 Okay, so how many of you were not there in last class, last physics class? Fine, so last physics class we have finished the bridge program and we have started class 11th Okay, I hope you know it and we have spent around one hour, we have just started actually Okay, so we have introduced, we got introduced to various types of units that are there Okay, why units are important in physics so that we can properly measure any physical quantity We cannot measure the length in terms of seconds, similarly we cannot measure let's say mass in terms of meters So that's why they are different from units, okay, so we got to know that there are seven fundamental units Okay, and every other unit is derived from these units like velocity is derived from length and time Okay, similarly each and every unit is derived from these seven units, so basically the universe is seven dimensional Okay, so if you know these seven physical quantities you essentially know everything about that particular thing Okay, now we have introduced these units and we came to know that you know since during those times Different different units might be discovered at different different places because a person who might be developing a unit of length as Let's say kilometer may not know that somebody else is developing length as millimeter, I'm just giving example you know It could be inch or yard or something else, so that's why there are different different units that are there During those times it was very difficult to communicate that listen we are all doing, we are all measuring length in terms of meters So let's all do that, so it was very difficult to communicate there was no mobile phone Even for travel also they used to use horses, so they can't travel using horse from US to India, right So that's why there are different different units and several units came up CGS unit was one of them very popular, MKS was another very popular unit Okay, so like that there are many units, many system of units who are using different different units for these seven basic quantities Okay, so later on as entire world was working together all the economy got you know there is a global economy right So because of that trade and everything all the communication that happens between different countries So it made sense to create a single set of units so that it is easy to communicate and trade and so on and so forth So there comes SI system of units, okay, in SI system of units I think you might have already got introduced to different SI units For example, length is measured in meters, mass is in kilogram, time in seconds like that Okay, so we got introduced to these seven basic quantities and also got introduced to SI system of units And then we have also introduced two supplementary units which are angles Okay, angles basically measure the amount of opening Okay, now that amount of opening Alright, so we got introduced to something called angles What angle measure? Angle measure the amount of opening Try to quantify how much is the opening, alright That opening could be between the two lines like this This is called the you can say the planar angle Okay, this is the planar angle which is measured in terms of radiance Okay, so we should know a way to measure the radiance or the amount of opening Which is a planar angle I am talking about Okay, so how we have defined the angle, the planar angle Suppose this is the angle which is represented by theta How we get to know what is theta? The length of the arc by the radius We should take this as a center, take this as a center and draw an arc of any radius Alright, then measure this length, if this length is L And the radius of the arc was R, then L by R we say is angle Understood, okay, so this is the angle and it has no dimension as such Because it is a ratio between two lengths Okay, but then this is one of the physical quantities So it takes, I mean we should name some unit against it So we call it radiance Alright, so this is how the angle is quantified You can take any radius, the ratio between arc length divided by R will be always fixed And more is opening, more is L and R Sorry, more is opening, more is L, R is keeping fixed So the angle will increase Okay, now here if let us say this R is very very large, extremely large Then will this be a close to a straight line or not? It will be close to a straight line Okay, so we are going to use this kind of approximation to find out the great distances soon Okay, just I mean I have coined this thing that if radius is very large Then this is close to the straight line Okay, and if it is a straight line like this You can claim that okay, this is R, this is some other length That is some other length because this length is less than the R Okay, but essentially we are treating it like an arc if R is very large So all these lengths, the point connecting this point to any point on the straight line should be same We are treating it same for all practical purposes Okay, if R is extremely large like 1 lakh kilometer and things like that Okay, and more so if theta is less If theta is like 0.01 degrees, then it will be like this Extremely less angle, I mean this angle is very large This is like more than 2 degrees I am talking about 1 by 1000 of this angle Then the arc length you can even more approximate like a straight line Okay, so we are going to use this approximation soon Okay, similarly we also quantified last class something called solid angle What is a solid angle? The amount of opening which has through the surface like this This is the amount of opening in 3D Okay, this is also quantified What is the value of this? Suppose this is the amount of opening, this one How we quantified this? This is related by sigma, sorry ohm So how to quantify this? It is still radians It is equal to surface area You draw a sphere of radius R Whatever is the surface area, this surface area divided by R square Is this solid angle This we are not using much in physics It is just good to know The surface area divided by the radius square is a solid angle Here we draw a circular arc, here you draw a sphere Are you getting it? These are all imaginary If you don't need to actually draw it, you can imagine a sphere Whatever is the cutout of the surface area through the solid opening That divided by R square is a solid angle For example here, if using this column if I draw a sphere Only one eighth of the sphere will be enclosed by this solid opening You understood what I am saying? Look at that That corner, if I draw a sphere of radius R Then only one eighth of the sphere will be covered One by eight So the surface area of one by eight sphere is one by eight into four pi R square That divided by R square is the solid angle of that Getting it? So like that we define the solid angle also So now if we define the angle It really helps us to calculate the grid distances One such example we have seen in the previous class towards the end We used what? Parallax method We used parallax method to determine the distance I will just quickly revise it Right on parallax method Till what we did last class What we did was we knew that distance between the two eyes Let's say this is I1 and this is I2 Okay, keep quiet What we did last class was that we have all of us have two eyes And suppose we know the distance between the two eyes What we do is that we place let us say a chalk or anything in front of us Then we close one of the eyes Suppose chalk is over here And then look that chalk What will happen is that your line of sight will pass through the eye like this And suppose there is an obstacle on the board Those who did not come We have to do this again probably So what we did was we have placed few markers on the board like this One, two, three, four, five, six like that And then what we did was we placed a chalk in front of us or a pen Then we looked through one of the eyes What will happen is that the chalk may coincide with marker I If you look from the right eye it may coincide with I So that is what this, let's say this I1 If you are looking from I1 this could be a marker I Then you close the first eye and open the second eye You see that the marker which coincides with chalk is now let's say 6 So you will see that it is 6 You can do it now also You see that if you look at the object through one eye and then through the other eye The object seems to be moved related to the board Now this is what the diagram of that This is your pen or chalk These are your two eyes And this is marker I and marker VI So if you know the distance between marker I and VI You see that these are alternate opposite angles Angle is same So arc length divided by this distance Should be equal to this arc length divided by that distance So if you know how far is the chalk from your eye Let's say this is D1 This is L1 This is L2 And this is D2 So you can say that L1 by D1 is equal to L2 by D2 So you can get the value of D2 if everything else is known This is what we did last class term Understood So we continue from here We are going to use parallax method And we will calculate the distances of L1 by D1 L1 by D1 Arc length divided by radius This is angle This angle That arc length divided by D2 is this angle Both are same Don't miss any class It becomes difficult for me to revise What we did in 3 hours in just 15 minutes