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In order to be able to answer all scientific inquiries into a universally intelligible format, one has to develop a commonly accepted language in which to converse. It was this need which led to the development of units and dimensions. It is an effort to do away with subjectivity of forms and personal prejudices and introduce a common objectivity. If we are to report the result of a measurement to someone who wishes to reproduce this measurement, a standard must be defined. Therefore, in order to reduce and eliminate such and other discrepancies, an international committee set up in 1960, established a set of standards for measuring the fundamental quantities.

From the IIT JEE point of view Measurement, Dimensions, Vectors and Scalarsdo not hold lot of significance as we cannot expect a number of questions directly based on this. However, we cannot completely ignore this chapter as this forms the basis of all chapters to follow

Topics covered under IIT JEE General Physics are:-

1. Dimensions
2. Applications of Dimensions
3. Scalars and Vectors
4. Addition and Subtraction of Vectors
5. Multiplication of Vectors
6. Vector Components


Mechanics is one of the basic units in the preparation of IIT JEE, AIEEE and other engineering examinations. A beginner mostly starts with this unit in Physics. Mechanics is not only a lengthy portion in Physics but it forms the basis of entire Physics. It will not be an exaggeration to say that it is the most important unit in Physics from the point of view of preparation of IIT JEE, AIEEE and other engineering examination.

Mechanics begins with Kinematics which deals with the motion of particle in one and two dimension. This portion along with the next topic Newton’s Laws of Motion fetches 2-3 questions in the IIT JEE, AIEEE and other engineering examinations every year. Work Power and Energy, Conservation of Momentum and Collision, Centre of Mass and Rotational Dynamics becomes very important portion from the viewpoint of Examination. These topics together form the heart of Mechanics.IIT JEE, AIEEE and other engineering examination fetches about 15 % of the total Physics questions. Those who get good IIT JEE rank always do well in this section. Simple harmonic Motion and Hydrostatics are also important as this fetches question in the IIT JEE, AIEEE and other engineering examination almost every year.

It is a point to note that this unit of Mechanics can be easily dealt with the proper understanding of the concept which is strengthened with practice of numerical problems.

Following topics are covered under mechanics:

  • Kinematics
  • Newtons Laws of Motion
  • Conservation of Momentum
  • Work Energy and Power
  • Gravitation
  • Fluid Mechanics
  • Thermal Physics


Waves are present everywhere. Whether we recognize it or not, we encounter waves on a daily basis. We experience a variety of waves on daily basis including sound waves, radio waves, microwaves, water waves, visible light waves, sine waves, stadium waves, earthquake waves, cosine waves and waves on a string. Besides these waves we also experience various other motions which are similar to those of waves and are better referred as wavelike. These phenomena include the motion of a pendulum, the motion of a mass suspended by a spring and the motion of a child on a swing. Wave phenomena emerge in unexpected contexts. The flow of traffic along a road can support a variety of wave-like disturbances as anybody who has experienced a slowly moving traffic will know. The beat of your heart is regulated by spiral waves of chemical activity that swirl across its surface. You control the movement of your body through the action of electrochemical waves in your nervous system. Finally, quantum physics has revealed that, on a small enough scale, everything around us can only be described in terms of waves. The universe isn’t really mechanical in nature. It’s made of fields of force. When a radio antenna makes a disturbance in the electric and magnetic fields, those disturbances travel outward like ripples of water in a pond. In other words, waves are fundamental to the way the universe works.



Wave Motion Definition:

A waves motion can be defined as a disturbance that travels through a medium from one place to another. We consider the case of a slinky wave. When the slinky is stretched from end to end and is held at rest, it assumes an equilibrium position which is the position of rest. In order to induce a wave in slinky we first displace a particle of slinky from its position of rest. Wherever we move the coil whether upward or downward, forward or backward, it returns to its original position. But this movement creates a disturbance. If the slinky was moved in a back and forth direction then the disturbance observed in the slinky is called a slinky pulse. A pulse is a single disturbance that moves through a medium form one place to another. However, if the first coil of the slinky is continuously and periodically vibrated in a back-and-forth manner, it induces a repeating disturbance that continues for a longer duration. This disturbance is termed as a wave.

Frequency and Period of Wave: The frequency of a wave refers to how often the particles of the medium vibrate when a wave passes through the medium. In mathematical terms, the frequency is the number of complete vibrational cycles of a medium per a given amount of time. The unit of frequency is the Hertz (abbreviated Hz) where 1 Hz is equivalent to 1 cycle/second. If a coil of slinky makes 2 vibrational cycles in one second, then the frequency is 2 Hz. If a coil of slinky makes 3 vibrational cycles in one second, then the frequency is 3 Hz. The period of a wave is the time for a particle on a medium to make one complete vibrational cycle. Period, being a time, is measured in units of time such as seconds, hours, days or years. The period of orbit for the Earth around the Sun is approximately 365 days; it takes 365 days for the Earth to complete a cycle. Types of Wave Motion: Waves come in various shapes and forms. Though the basic characteristics of wave motion are same and present in all waves but they can be distinguished on the basis of some distinguishing features. Transverse Wave Motion: The wave in which particles of the medium move in a direction perpendicular to the direction of the wave is called a transverse wave. Now again if we consider the case of a slinky then if it is stretched in a horizontal direction and a movement is produced in the first coil by moving it up and down, energy is transported from left to right. Since the movement of particles is perpendicular to the direction of movemnt of wave so it is an example of traneverse wave.
Longitudinal Wave Motion: The wave in which the particles move in a direction parallel to the direction of the movement of the wave is called a longitudinal wave. As discussed in the last case, in a slinky, once a disturbance is produced, the energy is transported from left to right. The particles of the medium move in a direction parallel to that of the pulse. Hence, such waves are longitudinal waves.
Waves can also be categorized on the basis of their capability of transferring energy through a vacuum. Electromagnetic wave Motion: Waves which are capable of transmitting energy through a vacuum and are produced by the vibration of charged particles are called electromagnetic waves. Light waves are an example of these waves. Electromagnetic waves are produced on Sun and travel to Earth through vacuum. These waves are responsible for the existence of life on Earth. Mechanical Wave Motion: Those waves which cannot transmit their energy through a vacuum and require a medium for same are called mechanical waves. Various examples include sound waves, water waves, slinky waves etc. Equation of Wave Motion: The wave motion equation can be expressed as Speed = Wavelength * Frequency It states the mathematical relationship between the speed (v) of a wave and its wavelength () and frequency (f). Using the symbols v, λ , and f, the equation can be rewritten as v = f *λ . Wave Motion is an important topic in the Physics syllabus of the IIT JEE. The topic usually fetches around 5-6 questions on an average.
Electrostatics is a vital branch of Physics. It is an interesting branch and questions are often asked from it in the JEE. It is important to have a strong grip on the topics of electrostatics in order to remain competitive in the JEE. Electrostatics is the branch of Physics which is concerned with the study of those electric charges which are at rest or are stationary. It goes way beyond the study and exploration of the various properties of electricity and its applications. We illustrate this concept with the help of an example. When a rod of plastic is rubbed with fur or a glass rod is rubbed against silk, then it is generally observed that the rods start attracting some pieces of paper and seem to be electrically charged. While the charge on plastic is defined to be negative, that on silk is considered positive. The vast amount of charge in an everyday object is usually hidden, comprising equal amount of two kinds – positive and negative. The imbalance is always small compared to the total amounts of positive charge and negative charge contained in the object. Electrostatics involves the building up of charge on the surface of the objects as a result of contact with other surfaces. The charge exchange occurs only when two surfaces come in contact and then finally separate. The effects as a result of this exchange can be noticed only when at least one of the two surfaces who came in contact is highly resistive to the electrical flow. The reason behind this is that these kinds of charges which are transmitted to or from highly resistive surface remain trapped there for a sufficient duration so that their effects can be observed. These charges stay there and ultimately they either ooze out in the form of bleeding to the ground or need to be immediately neutralized by a discharge. The electromagnetic forces are vital forces which interact with particles in a variety of ways and this includes the minimal reactions of electrostatics. Types of charges and their nature… We have already discussed that there are two types of charges- positive and negative. It is a fundamental fact that while like charges repel, the unlike charges attract each other. This law forms the base of electrostatics. If two unlike charges are brought close to one another, they are pulled towards each other whereas if two like charges are brought close they are pulled away
from each other. Electric charge We discuss some of the characteristic features of an electrically charged object: Firstly, the law which has already been discussed applies i.e. like charges repel and unlike charges attract. Main point to be note here is that the charge is conserved. As discussed in the earlier example of rod and fur, the net negative charge on the rod is same as the net positive charge on the fur. View this video for more on electrostatics Concepts of conductor and insulator… As the name suggests, a conductor is the material which conducts electric charges or through which the charges can easily pass. Contrary to this is the concept of insulators. Insulators do not allow electric charges to pass through them easily. The charges on a conductor always assemble at the sharp points as a result of properties of electric fields. Let us consider the example of a metal cone. Obviously, due to the result explained just now, the charged cone will have maximum charge on its sharp edge and less charge elsewhere. Remarks:

                      1. Human body acts like a conductor and lets current to easily flow through it. It is for this reason that one should be careful with the useful of electrical appliances.



                    • Each type of material has a different arrangement of atoms, electrons and protons. This arrangement makes it a conductor or an insulator.



                    • Metals are considered to be very good conductors while rubber is an insulator as it does not allow electric current to pass through it easily.



                    • We list some of the items which are considered to be positively charged:



                      •  Human hair
                          • Wool


                      • Silk
                      • Nylon
                      • Cotton
                      • Teflon
                      • Wood


Applications of Electrostatics Electrostatics deals with electromagnets and is used in numerous fields. Its major application is in paint spraying. Other uses include:

                      • Smokestacks



                    • Air fresheners



                    • Xerography



                    • Painting cars



                    • Insecticide spraying



                    • Inkjet printers



                    • Photocopiers


Magnetism is a class of physical phenomena that includes forces exerted by magnets on other magnets. It has its origin in electric currents and the fundamental magnetic moments of elementary particles. Now we answer the question what is magnetism? Magnetism is the force by which the objects are attracted or repelled by one another. Usually these objects are metals such as iron. Besides iron, other materials that are easily magnetized when placed in a magnetic field include nickel and cobalt. Magnetism is a force of attraction or repulsion that acts at a distance. It is due to a magnetic field, which is caused by moving electrically charged particles. Iron is not the only material that is easily magnetized when placed in a magnetic field; others include nickel and cobalt. Magnets can also be formed and such magnets are called electromagnets. A simple electromagnet is formed with a battery and copper wire coiled around a metal rod such as a nail. There is evidence that there is an electrical basis for magnetism. Pierre de Mari court checked angles pointed out by an iron rod placed at various points of a natural magnet. He found that the directions were in such a way that they rounded the sphere and passed through two points diagonally opposite, which he called the ends or poles of the magnet. Later experiments showed that every magnet, regardless of its shape, has two poles, called north and south poles, that exert repulsive as well as attractive forces on other magnetic poles just as electric charges exert forces on one another. Later William Gilbert extended de Mari court’s experiments to a variety of materials. Using the fact that a iron rod orients in some preferred directions, as per his hypothesis Earth itself is a large permanent magnet. Further a Torsion Balance was used for experiments and it was postulated that the force exerted varies inversely with the square of distance between them. Magnetic Poles, Forces, and Fields Magnetic Poles: Every magnet has two poles. The poles are the points in a magnet where the magnetic strength is at its peak. These poles are called the north and the south poles or the north seeking and south seeking poles. When a magnet is suspended or hung somewhere the magnet lines up in a north – south direction. As we know that the like charges repel and the unlike charges attract, so when the North Pole of one magnet is kept close to the north pole of another magnet, the poles are repelled. When the south poles of two magnets are placed near one another, they also are repelled from one another. When the north and south poles of two magnets are placed near one another, they attract each other.


The attraction or repulsion of two magnets towards one another depends on how close they are to each other and how strong the magnetic force is within the magnet. The further apart of the magnets are the less they are attracted or repelled to one another. Note: Even when a magnet is broken into pieces each broken piece has its own north and South Pole. Magnetic Field: The imaginary lines of flux originating from moving or spinning electrically charged particles constitute the magnetic field. For example the spin of a proton and the motion of electrons through a wire in an electric circuit constitute magnetic fields. It is undoubtedly a special property of space. All materials are influenced to some extent by a magnetic field. Most materials do not have permanent moments. Some are attracted to a magnetic field, others are repulsed by a magnetic field while others have a much more complex relationship with an applied magnetic field. Substances that are negligibly affected by magnetic fields are known as non-magnetic substances. They include copper, aluminium, gases and plastic. Even pure oxygen exhibits magnetic properties when cooled to a liquid state.


Magnetic Force: The magnetic field of an object can create a magnetic force on other objects with magnetic fields. When a magnetic field is applied to a moving electric charge, such as a moving proton or the electrical current in a wire, the force on the charge is called a Lorentz force. Attraction When two magnets or magnetic objects are close to each other, there is a force that attracts the poles together. Attraction always occurs between unlike poles. Except iron, magnets also attract nickel and cobalt.


Repulsion When two magnetic objects have like poles facing each other, the magnetic force pushes them apart. Magnets might also repel


diamagnetic materials Magnetic and electric fields There is a close relation between the magnetic and electric fields. They are similar as well as different. Electric charges and magnetism similar The poles of a magnet behave in the same way as the electric charges. The positive (+) and the negative (-) electrical charges attract each other and so do the North and the South Poles in a magnet. In electricity like charges repel, and in magnetism like poles repel. Electric charges and magnetism different The magnetic field is a dipole field as every magnet has exactly two poles. But in electricity, a positive (+) or a negative (-) charge can exist independently. Electrical charges are called monopoles, since they can exist without the opposite charge but a single magnetic pole can never be isolated.

Electric current in simple words refers to the rate at which the electric charge flows in an electric field or an electric circuit.

Basic concept of current:

Electric current can also be defined as the rate of flow of charge through a particular area of cross section of a conductor. The current always flows in a direction which is from a region of higher potential to a region of lower potential. The direction of flow of electrons is opposite to direction of current because they carry negative charge and will move from a region of higher potential. Electric current is a scalar quantity. If we consider the case of water pipes, the water current flowing through the pipe can be assumed to be the electric current. The unit of measurement of electric current is ampere (amp). If we consider the case of electric charges, then the rate at which electric charges pass through a conductor is also defined to be electric current. These charged particles may have any charge either positive or negative. Generally, some kind of force or a push is required by a charge to flow and this force is provided by either voltage or potential difference. The word ‘current’ is indeed an abbreviation for electric current. When we discuss this topic, the context of the situation is such that it automatically implies the adjective ‘electrical’. Current in gases and liquids includes flow of positive ions in one direction and of negative ions in the direction opposite to the first direction. If there exists a current of negative charge which is moving in opposite direction, then even that is included in the total current as it is assumed to be equal to positive charge of the same magnitude moving in the usual direction. Electric current also leads to the formation of magnetic fields similar to the case of electromagnetics. Any kind of heat loss or loss of energy that occurs in a conductor by electric current is proportional to the square of the current. CURRENT DENSITY Current density, as it follows from the word itself refers to the density of the current. Mathematically, current density is the ratio of the electric current that flows in a conductor at a particular point to the cross-sectional area of the conductor. Hence, it denotes the amount of current flowing across a particular area. It is denoted by the symbol ‘J’ and its unit of measurement is amperes per square metre.


The mathematical formula for the calculation of current density is given by J = I/A, where ‘I’ is the current in amperes that flows through the conductor. ‘A’ is the cross sectional area in m2. Current density is a vector quantity and has the same direction as that of current. If we consider ‘I’ to denote the total electric current then the relationship between ‘I’ to the current density can be represented as I = ∫J. dS, where the integral runs over the area where current is flowing This shows that the total current (I) equals the summation of current density over the area where charge is flowing. Illustration: A copper wire of area 5 mm2 has a current of 5 mA of current flowing through it. Calculate the current density? Solution: Given: Total Current I = 5 mA, Total Area A = 5 mm2 The Current density is given by J = IA = 5*10-3A5*10-3m = 1 A/m2. Drift Velocity: It is a known fact that charged particles don’t travel in straight lines in a conductor due to the obvious reason that they often collide with other particles present in the material. Therefore, the average speed at which the particle travels along the conductor is called the drift velocity. Inn other terms, the drift velocity may be defined as the average or the mean velocity attained by a particle as a result of electric field. It can also be called as the axial drift velocity since the particles are assumed to be moving in the plane. Drift velocity formula: The mathematical formula for calculation of drift velocity in a material exhibiting constant cross-sectional area is given by: v = I/ nAq, where v is the drift velocity of electrons I is the current flowing through the conductor n is the density of the charge-carrier q is the charge on carrier A is the area of the cross-section

Electromagnetic induction refers to the production of a voltage or a potential difference across a conductor when it is exposed to a changing magnetic field. The name of Faraday is generally acknowledged with the discovery of induction. We first discuss the terms which will be used frequently in this topic and later move on to the Faraday Law of electromagnetic Induction. Flux: Flux is defined as the rate of flow of a property per unit area. For example, the magnitude of a river’s current which gives the quantity of water flowing through a cross-section of the river each second is a kind of flux. Emf: Emf is an abbreviation of electromagnetic force which is the voltage developed by any source of electrical energy such as a battery. It is denoted by ℰ and is measured in volts. The EMF is also given by the rate of change of the magnetic flux: ℰ = – dφB/ dt, where ℰ is the electromagnetic force Emf in volts and ΦB is the magnetic flux.


Faraday’s laws of electromagnetic induction is a basic law of electromagnetism which describes the interaction of a magnetic field with an electric circuit to produce an emf I. It is the prime operating principle of various kinds of motors and generators. Christian Oersted’+s discovery of magnetic field around a current carrying conductor was quite accidental. If a flow of electric current can produce a magnetic field then why can’t a Magnetic field produce an electric current? While searching for an answer to this Michel Faraday ended up inventing generators. We now discuss in detail the Michael Faraday Law: Relationship between Induced Emf and Flux In this experiment Faraday took a magnet and a coil and connected a galvanometer across the coil. In the beginning the magnet is at rest so there is no deflection in the galvanometer and hence the needle of galvanometer is at center or zero position. When the magnet is moved toward the coil, the needle of galvanometer deflects in one direction. When the magnet is held stationary at that position, the needle of galvanometer returns back to zero position. Now when the magnet is moved away from the coil , there is some deflection in the needle but in opposite direction and again when the magnet becomes stationary at that point with respect to coil , the needle of galvanometer return back to zero position. Also if the magnet is held stationary and the coil is moved away and towards the magnet, the galvanometer shows deflection in a similar manner. It is also observed that faster the change in the magnetic field, the greater will be the induced emf or voltage in the coil. The induced electromotive force in any closed circuit is equal to the negative of the time rate of change of the magnetic flux through the circuit. This version of the Faraday’s law is valid only when the closed circuit is a loop of indefinitely thin wire.


Application of Electromagnetism in Physics (including the Faraday’s Law):

Faraday’s Law is a fundamental law of electromagnetism. This law has widespread applications in various fields including industries, electrical machines etc. some of the major ones are listed below: Electrical Transformers This is a static device which is used for increasing or decreasing thhe voltage or current. It has its applications in generating station, transmission and distribution system. The transformer works on Faraday’s law. Electrical Generators The basic working principle of electrical generator is Faraday’s law of mutual induction .Electric generator is used to convert mechanical energy into electrical energy. Induction Cookers The Induction cooker also works on principle of mutual induction. When current flows through the coil of copper wire placed below a cooking container, it produces a changing magnetic field. This alternating or changing magnetic field induces an emf and hence the current in the conductive container. Electromagnetic Flow Meters It is used to measure velocity of blood and certain fluids. When a magnetic field is applied to electrically insulating pipe in which conducting fluids are flowing then according to Faraday’s law an electromotive force is induced in it. This induced emf is proportional to velocity of fluid flowing. Musical Instruments It is also used in musical instruments like electric guitar, electric violin etc.

There are several ways to think about light in physics. One very useful way is to think of it in terms of rays. That is, to imagine light to be traveling in very narrow beams. When you do that, we say that you are modeling light as rays. This method allows one to develop an understanding of several light phenomena including common reflections and refractions. An image in which the rays of light radiating from a point on the object converge to a physical point in space is called a real image. Parallel to this is the concept of a virtual image. When the rays from an object point never actually converge towards a different physical point in space but simply appear to the eye as if they were radiating from an image point, we call the image a virtual image. Ray Optics covers a large variety of topics like the refractive index, mirror formula, lens formula, refraction at spherical surfaces, refraction through prism etc. We shall give a brief outline of these topics as they have been discussed in detail in the coming sections:


Reflection is a simple yet important concept. Almost all objects in the world reflect a certain amount of light falling on them. When light falls on the object, it gets reflected and this is the color that is visible to the human eye. The ray that falls on the surface is termed as the incident ray and the angle that it makes with the normal is called the incident angle. The normal is the imaginary line that is perpendicular to the surface at the point where it is intersected by the incident ray. This ray again springs back as the reflected ray and it has the same angle of reflection as the angle of incidence from the normal. Hence, from this discussion, we obtain the law of reflection which states that Angle of incidence = Angle of reflection One point to be noted here is that all these lines including the incident ray, the reflected ray and the normal to the surface lie in the same plan. Reflection can broadly be categorized as Specular Reflection and Diffuse Reflection. Specular Reflection: When light rays which are in the form of parallel lines strike against a smooth or a plane surface and then get reflected again in the form of parallel lines, then this form of reflection is called as the specular reflection. The following figure will prove useful in furthering clearing the concept of this kind of reflection:


Diffuse Reflection: When light rays fall in the form of parallel lines on a rough surface and as result they get reflected in all directions, such type of distortion is termed as diffuse reflection.


Refraction: The concept of refraction and the index of refraction are of immense importance. If light travels from point A to point B, then its speed will be highest if it travels in a straight line. But it has to pass through various materials then it will pass through them at different speeds and the motion will not be in a straight line. Hence, when it enters a new medium, it gets bent a bit and this bending is termed as refraction. The human eye always assumes light to be traveling in a straight line and hence when an object appears to be bent slightly due to refraction, we assume that the object is bent and not the light. The index of refraction depends on the medium through which light passes. The speed of light is more in medium which are less optically dense and less in more optically dense mediums. The mathematical formula for calculation of index of refraction is: n = Speed of light in vacuum/ Speed of light in the medium = c/v The index of refraction is represented by the letter ‘n’ and denotes the angle at which the light bends. When light travels from a medium with refractive index n1 to the other with refractive index n2, the relation between the angle of incidence θ1 and the angle of refraction θ2 is given by n1sin θ1 = n2 sin θ2 Since the speed of light in air is almost the same as the speed of light in a vacuum, so in most of the cases a value of one for the index of refraction of air. We have listed the indices of refraction for various substances in the table given below:

Index of refraction, n

Substance (at 20° C)
Diamond Sodium Chloride Water Benzene



Refraction through a glass prism: When the visible white light passes through an equilateral prism, it experiences dispersion. It was proposed by Newton that it was possible to divide the white light into its various component colors with the help of an isosceles prism having equal sides and angles. As soon as the light ray falls on the surface of a dispersing prism, on entering it gets refracted and then passes through the glass unless it reaches the second boundary. Again the light gets refracted then it follows a new path on exiting. When the waves pass through prism, they get deviated by a certain angle which can be calculated. We obtain the angle of minimum deviation when the angle at which the light wave enters the prism permits the beam to pass through the glass in a


parallel direction to the base. As the values of the refractive index of a prism are increased, it also leads to an increase in the angle of deviation of light passing through prism. Refractive index is also affected by wavelength of light. The shorter wavelengths are refracted at greater angles while the longer wavelengths like red light are refracted at small angles. This variation in the angle of deviation in prism is termed as dispersion. Ray optics discusses topics like refraction of light through prism or the angle of prism and it is quite different form Wave Optics. Ray theory does not describe phenomena such as interference and diffraction, which require wave theory (involving the phase of the wave). Difference between Deviation and Refraction Deviation and refraction are two concepts which are quite inter-related and often confused with each other. But there is a difference between the two. When light enters a different medium, the change that occurs in its path like bending or turning is termed as refraction. Deviation refers to the amount of this deflection in the path of light when it enters some other medium.

Wave optics, also termed as Physic optics is the branch of optics which deals with various phenomenon including diffraction, polarization of light, interference pattern in optics and solved problems, Young’s double slit experiment etc. It is an eminent branch which assumes great importance as a large number of questions in various competitions are generally asked from it. We shall discuss some of the chief topics of wave optics for IIT JEE here in brief as they have been discussed in detail in the coming sections: Huygens’ Wave Theory of Light: This is one of the most important principles of wave analysis which was introduced by an eminent physicist Huygens. The crux of the principle is that every point of a wave front can be treated as the source of secondary wavelets that spread out in all directions with the same speed as that of the speed of propagation of waves. This just implies that an edge of a wave can actually be viewed as creating a series of circular waves. Usually, these waves combine to carry on the propagation, but sometimes there are noteworthy evident results. The wave front which is defined as the surface, on which the wave disturbance is in phase, actually appears to be tangent to all the circular waves. Though these results can be easily derived from Maxwell’s equations as well, but Huygens’Principle is better suited for performing calculations on waves. Maxwell was the one who provided solid theoretical basis to what Huygens’ had already anticipated around two centuries back. According to this principle, a plane light wave passes through free space at the speed of light. The below figure demonstrates the motion of light rays associated with the propagation of wave front. They move in straight lines as shown here:

A critical description of the Huygens’ Principle is:

(i) Each point on a wave front acts as a source of a new disturbance and therefore emits its own set of spherical waves which are called secondary wavelets. The secondary wavelets travel in all directions with the velocity of light as long as they move in the same medium.

(ii) The locus or the envelope of these wavelets in the forward direction indicates the position of new wave front at any subsequent time.

Diffraction: Diffraction basically refers to the bending of light around hindrances. This basically means that it creates some sort of interference in the passage of light. Another associated concept is of a diffraction grating. A diffraction grating refers to the screen with a bunch of parallel slits which are placed at a distance ‘d’ from each other. Diffraction is in fact a special case of interference. It takes place when a wave hits against the barrier of an edge. The passing of light through some edge or gap is involved in almost all optical phenomena which clearly imply that diffraction takes place in almost all of them, though the impact might be negligible. A wave tends to bend around the hindrance as a result of diffraction. Diffraction can also be used for studying the structure of particular objects. It is even possible to reverse and move backward from the diffraction pattern to know


about the nature of the object.

Young’s Double-Slit Experiment

As a result of double slit experiment by Thomas Young in 1801, the wave theory of light came into the limelight. The double-slit experiment is based on the doctrines of constructive interference and destructive interference and hence proves that light resembles some of the properties of waves.

The experiment involves throwing up of light on a screen containing two narrow slits separated by a distance ‘d’. At a distance ‘L’ from the first screen, a second screen is placed and the light which passes through the two slits shines on falling on this



It is apparent form the figure that the light of single wavelength λ falls on the first screen and since the slits are narrower than λ, so the light passes and spreads all over the second screen. As depicted in the figure above the point P on the back screen is the point which receives light from two different sources.

Modern Physics is a very important constituent of Physics portion of the IIT JEE. It is interesting as well as usually fetches many questions in the JEE. It includes topics like Nuclear Fission and Fusion which are easy to master. These topics are quite fascinating but involve concepts which must be understood properly.

Modern Physics for IIT JEE refers to the Physics based on the two major branches: relativity and quantum mechanics. Classical Physics refers to the traditional Physics which was based on the concepts before coming up of Modern Physics. There were various theoretical and experimental paradoxes that forced thinking out of the traditional path. Modern physics is generally encountered when dealing with extreme conditions. Quantum mechanical effects appear in circumstances dealing with “lows” (low temperatures, small distances), while relativistic effects tend to appear when dealing with “highs” (high velocities, large distances), the “middles” being classical behavior. The Classical Physics was indeed in accord with common sense. Modern Physics has in fact come over that and imparts a better understanding of nature. Modern Physics in IIT JEE syllabus is the most scoring part.


Nuclear Fission and Fusion: Nuclear Fission and Fusion are two different kinds of energy releasing reactions. In these reactions, the energy is released from high- powered atomic bonds between the particles present in the nucleus. The two processes are quite opposite in nature. While Fission involves the splitting of an atom into two or more atoms, in Fusion, two or more smaller atoms combine to form a larger atom. We discuss both the processes one by one.

Nuclear Fission:Nuclear Fission is the process of splitting atoms. It is a process in nuclear physics in which the nucleus of the atom into smaller nuclei as fission products along with some by-produce particles. Fission hence may be termed as a form of elemental transmutation.

The by-products comprise free neutrons and photons which are generally in the form of gamma rays in addition to other nuclear fragments such as beta particles and alpha particles. Fission is an exothermic reaction which means there is a release of huge amount of energy when it takes place. Fission of heavy elements releases considerable amount of useful energy either in the form of gamma rays or as kinetic energy of the fragments. This energy may be used for nuclear power or for the explosion of nuclear weapons.


The sum of the masses of these fragments is less than the original mass. This gap in the mass which is around 0.1 percent of the original total mass has been converted into energy according to Einstein’s equation.

Nuclear Fusion: In simple words, Fission refers to the process in which two or more atoms combine to form a larger atom. Nuclear energy can also be released by fusion of two light elements (elements with low atomic numbers). The power that fuels the sun and the stars is nuclear fusion. In a hydrogen bomb, two isotopes of hydrogen, deuterium and tritium are fused to form a nucleus of helium and a neutron. It may also be defined as the process in which multiple nuclei join together to form a heavier nucleus. It is accompanied by the release or absorption of energy depending on the masses of the nuclei involved.


Radioactive Decay of Substances:

Radioactive decay, as the word suggests refers to the decay to attain stability. It refers to the loss of particles from an unstable atom in order to attain more stability. The unstable elements emit some particles from their nucleus to gain stability and this process is termed as radio-activity. For elements, uniformity is produced by having an equal number of neutrons and protons which determines and henceforth directs the nuclear forces to keep the nuclear particles inside the nucleus. There may be cases when a particle becomes more frequent than another and hence creates an unstable nucleus. The unstable nucleus then releases radiation in order to gain stability.
This radio-active decay can occur in five forms:

. Alpha emission

· Beta emission

· Positron emission

· Electron capture

· Gamma emission

As stated above, each decay emits some specific particle which also changes the type of product produces. The nuclei produced from the decay are called the daughter nuclei. The type of decay also determines the number of neutrons and protons found in the daughter nuclei. Let us consider an example of a radioactive substance.

The stable Beryllium contains 4 protons and 5 neutrons in its nucleus. A lighter isotope of beryllium is also available which contains 4 protons and only 3 neutrons, which gives a total mass of 7 amu. This isotope decays into Lithium-7 through electron capture. A proton from Beryllium-7 captures a single electron and becomes a neutron. This reaction produces a new isotope (Lithium-7) that has the same atomic mass unit as Beryllium-7 but one less proton which stabilizes the element.


Beta decay occurs when the neutron to proton ratio is too great in the nucleus and causes instability. In basic beta decay, a neutron is turned into a proton and an electron. The electron is then emitted. Here’s a diagram of beta decay with hydrogen-3:



Half-Life is a very common term associated with radio-active decay. It cannot be easily detected when a single radioactive atom will decay. But, we can get an idea about the time required for half a large number of identical radioactive atoms to decay. This time is called the half-life.

Structure of Atom and Nucleus:

An atom is made up of three subatomic particles: protons, neutrons and electrons. The protons and neutrons are placed inside the nucleus. The nucleus is at the center of the atom. The electrons keep on moving in orbits around the nucleus. The nature of the atom is determined by the number of protons. The protons carry positive charge, while electrons are negatively charged. Neutrons, as the name suggests are neutral and do not carry any charge. If the nucleus contains 17 protons, then the atom is chlorine. An atom of oxygen contains 8 protons in its nucleus.


The nucleus is the dense central core of the atom which contains both the protons as well as the neutrons. Electrons are outside the nucleus in energy levels. Protons have a positive charge, neutrons have no charge, and electrons have a negative charge. An atom is said to be neutral of it has the same number of protons and electrons. The neutrons can vary in number in the atom of a particular element. Atoms of the same element that have differing numbers of neutrons are called isotopes.


The formula for finding the atomic number of an elemnet is given by

Atomic Number = Number of electrons – Number of Protons

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