2nd on Editi

LECTURE NOTES IN

PHYSICS (CLASS XI) VOLUME - I

Dr. Manjeet Singh

LECTURE NOTES IN PHYSICS (CLASS XI) VOLUME - I

LECTURE NOTES IN PHYSICS: (CLASS XI) VOLUME - I

Dr. Manjeet Singh M.Sc. (Physics), Ph.D., NET-JRF, GATE, Haryana SLET, Rajasthan SLET, H.P. SLET Qualified (RESONANCE ACADEMY, CHARKHI DADRI) *Ex. Asst. Prof. Department of Physics Amity University, Noida - 201301 (U.P.)

2/25, Ansari Road, Darya Ganj, New Delhi-110 002

First Edition : 2020

PREfACE The book entitled: LECTURE NOTES IN PHYSICS: CLASS XI has been written as a text book (Study Material) of Physics for XI class students. This text book is divided into two volumes. VOLUME - I contain seven chapters (1 - 7): Introduction, Units and Measurement, Motion in a Straight Line, Motion in a Plane, Laws of Motion, Work Energy and Power, System of Particles and Rotational Motion. VOLUME - II contain eight chapters (8 - 15): Gravitation, Mechanical Properties of Solids, Mechanical Properties of Fluids, Thermal Properties of Matter, Thermodynamics, Kinetic Theory, Oscillations, Waves. Following are the salient features of the book: • It represents a simple language and lucid style the fundamental principles of Physics in a manner such that the student may feel no difficulty in following them. • Each section/article is self contained and explained in a comprehensive style. • The mathematical calculations are clear and complete without any jumping and have been made simple, logical and easily understandable. • S.I. unit have been used throughout the text. However, C.G.S. units have been used, wherever necessary. • The point of view of students has always been kept in mind while preparing the present solution and hence it is hoped that the reader will experience no difficulty, whatsoever, in understanding the subject. I am greatly indebted to Prof. Praveen Aghamkar, Department of Physics, Chaudhary DeviLal University, Sirsa for his interest, inspiring guidance, and encouragement in this endeavor. I am thankful to Dr. Surender Duhan, Assistant Prof., Department of Material Science & Nano Technology, Deenbandhu Chhotu Ram University of Science & Technology, Murthal (Sonepat), Dr. Navneet Singh, Assistant Prof., Department of Physics, A.I.J.H.M. College, Rohtak, Mr. Jaivir Suhag, Mr. Vipin Pal Singh, J.V.M.G.R.R. College, Charkhi Dadri, for the help during the time when this book was written. I am very much indebted to many friends, Mr. Anil Bansal, Scientist C, IRDE (DRDO), Dehradun, Mr. Leeladhar, Scientist C, LASTEC (DRDO), New Delhi, Dr. Raj Kumar, Scientist C, CSIO (CSIR), Chandigarh, Mr. Devender Dudy, Government College, Birohar for their encouragement. I am thankful to Prof. Devendra Mohan, Prof. Ashish Aggarwal, Prof. Sujata Sanghi, Prof. Sneh Lata Goyal, Dr. David Joseph, Dr. Rajesh Punia and Dr. Neetu Ahlawat, Department of Applied Physics, Guru Jambheshwar University of Science & Technology, Hisar for their inspiration. I am very thankful to Mr. Ajay Chahal, Research Scholar, Indian Institute of Technology, Chennai, Mr. Kuldeep, Research Scholar, Indian Institute of Technology, Chennai and Mr. Tarun Garg, Research Scholar, Indian Institute of Technology, Bombay for the help whenever needed. Thanks to R.K. Jain, my publisher who encouraged me. Dr. Manjeet Singh

CONTENTS (VOLUME - II) CHAPTER 8: (GRAVITATION)................................................................................................................................(1-34) CHAPTER 9: (MECHANICAL PROPERTIES OF SOLIDS)..............................................................................(35-52) CHAPTER 10: (MECHANICAL PROPERTIES OF FLUIDS)...........................................................................(53-105) CHAPTER 11: (THERMAL PROPERTIES OF MATTER)...............................................................................(106-116) CHAPTER 12: (THERMODYNAMICS)............................................................................................................(117-145) CHAPTER 13: (KINETIC THEORY).................................................................................................................(146-159) CHAPTER 14: (OSCILLATIONS).....................................................................................................................(160-183) CHAPTER 15: (WAVES)......................................................................................................................................(184-222)

Introduction

1

C H A P TE R

1

INTRODUCTION

What is Science?  The knowledge which humans have gained through observations and experiments, when organised systematically is called Science.  The knowledge so collected has become so vast today that it has been divided into many branches.  The science which deals with non-living things are called Physical Sciences. For example, Physics, Chemistry, Geography, Astronomy, Astrology, Oceanology etc.  The science which deals with the living things are called Biological Sciences. For example, Botany, Zoology, Ornithology, Anthropology, Entomology, Forensic science etc.  According to Albert Einstein, the greatest scientist of all times, "Science is not just a collection of laws, a catalogue of unrelated facts. It is a certain of human mind, with its freely invented ideas and concepts." The same scientist once remarked: "The most incomprehensible thing about the world is that it is comprehensible." This statement is based on a simple fact that the behaviour of everything in this vast universe is governed by a few laws, which are well defined.  According to Burce Lindsay, "Science is a method for describing, creating and understanding human experience."  In the words of famous scientist Neils Bohr, "The task of science is both to extend the range of our experience and to reduce it to order."  According to Gerald Holton, "Science is ever unfinished quest to discover all facts, the relationship between things and laws by which the world runs."  In the words of Phillips Feyman, "I would like not to underestimate the value of the world view, which the result of scientific effort."  According to Heisenberg, "The two processes, that of Science and that of Art are not very different. Both Science and Art, form in the course of centuries, a human language, by which we can speak about the more real part of reality."  A famous Philospher, Bertrand Russel comments on Science as follows: "We know very little and yet it is astonishing that we know so much, and still more astonishing that so little knowledge (of science) can give us so much power."

The Scientific Method and the Scientific Theory  We know that science is an systematic attempt to explore and understand natural phenomena in as much detail and depth as possible. The knowledge so gained is used to predict, modify and control the phenomena. The scientific method involves the following steps:

• Taking a large number of systematic observations through controlled experiments. • Studying these observations and looking for their logical behaviour based on qualitative and quantitative reasoning.

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Lecture Notes in Physics: Class XI

• Mathematical modelling, i.e., suggesting some model to account for the observed behaviour. • Theoretical prediction of what is not actually observed on the basis of the suggested model. • Verification or falsification of the model.  Speculation and conjecturing also have a place in the scientific method.  Science is ever dynamic. There is no final theory in science and no unquestioned authority amongst scientists.  Occasionally, existing theory is simply unable to explain new observations. This causes major upheaval in science leading to the development of entirely new theories.  Some of the striking examples where small discrepancies have led to new theories in Physics are:

• The concept of flat earth was replaced by the concept of spherical earth, from the observations of distant ships in a sea.

• Geocentric theory imagining earth to be at the centre of the universe was replaced by Heliocentric theory imagining sun to be stationary and all planets revolving around it.

• The corpuscular theory of light given by Newton was replaced first by Huygens wave theory of light, which was replaced later by Planck's quantum theory of light. Finally, dual theory of light was given by de-Broglie to account for all the phenomena observed in case of light.  Thus, in science, the approach is always 'open minded', in which no points of viw are overlooked without logical reasons. In fact, all theories of science have to be updated, whenever required, so that they are consistent with all the experimental data collected by that time.

What is Physics?  Physics is a basic descipline in the category of 'Natural Sciences'. The word 'Physics' comes from the Greek word 'fusis' meaning nature. Its Sanskrit equivalent is 'Bhautiki' that is used to refer to the study of the physical world.  Hence, 'Physics is the branch of science which is devoted to the study of nature and natural phenomena.'  Thus, Physics is the most basic of all sciences.  In the study of Physics, there are two principal thrusts: Unification and Reductionism.  Unification means attempting to explain diverse physical phenomena in terms of a few concepts and laws. For example, the same law of gravitation given by Newton accounts for: (i) fall of an apple to the ground, (ii) motion of satellites around the planets, (iii) motion of planets around the sun. Similarly, the basic laws of electromagnetism in the form of Maxwell's equations explain all the electric and magnetic phenomena.  Reductionism means attempting to derive the properties of a bigger, more complex system from the properties of its constituent simpler parts. For example, the subject of thermodynamics deals with bulk systems in terms of a macroscopic quantities like temperature, internal energy, entropy etc. The later developments of kinetic theory and statistical mechanics interpreted these quantities in terms of the properties of the molecular constituents of the bulk systems. For example, temperature of the bulk system was related to the average kinetic energy of the molecules of the system.

Introduction

3

Scope and Excitment of Physics  The two domains of interest in Physics are: Macroscopic and Microscopic.  The macroscopic domain includes the study of phenomena involving objects of finite size on terrestrial scale and even on astronomical scale. This makes up 'Classical Physics'. Most of it was developed up to the year 1900.  The misoscopic domain includes the study of phenomena involving molecules, atoms, nuclei, electrons and other elementary particles. This makes up 'Modern Physics'. Most of it was developed after the year 1900.  Recently, the domain intermediate between the macroscopic and microscopic domains has emerged. It involves the study of a few tens or hundreds of atoms or molecules. It is called 'Mesoscopic Physics'. This domain is emerging as an exciting field of research.  The 'Classical Physics' includes subjects like Mechanics, Thermodynamics, Electrodynamics and Optics. 'Mechanics' deals with the study of gaseous systems. The changes in temperature, internal energy and entropy of the system through external work are investigated. Modes of transfer of heat, efficiency of heat engines and refrigerators are also included in thermodynamics. 'Electrodynamics' delas with the study of electric and magnetic phenomena associated with charged particles and magnetic materials. The basic laws governing these phenomena were given by Coulomb, Orested, Ampere and Faraday. These laws were encapsulated by Maxwell in famous set of equations. The generation of electric power, response of a circuit to alternating current, propagation of electromagnetic waves etc. also come under electrodynamics. 'Optics' involves the study of various phenomena connected with light and optical instruments like microscope, telescope etc.  The Classical Physics' is inadequate to handle the microscopic domain, where we deal with the constitution and structure of matter at the minute scale of atoms, nuclei, and even smaller scales of length. Quantum Theory is currently accepted as the proper framework for explaining microscopic domain.  From what we have studied above, you can realize that the scope of Physics is truely vast. It covers a very wide range of magnitudes of physical quantities like length, mass, time, energy etc.  At one end, Physics includes the study of electron, proton, nuclei etc. of size 10 -14 m or even less. And at the other end, it deals with astronomical phenomena involving galaxies and even the entire universe of size  1026 . The two length scales are differ by a factor of 1040 or even more.  The corresponding range of time scales involves in Physics is obtained by dividing the length scales by the speed of light (  108 m/s). The time scales would range from

1014 1026  1022 to  1018 . 8 10 108

 The range of masses involved in the study of Physics vary from 10-30 kg (mass of an electron) to 1055 kg (mass of known observable universe). The terrestial phenomena lie somewhat in the middle of these ranges.  The phenomenal progress of Physics in the last few centuries is due to the following three reasons:

• Quantitative measurement is central to the growth of Physics as the laws of nature can be expressed in precise mathematical equations.

• The basic laws of Physics are universal, i.e., the same basic laws can explain diverse physical phenomena.

Lecture Notes in Physics: Class XI

4

• The strategy of approximation is very successful. Most of the observed phenomena in daily life are rather complex manifestation of the simple basic laws. Therefore, it is good to focus first on the essential features, discover the basic principles and then introduce modifications to build a more refined theory of the phenomena.  The study of Physics is exciting in many ways. For example:

• A few concepts and laws can explain diverse physical phemomena. • Carrying out imaginative new experiments to unlock secrets of nature by verifying or falsifying the existing theories.

• The most interesting part is designing useful devices based on the physical laws.  For a lyman, the study of Physics is exciting. For example:

• • • • • • • • •

live transmission of events thousands of kilometres away on the television, S.T.D., I.S.D., FAX, Pager, Cellular phone etc., the speed and memory of the fifth generation of computers, use of robots, journey to moon and to some nearby planets with controls from ground, technological advances in health sciences, lasers and their ever increasing applications, exploring the new sources of energy, study of various types of forces in nature, and so on.

Physics in Relation to Other Sceinces  As Physics involves a basic study of the various natural phenomena, it can rightly be regarded as the most fundamental of all sciences. Physics has played a key role in the development of many other branches of science.  Physics in relation to science, society and technology: Technology has also a very important part in a society. People reach another level, countries grow, economy grows because technology and inventions appear and help people produce. Technology helps communication develop also. Communication Technology In Society, is recognized by all the gadgets and all the things through which people communicate easily. For example mobile phones or computers and Internet. Each day something new appears and brings us to another level. Among the various disciplines of science, the only discipline which can be regarded as being most fundamental is physics.

Introduction

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It has played a key role in the development of all other disciplines.  Physics in relation to chemistry: The study of structure of atoms, radioactivity, X-ray, diffraction, etc., in physics has enabled chemists to rearrange elements in the periodic table and to have a better understanding of chemical bonding and complex chemical structures.  Physics in relation to Biological science: The optical microscopes developed in physics are extensively used in the study of biological samples. Electron microscope, X-rays and radio isotopes are used widely in medical sciences.  Physics in relation to astronomy: The giant astronomical telescopes and radio telescopes have enabled the astronomers to observe planets and other heavenly objects. Physics related to mathematics: Mathematics has served as a powerful tool in the development of modern theoretical physics.  Physics related to other sciences: The other sciences like Biophysics, Geology, Heterology and Oceanography and Seismology use some of the laws of physics.  Physics related to society and technology: The development of telephone, telegraph and telex enables us to transmit messages instantly. The development of radio and television satellites has revolutionised the means of communication. Advances in electronics (computers, calculators and lasers) have greatly enriched the society. Rapid means of transport are important for the society. Generation of power from nuclear reactors is based on the phenomenon of controlled nuclear chain reaction. Digital electronics is widely used in modern technological developments.

Self Assignment Questions 1. What is Physics? What are the five main branches of Physics? 2. Physics is more of a philosophy, may more of a mathematical science. Which is true? 3. List some key contemporary areas of science and technology responsible for industrial revolution of the present age. 4. Name some key scientific and technological advances which led to first industrial revolution in England and Europe. 5. Should a scientific discovery which has nothing but dangerous consequences for mankind be made public? 6. 'The most incomprehensible thing about the world is that it is comprehensible.' Who made these remarks? Give some evidence in support of it.

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Lecture Notes in Physics: Class XI

Some Great Physicists and Their Contributions Classical Period William Gilbert (1544-1603, English): hypothesized that the Earth is a giant magnet. Galileo Galilei (1564-1642, Italian): performed fundamental observations, experiments, and mathematical analyses in astronomy and physics; discovered mountains and craters on the moon, the phases of Venus, and the four largest satellites of Jupiter: Io, Europa, Callisto, and Ganymede. Willebrod Snell (1580-1626, Dutch) discovered law of refraction (Snell's law). Blaise Pascal (1623-1662, French): discovered that pressure applied to an enclosed fluid is transmitted undiminished to every part of the fluid and to the walls of its container (Pascal's principle). Christiaan Huygens (1629-1695, Dutch): proposed a simple geometrical wave theory of light, now known as "Huygen's principle''; pioneered use of the pendulum in clocks. Robert Hooke (1635-1703, English): discovered Hooke's law of elasticity. Sir Isaac Newton (1643-1727, English): developed theories of gravitation and mechanics, and invented differential calculus. Daniel Bernoulli (1700-1782, Swiss): developed the fundamental relationship of fluid flow now known as Bernoulli's principle. Benjamin Franklin (1706-1790, American): the first American physicist; characterized two kinds of electric charge, which he named ``positive'' and "negative''. Leonard Euler (1707-1783, Swiss): made fundamental contributions to fluid dynamics, lunar orbit theory (tides), and mechanics; also contributed prolifically to all areas of classical mathematics. Henry Cavendish (1731-1810, British): discovered and studied hydrogen; first to measure Newton's gravitational constant; calculated mass and mean density of Earth. Charles Augustin de Coulomb (1736-1806, French): experiments on elasticity, electricity, and magnetism; established experimentally nature of the force between two charges. Joseph-Louis Lagrange (1736-1813, French): developed new methods of analytical mechanics. James Watt (1736-1819, Scottish): invented the modern condensing steam engine and a centrifugal governor Count Alessandro Volta (1745-1827, Italian): pioneer in study of electricity; invented the first electric battery. Joseph Fourier (1768-1830, French): established the differential equation governing heat diffusion and solved it by devising an infinite series of sines and cosines capable of approximating a wide variety of functions. Thomas Young (1773-1829, British): studied light and color; known for his double-slit experiment that demonstrated the wave nature of light. Jean-Babtiste Biot (1774-1862, French): studied polarization of light; co-discovered that intensity of magnetic field set up by a current flowing through a wire varies inversely with the distance from the wire. André Marie Ampère (1775-1836, French): father of electrodynamics. Amadeo Avogadro (1776-1856, Italian): developed hypothesis that all gases at same volume, pressure, and temperature contain same number of atoms. Johann Carl Friedrich Gauss (1777-1855, German): formulated separate electrostatic and electrodynamical laws, including "Gauss' law''; contributed to development of number theory, differential geometry, potential theory, theory of terrestrial magnetism, and methods of calculating planetary orbits.

Introduction

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Hans Christian Oersted (1777-1851, Danish): discovered that a current in a wire can produce magnetic effects. Sir David Brewster (1781-1868, English): deduced ``Brewster's law'' giving the angle of incidence that produces reflected light which is completely polarized; invented the kaleidoscope and the stereoscope, and improved the spectroscope. Augustin-Jean Fresnel (1788-1827, French): studied transverse nature of light waves. Georg Ohm (1789-1854, German): discovered that current flow is proportional to potential difference and inversely proportional to resistance (Ohm's law). Michael Faraday (1791-1867, English): discovered electromagnetic induction and devised first electrical transformer. Felix Savart (1791-1841, Frenchco): discovered that intensity of magnetic field set up by a current flowing through a wire varies inversely with the distance from the wire. Sadi Carnot (1796-1832, French): founded the science of thermodynamics. Joseph Henry (1797-1878, American): performed extensive fundamental studies of electromagnetic phenomena; devised first practical electric motor. Christian Doppler (1803-1853, Austrian): experimented with sound waves; derived an expression for the apparent change in wavelength of a wave due to relative motion between the source and observer. Wilhelm E. Weber (1804-1891, German): developed sensitive magnetometers; worked in electrodynamics and the electrical structure of matter. Sir William Hamilton (1805-1865, Irish): developed the principle of least action and the Hamiltonian form of classical mechanics. James Prescott Joule (1818-1889, British): discovered mechanical equivalent of heat. Armand-Hippolyte-Louis Fizeau (1819-1896, French): made the first terrestrial measurement of the speed of light; invented one of the first interferometers; took the first pictures of the Sun on daguerreotypes; argued that the Doppler effect with respect to sound should also apply to any wave motion, particularly that of light. Jean-Bernard-Léon Foucault (1819-1868, French): accurately measured speed of light; invented the gyroscope; demonstrated the Earth's rotation. Sir George Gabriel Stokes (1819-1903, British): described the motion of viscous fluids by independently discovering the Navier-Stokes equations of fluid mechanics (or hydrodynamics); developed Stokes theorem by which certain surface integrals may be reduced to line integrals; discovered fluorescence. Hermann von Helmholtz (1821-1894, German): developed first law of thermodynamics, a statement of conservation of energy. Rudolf Clausius (1822-1888, German): developed second law of thermodynamics, a statement that the entropy of the Universe always increases. Lord Kelvin (born William Thomson) (1824-1907, British): proposed absolute temperature scale, of essence to development of thermodynamics. Gustav Kirchhoff (1824-1887, German): developed three laws of spectral analysis and three rules of electric circuit analysis; also contributed to optics. Johann Balmer (1825-1898, Swiss): developed empirical formula to describe hydrogen spectrum. Sir Joseph Wilson Swan (1828-1914, British): developed a carbon-filament incandescent light; patented the carbon process for printing photographs in permanent pigment.

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Lecture Notes in Physics: Class XI

James Clerk Maxwell (1831-1879, Scottish): propounded the theory of electromagnetism; developed the kinetic theory of gases. Josef Stefan (1835-1893, Austrian): studied blackbody radiation. Ernst Mach (1838-1916, Austrian): studied conditions that occur when an object moves through a fluid at high speed (the ``Mach number'' gives the ratio of the speed of the object to the speed of sound in the fluid); proposed ``Mach's principle,'' which states that the inertia of an object is due to the interaction between the object and the rest of the universe. Josiah Gibbs (1839-1903, American): developed chemical thermodynamics; introduced concepts of free energy and chemical potential. James Dewar (1842-1923, British): liquified nitrogen and invented the Dewar flask, which is critical for lowtemperature work. Osborne Reynolds (1842-1912, British): contributed to the fields of hydraulics and hydrodynamics; developed mathematical framework for turbulence and introduced the ``Reynolds number,'' which provides a criterion for dynamic similarity and correct modeling in many fluid-flow experiments. Ludwig Boltzmann (1844-1906, Austrian): developed statistical mechanics and applied it to kinetic theory of gases. Roland Eötvös (1848-1919, Hungarian): demonstrated equivalence of gravitational and inertial mass. Oliver Heaviside (1850-1925, English): contributed to the development of electromagnetism; introduced operational calculus and invented the modern notation for vector calculus; predicted existence of the Heaviside layer (a layer of the Earth's ionosphere). George Francis FitzGerald (1851-1901, Irish): hypothesized foreshortening of moving bodies (LorentzFitzGerald contraction) to explain the result of the Michelson-Morley experiment. John Henry Poynting (1852-1914, British): demonstrated that the energy flow of electromagnetic waves could be calculated by an equation (now called Poynting's vector). Henri Poincaré (1854-1912, French): founded qualitative dynamics (the mathematical theory of dynamical systems); created topology; contributed to solution of the three-body problem; first described many properties of deterministic chaos; contributed to the development of special relativity. Janne Rydberg (1854-1919, Swedish): anlyzed the spectra of many elements; discovered many line series were described by a formula that depended on a universal constant (the Rydberg constant). Edwin H. Hall (1855-1938, American): discovered the "Hall effect,'' which occurs when charge carriers moving through a material are deflected because of an applied magnetic field - the deflection results in a potential difference across the side of the material that is transverse to both the magnetic field and the current direction. Heinrich Hertz (1857-1894, German): orked on electromagnetic phenomena; discovered radio waves and the photoelectric effect. Nikola Tesla (1857-1943, Serbian-born American): created alternating current. Nobel Laureates: Johannes van der Waals (1837-1923, Dutch): worked on equations of state for gases and liquids. Lord Rayleigh (born John William Strutt) (1842-1919, British): discovered argon; explained how light scattering is responsible for red color of sunset and blue color of sky. Wilhelm Röntgen (1845-1923, German): discovered and studied X rays. Antoine Henri Becquerel (1852-1908, French): discovered natural radioactivity.

LECTURE NOTES IN PHYSICS (CLASS-XI) Vol. I About the Book LECTURE NOTES IN PHYSICS: CLASS XI has been written as a text book (Study Material) of Physics for XI class students. This text is divided into two volumes. VOLUME - I contain seven chapters (1 - 7): Introduction, Units and Measurement, Motion in a Straight Line, Motion in a Plane, Laws of Motion, Work Energy and Power, System of Particles and Rotational Motion. VOLUME - II contain eight chapters (8 - 15): Gravitation, Mechanical Properties of Solids, Mechanical Properties of Fluids, Thermal Properties of Matter, Thermodynamics, Kinetic Theory, Oscillations, Waves. Following are the salient features of the book: l It represents a simple language and lucid style the fundamental principles of Physics in a manner such that the student may feel no difficulty in following them. l Each section/article is self contained and explained in a comprehensive style. l The mathematical calculations are clear and complete without any jumping and have been made simple, logical and easily understandable. l S.I. unit have been used throughout the text. However, C.G.S. units have been used, wherever necessary. l The point of view of students has always been kept in mind while preparing the present text and hence it is hoped that the book will be helpful for the preparation of competitive exams such as IIT - JEE, AIPMT, NDA etc. About the Author Dr. Manjeet Singh received his Ph.D. degree in the area of Nonlinear Optics from Guru Jambheshwar University of Science & Technology, Hisar in 2008. He has qualified NET - JRF (2014), Haryana SLET (2004), Rajasthan SLET (2005), Himachal Pradesh SLET (2006). He has published more than 100 research papers in reputed International journals, National & International Conferences/ Workshops/ Symposia/ Seminars etc. including several independent research papers. He has organized many national conferences. He is regular reviewer of many international journals, viz. Physical Review B (American Physical Society, USA), Optics & Laser Technology (Elsevier, UK), Optics Communications (Elsevier, UK), Chinese Physics Letters (Institute of Physics, CHINA), Mat. Chem. & Phys. (Elsevier, UK). His research interests include nonlinear optical effects in bulk semiconductors, photorefractive effects in photorefractive semiconductors, nano materials etc. He has authored more than 50 books on various areas of Physics (School, U.G. and P.G. level) and Mathematics. His books have been highly appreciated by the students. Dr. Singh has worked as Assistant Professor in Department of Physics, Amity Institute of Applied Science, Amity School of Engineering & Technology, Amity University, Noida.

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