………………………………………………………………………………. 5.8

5.4.2 Sputtering Deposition …………………………………………………………………………………………………… 5.9

5.4.3 Solgel ……………………………………………………………………………………………………………………………… 5.11

5.4.4 Vapour Deposition ………………………………………………………………………………………………………. 5.13

5.5 Tools for Characterization of Nanoparticles ……………………………………………………………………… 5.15

5.5.1 Scanning Electron Microscope (SEM) ………………………………………………………………………. 5.15

5.5.2 Transmission Electron Microscope (TEM) ………………………………………………………………… 5.17

5.5.3 Atomic Force Microscope (AFM) ………………………………………………………………………………. 5.20

5.6 Applications …………………………………………………………………………………………………………………………….. 5.22

• Summary ………………………………………………………………………………………………………………………………….. 5.24

• University Questions ………………………………………………………………………………………………………………. 5.25

Chapter – 6 : Physics of Sensors

6.1 Introduction ………………………………………………………………………………………………………………………………. 6.1

6.2 Resistive Sensors ………………………………………………………………………………………………………………………. 6.4

6.3 Pressure Sensor (Capacitance Transducer) ………………………………………………………………………….. 6.8

6.4 Inductive Transducer ……………………………………………………………………………………………………………….. 6.9

6.4.1 Change in Self Inductance with Number of Turns …………………………………………………. 6.10

6.4.2 Change in Self-Inductance with Change in Permeability ……………………………………… 6.10

6.4.3 Variable Reluctance Type Transducer ………………………………………………………………………. 6.11

6.4.4 Analog Pressure Sensor ………………………………………………………………………………………………. 6.12

6.5 Piezoelectric Transducer ……………………………………………………………………………………………………….. 6.12

6.5.1 Piezoelectric Ultrasonic Transducer ………………………………………………………………………….. 6.14

6.5.2 Ultrasonic Distance Meter (Sensor) ………………………………………………………………………….. 6.15

6.6 Optical Sensor (Photodiode) ………………………………………………………………………………………………… 6.15

6.7 Pyroelectric Sensor …………………………………………………………………………………………………………………. 6.17

6.7.1 Bolometer (Application of Pyroelectric Sensor) ……………………………………………………… 6.18

• Questions …………………………………………………………………………………………………………………………………. 6.20

• References ……………………………………………………………………………………………………………………………….. 6.20