hi friends refraction means bending of light light bends when it travels from one medium to another for example light bends when it travels from Air to glass or from air to water but why does light Bend because the speed of light changes when it travels from one material to another in this video we'll talk about a number called refractive index of a material that measures how much the light slows down in the material or how much it bends have you heard of this term refractive index in your everyday lives if you go to an eyeglass shop when choosing the lens you'll hear about this term refractive index higher refractive index means the lens can bend the light more efficiently so your lens will be thinner and more expensive let's learn all about refractive index in this video let's start with the rad diagram for light traveling from Air to glass light is traveling in air at a speed of 3 into 10 ^ 8 m/s now when light hits the glass its speed slows down the speed in glass is 2 into 10 ^ 8 m/s so can you see that due to the change in speed the light bends light changes its direction from its original path now if you draw a normal at the point of incidence can you see that the light bends towards the normal in the glass refractive index of a material is defined as the speed of light in vacuum or air divided by the speed of light in the material the formula can be written as n = c by V where n represents the refractive index of the material C in physics is used to denote the speed of light in vacuum remember Einstein's famous Formula E equal to mc² even here C represents the speed of light in vacuum 3 into 10 ^ 8 m/s now the speed of light in air is a bit slower than vacuum but we take it to be approximately the same so RC represents the speed of light in vacuum or air and V represents the speed of light in the material now let's apply this formula and calculate the refractive index of glass in our example light is traveling from Air to Glass so the refractive index of glass is going to be the speed of light in air divided by the speed of light in glass let's put in the values in our formula we get the refractive index of glass as 3x2 or 1.5 now what is the unit of refractive index that's right it has no units since it's a ratio of speeds so the unit m/s is going to get cancelled out next let's consider the example of water let's say we are given the refractive index of water as 1.33 and we want to calculate the speed of light in water so light is traveling from air to water once again we can use the refractive index formula refractive index of water is the speed of light in air by the speed of light in water on substituting the values and solving we get the speed of light in water as 2.25 into 10 ^ 8 m/s so light is slowing down when it enters water from a speed of 3 into 10^ 8 m/s to 2.25 into 10 ^ 8 m/s now why is that because water is a denser medium compared to air let's place this formula of refractive index on our concept board refract itive index of a material equals speed of light in vacuum or air divided by the speed of light in that material let's compare the refraction of light in glass and in water the refractive index of glass is 1.5 it's more than the refractive index of water which is 1.33 now let's compare the speed of light as you can see the speed of light in glass is lower than the speed of light in water so what does this tell us a higher refractive index number means the speed of light is going to be lower in fact the refractive index tells us how much the material slows down the speed of light so in glass the speed of light is 1.5 times slower than in air similarly in water the speed of light is 1.33 times slower than in air now in which case does light Bend more that's right the correct answer answer is glass because glass has a higher refractive index in both cases glass and water light is coming from Air so the first medium here is air when the first medium is air the refractive index is known as the absolute refractive index of the material so we have the absolute refractive index of glass is 1.5 and the absolute refractive index of water is 1.33 the more accurate definition of absolute refractive index takes the first Medium as vacuum but since the speed of light in air is approximately same as the speed of light in vacuum we can use either vacuum or air now let's talk about the case where light is traveling from water to Glass since the first medium here is not vacuum or air we can't call it the absolute refractive index so here we can talk about the refractive IND index of glass with respect to water this is represented by the symbol n GW so it's the refractive index of glass with respect to water in some places you may see the symbol mu being used but for this video we're going to use the symbol n so NW equals the speed of light in Water by the speed of light in glass now we can generalize this let's say light is traveling from medium 1 to medium 2 so this is going to be denoted by the symbol n21 so the refractive index of 2 with respect to one is the speed of light in medium 1 by the speed of light in medium 2 let's place our general formula of refractive index on our concept board refractive index of medium 2 with respect to medium 1 equals speed of light in medium 1 divided by the speed of light in medium 2 till now we have talked about refractive index based on speed of light now let's talk about refractive index based on angles the angle of incidence and angle of refraction do you remember these two laws of refraction here we are going to use the second law of refraction sin I by sin R is a constant where I is the angle of incidence and R is the angle of refraction now this ratio sign I by sin R which is a constant is the refractive index it's the refractive index of medium 2 with respect to medium 1 so what does this law tell us that if you change the angle of incidence by Shifting the incident rate the angle of refraction will change accordingly so that the ratio sin I by sin R remains constant let's take the example of glass refractive index of glass with resp respect to air is sin I by sin R just like velocity it's similar to the formula based on speed of light which was VS1 by vs2 here it is the S of the angle in medium 1 by S of the angle in medium 2 let's say the angle of incidence I is 37° and the angle of refraction is 24° if we take this ratio sin 37 by sin 24 as you can see we get 1.5 if we use the refractive index formula based on speed of light or this formula sin I by sin R we get the same refractive index for glass which is 1.5 now if you had to experimentally calculate the refractive index of a medium which formula would you use that's right the formula sin I by sin R because it's much easier to measure the angles that light makes than to measure the speed of the light in the medium to measure the angles you just need a simple protractor let's place the formula of refractive index based on angles on our concept board refractive index of medium 2 with respect to medium 1 equals sin I by sin r as we learned for refraction and refractive index you need two media two materials if the first medium is vacuum or air it's known as absolute refractive index let's say we are given the absolute refractive index of glass and water and we need to calculate the refractive index of glass with respect to water so light is traveling from water to Glass let's use the refractive index formula refractive index of glass with respect to water is speed of light in water divided by the speed of light in glass since we are not given the speeds here let's see if we can do something interesting with this formula we can break this fraction and add the speed of light in air as the numerator and denominator can you see that the left part VA by VG is the refractive index of glass with respect to Air and the right part VW by VA is the refractive index of air with respect to water which is 1 by the refractive index of water with respect to air so our magic formula becomes refract index of glass with respect to water is equal to refractive index of glass with respect to air divided by the refractive index of water with respect to air we can generalize this formula for any medium so we can write it as refractive index of medium 3 with respect to medium 2 is equal to the refractive index of medium 3 with respect to medium 1 divided by the refractive index of medium 2 with respect to medium 1 I think it's easier to remember remember this formula using the glass Water and Air example let's use our magic formula to find the refractive index of glass with respect to water we are given the absolute refractive index of glass and water absolute refractive index of glass is 3x2 so the refractive index of glass with respect to vacuum or air is 3x2 and the absolute refractive index of water is given as 4x3 so refractive index of water with respect to air is 4x3 now we can use our magic formula refractive index of glass with respect to water is equal to refractive index of glass divided by the refractive index of water substituting the values and solving we get the refractive index of glass with respect to water as 9 by 8 what do you think will be the refractive index of water with respect to Glass you're right it is 8 by9 we simply have to take the reciprocal since refractive index of water with respect to glass is one by the refractive index of glass with respect to water let's pin this formula on our concept board refractive index of glass with respect to water equals refractive index of glass divided by the refractive index of water and the general formula is refractive index of medium 3 with respect to medium 2 equals ref active index of medium 3 with respect to medium 1 divided by the refractive index of medium 2 with respect to medium 1 next time you go to the shop to buy your eyeglasses I would encourage you to ask for the refractive index of the lens you're planning to buy remember higher the refractive index the lens will be thinner but also more expensive people who have high power usually go for a higher refractive index lens so that it's thin but if you have low power then a lower refractive index is probably fine and do remember to subscribe to my YouTube channel and do check out my website manocha academy.com