 This is light pushing something. How can it do that? When I saw this for the first time, it absolutely blew my mind because our everyday experience with light is so different. It is never the case that we feel pushed down by the sunlight or when we open the fridge we are blown away by the light or even if I shine a laser light on a piece of paper, it doesn't move it at all. You can always say that the push of the light might be extremely, extremely weak, something that we can never notice and if you do say that you won't be wrong really. The goal of this video is to figure out exactly how does light or electromagnetic wave pushes or applies forces on things and also how the same ability of light results in some beautiful astronomical phenomena with comets and a really cool application with solar sails. Let's start off by thinking about why does light exert a force? The first thing that we learned in physics is f is equals to ma but light does not have a mass. So that means f should be zero. Although we know that f is also equal to the rate of change of momentum. This is from Newton's second law. So if light is exerting a force then it must also have momentum. Let's think about this by taking a familiar example. So we have a ball that is moving to the right with some velocity. It has some kinetic energy and when it collides with a bigger ball it loses or transfers some of its kinetic energy to the bigger ball which then starts moving slowly. So in this process some energy has been transferred. We can also say that the smaller ball had a momentum of mv to begin with and upon colliding or interacting with a bigger ball let's say now it has a momentum of mv1. Now the velocity would be less than the original velocity. It has transferred some of its momentum to the ball. The momentum was changed or some of it was transferred from the small ball to the big one because when the balls collided there was a force on both of these objects. For the duration of collision which changed their motion. In this case we can say that the transfer of energy from one ball to the other also resulted in the transfer of some momentum. And in fact these two are also related. We know that ke is half mv square and momentum is mv. If we try to express one in the form of other with some working we can land at this expression right here where ke is equal to momentum square divided by 2m. Energy and momentum go hand in hand. Similarly in the case of light we have experienced its energy in the form of warmth when we stand outside in the sun. Some of the energy is transferred to us or absorbed by us. That should mean some momentum is also getting transferred from the light onto us. So light does have momentum. We could have ended the story just when we saw that light was pushing objects because whenever there is a force there will be some momentum. But we never really experience light's push in our everyday experience. So it's kind of difficult to believe that light has a momentum with it. But if we think about in this way that is whenever there is some energy transfer there is some momentum transfer that goes with it. And that is what happening with the case of light. And we always learn that momentum is given by mv. But it is not necessary for a thing to have mass to have momentum. Even without mass waves can have momentum. And particularly electromagnetic waves. All right now let's see how does exactly light interact with matter and how is this force produced. All right let's see how light from the sun would push our hand. We can have any source of electromagnetic radiation. In this case we are taking the sun and let's see how much it pushes our hand. So here we have the electromagnetic radiation coming from the sun and here we have our hand and it is falling it is falling on our hand. Our hand will absorb some of this radiation. And any material even our hand it is made up of atoms which has charges electrons and all those protons. So the electric and magnetic fields they must be interacting with charges on our hand. So let's let me make the hand a little transparent so that we can see the charge clearly there it is. Let's say we have a positive charge right at the center. This can very well be an electron also that doesn't really matter. Now why don't you pause the video and think about what will happen when these fields electric and magnetic fields when they interact with this positive charge. All right when the electric field interacts with a charge it exerts a force on it. So when the electric field is directed upwards there is a force on the charge in the upwards direction and the magnitude of this force is q times the field strength that is e. Because of this force the charge also gains some velocity in the upward direction. So the charge also has some velocity now of magnitude v. And as a result of that the charge experiences a Lorentz force in the direction of v cross p because force Lorentz force was after all this was q v cross p. Here when the electric field is upwards when the electric field is upwards we can see that the magnetic field will be pointing outside the plane of the screen. So if we use the right hand curl rule and we curl our fingers from v to b that is v cross b the direction of the thumb will be in the direction of the force. So the force is to the right this is the direction of force right here. And there it is there is the force on our hand in the direction of propagation of light or electromagnetic wave and that is how light or any electromagnetic radiation exerts a force. Let us try and figure out how strong this push is. So force is equal to q v cross b. Let's bring this right over here and because we are dealing with sinusoidal waves so the charges will be oscillating that means that the velocity will keep on changing and thus the force will also keep on changing. So we will talk about an average value of force and similarly an average value of velocity. Now for traveling electromagnetic waves we know that the magnitude of the magnetic field and electric field are related by this expression b equals to e divided by c. If we substitute this value of v over here when we do that we will get q into e into v by c and q e over here this factor q e over here this is the force on the electric charge by the electric field. So we can denote this we can write this as f e this is the force due to the electric field on the charge and this is multiplied with the velocity the average velocity with which the charge is moving divided by c and long back we also learned that force multiplied by the velocity this gives us the rate at which energy is transferred or this is the power the rate at which energy is transferred so let's write that this is d the rate at which energy because we have two e's I'm writing energy as en so this is d e by dt. Now let's place f e into v over here so when we do that finally we get the average value of the force to be as 1 by c that is 1 divided by the speed of light into the rate at which energy is transferred or absorbed by the hand this is d e divided by dt. Now have a look at this this is the magnitude of the force that is incident on your hand from the sunlight and imagine how small this value would be you are dividing this you are dividing the rate at which energy is being transferred by c which is a huge number this is 3 into 10 to the power 8 so imagine how small this force would be you will never be able to experience or feel this force but the interesting thing is now you can calculate how much force your light bulb is exerting on you your light bulb would either be 25 watts or 75 watts or 100 watts that is basically joules per second if it's a 100 watt light bulb that means every one second it is transferring an energy of 100 joules it is dissipating an energy of 100 joules so that would be your d e by dt and with some calculation something that we will not go into in this video with some calculation you will be able to figure out the force on your body just from a light bulb. Now at this point why don't you pause the video and maybe try to express the rate at which energy is being transferred in terms of momentum all right so from Newton's second law we know that force force is equal to the rate of change of momentum so if we substitute this value of force over here if we do that we will get the rate of change of momentum and that is equal to 1 by c into the rate at which energy is being transferred or absorbed by your hand we can cancel off these d t's so eventually what remains is the amount of momentum that is transferred that is equal to 1 by c into the amount of energy that is transferred or absorbed so that is how momentum and energy are related in the case of light and a relation that you will commonly see in textbooks will look like this the momentum of light that is equal to the energy of light divided by now finally because there is a force we can also talk about pressure and to be able to calculate pressure all you need to do is divide both of these sides by area so when we do that when we divide this by a you will get a a over here as well and the left hand side has a name left hand side is pressure this has a name this is called radiation pressure this is basically lights push on an area of 1 meter square per second and since you are also dividing this pressure by c even this pressure is extremely small but radiation pressure results in some very interesting phenomena in our solar system and it also has and it also has a really cool application in solar sales so let's let's understand what those are now radiation pressure is responsible for some interesting things with comets and comets usually have two tails this tail is called a dust tail of the comet and the other one is called an iron tail the dust tail is a consequence of radiation pressure whereas the iron tail is a result of something else altogether and it was Kepler who noticed that the tails of comets always pointed away from the sun no matter where the comet is in the orbit around the sun so over here we can see how the tail is always pointing away from the sun and the direction of the tail is the result of the radiation pressure the sunlight is fully absorbed by these dust particles and therefore they are pushed away now one really interesting application of radiation pressure is in solar sales most spacecraft most usual spacecrafts gets pushed through space with some kind of rocket fuel the momentum of the fuel goes in this direction and that pushes the spacecraft upwards kind of like how a fire extinguisher would work the momentum of all these chemicals is to the left and that is pushing the bottle to the right there are different kinds of fuel used in space travel but they all come out of a fuel tank that is on the spacecraft so they eventually they all run out of fuel but a solar sale spacecraft doesn't need ordinary fuel it gets pushed through space with a free supply of energy solar sale this is a method of moving in space using the radiation pressure from the sun on these large mirrors or reflective surfaces so when radiation is incident on the surface it gets reflected which changes the momentum of the radiation as its direction changes and that change in momentum exerts a force on the spacecraft in this direction scientists are developing very light circuits which can be mounted on these spacecrafts and the wings have to be made of foil extremely thin and of a highly reflective surface so that the pressure of light slowly pushes it solar sailing is a game changer these spacecraft can be steered a lot like sailing boats which uses wind to move through the waters with free supply of energy soon these spacecrafts could be sailing around the solar system and into deep space and maybe one day in the future we can even sail one to another star altogether all right so in this video we saw how light exerts a force on objects and also how light has momentum along with energy we also try to figure out the amount of force that our hand experiences under sunlight and finally we looked at the behavior of comets in an orbit around the sun which is the result of a radiation pressure and finally one really interesting application in the form of solar sails which uses radiation pressure to move through deep space