Refraction of Light

in this video we're going to focus on the refraction of light this is property of light that causes it to bend when it passes from one medium into another and this picture really shows the refraction of light you can see this glass rod is bent at the interface between air and water so here we have the interface between air and water and this vertical dashed line that i'm drawing represents the normal line the normal line is perpendicular to the interface between air and water it's at 90 degree angle now when light ray strikes the point of incidence three things could happen the light ray can reflect at the boundary it can refract or it could be absorbed by the material this is known as the incident ray this is the reflected ray and the one on the bottom is the refracted ray the angle of incidence is the angle between the incident ray and the normal line so let's say that's 45 degrees according to the law of reflection the angle of incidence is the same as the angle of refraction so these two angles must be equal to each other now my drawing is not precise so it may not look like they're the same but they should be the same now this angle here is known as the refracted angle and in order for us to calculate that we need to use something called snell's law also known as the law of refraction and it's n1 times sine theta 1 which is equal to n2 times sine theta 2. so that's snell's law it can help us to calculate the angle of refraction or the index of refraction the index of refraction for air is approximately one for pure vacuum where there's no molecules in the air it's exactly one the index of refraction for water is 1.33 so with this information we can calculate the angle of refraction so n1 we're going to say is 1 and n2 is going to be 1.33 so it's 1 times sine 45 and that's equal to 1.33 times sine theta 2. sine 45 that's equal to the square root of 2 divided by 2 which as decimal is 0.7071 if we divide that by 1.33 we'll get that 0.53166 is equal to sine of the second angle now in order to calculate that angle we need to use the arc sine or the inverse sine function and that will give us theta 2 which is the angle of refraction so if you type in an arc sine 0.53166 it'll give you an angle of 32.1 degrees so that is the angle of refraction so notice that as the incident ray moves from material with low index of refraction to material with higher index of refraction the ray bends closer to the normal line the angle decreased from 45 to 32.1 now the reverse is true if the incident ray traveled from material with high index of refraction to material with low index of refraction the angle is going to increase and so it's going to bend away from the normal line as opposed to toward the normal line now another interesting fact that you want to know for this topic is the speed of light the speed of light is not always 3 times 10 to 8 meters per second in fact it changes based on the material that it is traveling in this is the speed of light in vacuum the speed at which light moves depends on the material it's moving in and here's how you can calculate the speed the speed is equal to the speed of light divided by the index of refraction so the speed of light in air is going to be 3 times 10 to the 8 meters per second divided by one which is three times ten to the eight meters per second now what about in water how fast does light travel in water well we can calculate that using the same formula so it's going to be is equal to over so is not going to change that's going to be 3 times 10 to the 8 meters per second if we divide it by 1.33 which is the index of refraction of water we can get the speed of light in water and so in water light travels at 2.256 times 10 to the 8 meters per second so notice the relationship between the speed of light and the index of refraction when light travels in material with high index of refraction the speed decreases so diamond for example has very high index of refraction if my memory hasn't failed me believe it's around 2.4 so light travels very slowly in diamond but it travels lot faster in water or air compared to diamond so far we've considered the example where light travels from material with low index of refraction to material with high index of refraction and we saw that the light then closer to the normal line now let's consider the other situation let's say we have glass on the bottom air on top the index of refraction for glass is 1.5 there's different types of glass out there but for the most part it's close to 1.5 so this is going to be the incident ray and this time the refracted ray is going to move away from the normal line let me make this angle smaller so i'm going to choose an angle of 40 degrees so that is the angle of incidence now let's calculate the refracted angle so it's n1 sine theta one which is equal to n2 sine theta two so n1 we're going to say that's for glass that's 1.5 times sine of 40 degrees that's equal to n2 the index of refraction for air times sine theta 2 or theta mean theta r4 the angle of refraction so 1.5 times sine 40 is 0.96418 so the refracted angle is going to equal arc sine of 0.96 so the refracted angle is 74.6 degrees so when light moves from an index from high let me say that again when light moves from material with high index of refraction to material with low index of refraction the light ray bends away from the normal line now there's something interesting that's about to happen here notice what's going to happen if we increase the angle of incidence if we increase it the rate is going to bend even further at some point the ray will travel in between the interface of air and glass and if we increase the angle even further something called total internal reflection will occur where all of the light rays will reflect and none of it will be refracted but before total internal reflection occurs there's something called the critical angle which the angle of refraction is equal to 90 degrees that's when the light ray is between the two boundaries as represented by the ray in red here let's calculate that critical angle so once again we could use snell's law so n1 is going to be 1.5 times sine the instant angle is the critical angle and two is one the instant angle is the critical angle when the refracted angle is equal to 90 degrees so sine 90 is one so we have 1 divided by 1.5 and that's equal to 0.6 repeating so the critical angle is going to equal arc sine 0.6 repeating or 2 over 3. so in this example the critical angle is 41.8 degrees if you choose an angle that's greater than this number total internal reflection will occur but if you make the instant angle equal to the critical angle then the refracted ray will travel along the boundary between air and glass which is an interesting phenomenon to see so that's basically it for this video hopefully it improve your understanding of the refraction of light and how to calculate the incident angle or the critical angle or even the refracted angle so keep in mind the incident angle could be anything between 0 and 90. the critical angle is specific incident angle when the refracted angle is 90. so even though the instant angle can take on many values the critical angle can only take on one value it is specific instant angle where the refracted angle is 90. just want to clarify that in case there was some confusion