 The year is 1897. Albert Einstein has not yet arrived in the scene and Max Planck is yet to give his famous postulate. Quantum Mechanical Theory will not take birth for at least the next 30 years. We are in the classical era of physics. One of the most successful, accomplished and confident eras of physics. So confident that it is said that Lord Kelvin, yes, the scientist after whose name the unit of temperature is given, is claimed to have said, there is nothing new to be discovered in physics now. All that remains is more and more precise measurement. And at this juncture in history, we start our lecture series in quantum mechanics with a very simple question. What is light? Light is what is coming out of my tube light, my bulb from a lamp, from a fire source, from the sun. Something that helps us see the world around us visually. But in terms of physics, it is much much more than that. Light is something that occupies a very special place at least in the birth of quantum mechanics because in five to ten years we will discover that there is a murky world where particles are behaving like waves and light is behaving like particles. It's a very confusing world out there. We will learn about wave particle duality, the dual nature of radiation. But before we learn about the dual nature of radiation, first it's important for you to understand the singular nature of radiation. And that is what today's video is all about. Today we are going to discuss what light is from the perspective of purely classical physics. So that once I can emphasize upon you what light is from the perspective of classical physics, then in the future lectures we can take the discussion forward to other characteristics of light which is going to blow your mind. So let's start the discussion with one of the greatest physicists of the 19th century, James Maxwell. Maxwell combined some of the known laws of electric and magnetic fields to come up with four equations that will act as the foundation of what is known as classical electromagnetic theory. One of the most successful branches of physics and these four equations are known as Maxwell's equations. I'm going to start from this perspective because it is these Maxwell's equations which are going to give us an idea about what light actually is. So to continue the discussion, let's take a moment to understand the Maxwell's equations and what the Maxwell's equations have to say about light. So the Maxwell's equations are essentially four equations that combines our understanding of electric charges, magnetic fields, electric currents, etc. and they can be written in the differential form in the following manner. The first Maxwell's equation also known as the Gauss law of electrostatics is essentially the divergence of electric field which is equal to rho upon epsilon naught, where epsilon naught is the permittivity of free space and rho is a charge enclosed in a volume. This equation gives us an idea about the relationship between static electric fields and electric charges. You see, electric fields are always pointed outwards from positive electric charges and towards negative electric charges. What the first equation tells us is that the net outflow of electric field lines from a closed surface is equal to the total amount of charge contained within that particular volume. The second equation is sometimes also called as the Gauss law of magnetostatics, which is essentially the divergence of magnetic field which is equal to 0. It simply means that magnetic monopoles do not exist. You see, whenever there is a magnetic field line, it is always associated with a dipole. That is the presence of a north and a south pole. So therefore, if we calculate the net outflow of a magnetic field from a closed surface, it always comes out to be 0. Next is the Faraday's law of electromagnetic induction, which is the curl of electric field, which is equal to the time derivative of the magnetic field. This equation says that the time variation of magnetic field corresponds to the curl of an electric field and this Faraday's laws of electromagnetic induction lies at the heart of electromagnetic generators. You see, whenever a magnet is in relative motion with respect to a coil, then that creates a changing magnetic field which results in the presence or the creation of a current in that particular coil. This is the principle because of which we actually have electricity in our homes. And lastly, the fourth equation of Maxwell's equations is the curl of magnetic field, which is equal to mu naught j plus del e upon del t. This is the Ampere's law with the added modification by Maxwell and essentially it says a similar thing just like equation number three that you can create magnetic fields due to time variation of electric fields. The reason I'm starting this entire discussion with the Maxwell's equation is because there is something very interesting about these Maxwell's equations. As you can see from here that electric fields can be generated not only by the presence of charges, but also by changing magnetic fields and magnetic fields can be generated not only by the presence of electric currents, but changing electric fields. This lies at the heart of what light is, which are essentially electromagnetic oscillations. And we can show that just by doing some small calculations using these Maxwell's equations. So let's take equation number three here and find the curl of equation number three. So if we take equation number three, it simply gives us the curl of the curl of electric field. Now, if you have studied mathematical physics or more specifically vector analysis and you are familiar with gradient and divergence and curl, then you are probably familiar with a certain identity and this identity simply says that if you have a vector field and you find the curl of the curl of a certain vector field, let's suppose the vector field is a. Now that is actually equal to the gradient of the divergence of the vector field minus the laplacian of the vector field. This is an identity which you would probably be familiar with. We are going to use this identity here to say that the curl of the curl of the electric field is equal to the gradient of the divergence of the electric field minus the laplacian of the electric field, which is essentially equal to the curl of the right hand side. That means curl of minus del B upon del T. Now this calculation that we are doing, we want to do in the absence of any kind of matter. So we want to do this calculation in vacuum. So these Maxwell's equations are the equations in the presence of charges and currents. But what if we look at the Maxwell's equations in the presence of nothing? For example, in vacuum, if charges go to zero, then this would probably go to zero in the presence of or in vacuum. And if currents are zero, then this term would also be zero. So in vacuum, the Maxwell's equations will be reduced to the first equation having zero in the right hand side. And the fourth equation, this term will go to zero because there are no charges and there are no currents. In that vacuum kind of scenario, if we are performing this calculation, in that situation, the divergence of electric field would go to zero. Therefore, I will be left with here. I can take the time derivative out and I end up getting del upon del T, the curl of magnetic field. But what is the curl of the magnetic field? This term is zero because we are looking at it from the perspective of a vacuum. I will end up getting this. So this is minus epsilon naught and mu naught, del upon del T, del upon del T. So del square upon del T square E. So essentially, I get an equation that can be rewritten here as the laplation of the electric field is equal to minus cancel. So we should be left with mu naught, epsilon naught, del 2 E upon del T2. So this is one equation that we have obtained. We will keep it just here. But first let us also look at equation number four and do the same thing. Let us do the curl of equation number four. So if we look at equation number four and we do the curl of the curl of magnetic field, then we should get something like the curl or again we use the same identity here first. So del del dot B minus laplations of B. So this is equal to the curl of this quantity which is curl of mu naught, epsilon naught, del E upon del T. So combining these two things, what is del dot B? Equation number two is zero. So I should get negative laplation B is equal to mu naught, epsilon naught, del. If I take del upon del T out, del cross E, del cross E is essentially minus this, del B upon del T. So essentially I should end up getting mu naught, epsilon naught, del 2 B upon del T2. So this is a second equation that we have obtained. What are these two equations? Some of you may be familiar with equations that look like this. These are equations of wave motion. So if you have studied waves before and you try to represent a wave in the form of a mathematical equation, then this is what it essentially looks like. So for example, if there is some kind of a wave that is traveling through a string, let's suppose, and the wave is traveling along the, I would say, z axis, all right, and the disturbance in the string, the amplitude, instantaneous amplitude, I would call that as let's suppose F, all right. It is propagating in the z axis, let's suppose in a one-dimensional string and the disturbance which is essentially the distance from the equilibrium position of the string at any given point in time is given by F. Then the wave equation for that kind of a disturbance which is traveling through a string is given by del 2 F upon del z2 is equal to 1 upon V square del 2 F upon del T square. This is a wave equation in one dimensions or a wave that is moving in one dimensions where F represents the disturbance which is the basically the displacement of the string from the equilibrium, z represents the direction of motion, V represents the velocity or the speed of that particular disturbance moving through space or we can say the speed of the wave itself, T here is with respect to time. If we write down the wave equation for let's suppose a three-dimensional disturbance that is propagating in the same fashion, instead of the del 2 upon del z square, we'll have del 2 upon del x square plus del 2 upon del y square plus del 2 upon del z square of F is equal to 1 upon V square del 2 F upon del T square which essentially is, this is the laplation of F is equal to 1 upon V square del 2 F upon del T square. This is a wave equation in three dimensions. So, if you make a comparison of the wave equations to these equations that we have obtained from the Maxwell's equations, you can clearly see that what these equations are suggesting is that electric field as a disturbance is propagating in a vacuum as well as magnetic field as a disturbance is propagating in vacuum in the manner that a wave propagates through a medium with a speed, a speed if we calculate the speed here of this kind of an electromagnetic disturbance, then from a comparison this V square is equal to 1 upon mu naught epsilon naught. So therefore, V is essentially equal to root over mu naught epsilon naught and if we plug in the values of permittivity of free space and permeability of free space, then those constants lead to a certain number and that number is 299,792,458 meters per second or 3 into 10 to the power 8 meters per second which is the speed of light as we know it. You see electromagnetic disturbances are propagating through vacuum in the speed of light because light itself is an electromagnetic disturbance. You see what the Maxwell's equations have predicted and the beauty of it that electric fields are the result of changing magnetic fields and magnetic fields are the result of changing electric fields. Therefore in vacuum it's possible for electric fields and their disturbances to propagate alongside magnetic fields and their disturbances at the speed of light. These fluctuations of electric and magnetic fields together known as electromagnetic oscillations propagate through vacuum at a constant speed which is a speed of light that is 3 into 10 to the power 8 meters per second. Light is nothing but an electromagnetic oscillation, an electromagnetic wave as predicted by the Maxwell's equations but later on in 1888 was experimentally demonstrated by Heinrich Hertz who essentially produced these electromagnetic oscillations through an electric setup and then he calculated the wavelength and the speed of these electromagnetic oscillations and he demonstrated that these electromagnetic oscillations travel at the speed of light and also demonstrated how they can experience reflection, refraction, diffraction etc. So this is the very first point that we're going to start with. Light as we know it is an electromagnetic wave and electromagnetic oscillation that permeates through space through vacuum and even through a medium just like a transverse wave propagate through a medium. So I think now the picture is getting slightly clearer. Light is an electromagnetic wave and electromagnetic oscillation propagating through space in a particular direction. It simply consists of these oscillating electric and magnetic field lines going from point A to point B and because it's an electromagnetic wave therefore it demonstrates so many of wave characteristics. For example, it has something called wavelength. Yes, wavelength is essentially the distance between two successive crest or two successive troughs that is the distance which gives us the quantity of wavelength that can also be calculated using the speed of the wave which is essentially the speed of light here and the frequency of the wave. We can also calculate the wavelength in terms of a wave number lambda is equal to 2 pi upon k where k is the wave number. It also has the physical quantity of frequency. So we will be using these words again and again frequency which is essentially the number of oscillations of these electromagnetic oscillations per unit time. So the frequency is equal to the inverse of the time period of one complete electromagnetic oscillation. It also has a property known as amplitude. So amplitude is essentially this electromagnetic disturbance. So for example, in terms of electric field what is this particular electric field with respect to its mean that would give you the amplitude or rather the maximum value of the electric field from its mean will give you the amplitude. Usually when we talk about light waves we talk about the amplitude in terms of the electric field most of the time. It also exists in a spectrum. You see the light that we are talking about the visual or the visible light is nothing but a small portion of a wide spectrum of electromagnetic radiation where visible electromagnetic radiation falls in a very small portion in between allowed wavelengths and beyond that there is a lot of electromagnetic spectrum or radiation out there in the world that we cannot detect with our own eyes but they do exist out there starting from radio waves up to gamma radiation. So we have an entire spectrum of electromagnetic radiation in this entire world out of which the visible light that we are familiar with is nothing but a very small portion of it and because light is a wave therefore it demonstrates some of the unique wave phenomena that we are familiar with. For example light demonstrates what we already know as diffraction. Now if you have studied optics or wave theory then you probably are familiar with what diffraction is. Diffraction is a bending of a wave front around sharp corners or obstacles or through apertures where the size of the apertures is comparable to the size of the wave that means the wavelength. So whenever an aperture is subjected by some kind of an incident wave front then the secondary wave front which passes through the aperture has a tendency to spread out. So you see that this is kind of very unique compared to particles because classical particles follow a specific tragic tree but when waves pass through an aperture they tend to spread out into secondary wave fronts. This is diffraction which is very unique wave behavior. The next is of course interference. You see two or more than two waves can interfere with each other which essentially means that the amplitudes of those waves will get added up to create a resultant wave. This is because waves follow what is known as the law of superposition or superposition principle. When two monochromatic radiation from the single source are in phase then they lead to constructive interference where the resultant wave has a greater amplitude and therefore a greater intensity. If two monochromatic waves from the same source are out of phase then they will result in destructive interference where they will completely vanish. One very common and popular experiment is the Young's double slit experiment where a monochromatic radiation passes through two slits creating two secondary wave fronts which interfere with each other because of the varying path lengths and end up resulting in alternating dark and light fringes. This is a very unique property of waves this interference pattern because if instead of waves we bombarded this screen with let's suppose particles then we would end up probably getting just one spot on the other end and a dark background but because we are dealing with waves and they have this property of superposition principle they end up interfering with each other and redistributing that wave energy in alternating dark and light fringes. Now why am I talking about these things? You have to keep in mind the reason I'm talking about these things is because we will come back to these properties later on. For example when we talk about interference we'll come back to this when we talk about electron interference experiment because when we go into this world of wave particle duality we will see that some of these properties do not really hold true for certain experiments for waves and some of these properties are actually demonstrated by classical particles. So therefore I want to emphasize to you in this particular lecture the classical properties of what waves are or what light is. So apart from interference we have another property which is a property of polarization or this is a phenomena demonstrated by waves or specially transverse waves where polarization basically gives you an idea about the geometrical orientation of the nature of these oscillations. So for example if you have a plane polarized light then the oscillations of electric field happens on a fixed direction. If you have a circularly polarized light or elliptically polarized light then the oscillations of electric field the direction keeps on changing with time or it keeps on rotating. So this is something very unique to electromagnetic waves or light. Now waves also carry energy and momentum so whenever light is moving from one point to another then it can carry with it energy and momentum. So this brings me to the six point energy and momentum. What does classical physics tells us about the energy contained in an electromagnetic wave and the momentum carried by an electromagnetic wave. Without going too much into the details of the mathematics classical electromagnetic theory can easily predict that the total amount of energy per unit time per unit area carried by electromagnetic wave from point A to point B is given by what is known as intensity and the intensity is essentially equal to what is known as the average the time average of a pointing vector which is in fact equal to half C epsilon naught E naught square. What I want to emphasize here in this particular expression is that intensity see when we talk about intensity you know day to day life when we say okay some light source is more intense compared to the other physically speaking what it simply means is that one light source is emitting more amount of energy into my eyes compared to the other. But what does this intensity actually refer to in terms of the wave characteristics. Well this intensity which is the energy emitted per unit area per unit time is actually equal to the amplitude square of the electromagnetic oscillation. E naught here is the amplitude of the electric field and E naught square basically gives us an idea about the intensity. This formula is very important because we will see later on when we are discussing wave particle duality that when we talk about energy carried by a light or a photon then we will no longer be talking about amplitude square but we will be talking about frequency and there will be a jump a certain change in the way we look at these quantities. But before we go there from the perspective of classical electromagnetic theory the energy or the intensity of a light wave is actually directly proportional to the square of the amplitude and whenever this kind of a light is incident on a surface it is also capable of transferring momentum which results in what is known as radiation pressure that means a force exerted onto a surface per unit area and that momentum is actually equal to this intensity upon c the speed of light. These are very important formulas for electromagnetic waves in classical electromagnetic theory. And lastly I want to talk about the continuous absorption and emission of radiation from matter. What does this mean? You see light or electromagnetic radiation is capable of interacting with matter. In fact matter can absorb electromagnetic radiation and it can emit electromagnetic radiation. In fact the very source of creating an electromagnetic oscillation is an accelerating charged particle or an oscillating charged particle. An oscillating charged particle can release its energy in the form of an electromagnetic oscillation straggling through space. So therefore matter can absorb and emit electromagnetic radiation. Now what classical physics tells us about this? It says that the manner in which electromagnetic energy is absorbed or emitted by matter is a very continuous fashion. So for example let's suppose you take an object and take it out in a sunny day and put it in the sun right then the object is going to get heated up over a period of time because it is going to absorb all the light energy and that light energy is going to get converted into thermal energy and the object is going to get heated up. This happens in a very continuous fashion because there is no restriction that classical physics puts as to what kind of a electromagnetic wave will be absorbed by a particular material or what not. So for example if an electron is or a charged particle is in the presence of electromagnetic wave it will absorb that energy and it will start oscillating with greater amount of energy which is called excitation and it might release that energy de-excitation and that excess energy will create a new electromagnetic oscillation right. So energy can be absorbed by matter and emitted by matter in a very continuous fashion without any sort of restrictions and the reason I am emphasizing on this as well as the reason I'm emphasizing on all these properties is because these are the classical properties of waves and essentially electromagnetic oscillations. Light is an electromagnetic oscillation that has wave properties like wavelength frequency amplitude. It exists in a spectrum of electromagnetic oscillations other than what we know as visible light. It demonstrates properties like diffraction interference polarization. It carries energy and momentum energy is directly proportional to amplitude square. It interacts with matter in a very simple continuous fashion without any restrictions. We will see that these ideas about what waves are, what light is, what electromagnetic oscillations are are going to be challenged in the coming five to ten years. In fact in five to ten years we will experience a moment something like this. Yeah a meme worthy moment because we will see that many of these things that we know and hold to be true with such confidence we are going to be challenged in different kinds of experiments. In certain experiments we will see that the energy of a light wave or a light photon would not be proportional to the amplitude square but rather would be related to frequency. Frequency? Yeah frequency we'll see that. We will see that in certain cases when light energy is absorbed or emitted by a surface it is not done in a continuous fashion but in discrete quantized amounts. We will see that in certain experiments light as we know of as an electromagnetic oscillation do not really behaves like an oscillating spread out object but concentrated packets of energy known as photons. It behaves like particles that can experience collisions with other particles and that is going to open up a whole new interesting world. So that is all for today and Divya Jyoti Das this is for the love of physics. Thank you very much I'll see you next time. Bye-bye.