SNELL'S LAW IN KINEMATICS 😉|| JEE MAINS || ADV || JEEXTAR IITKGP

Added: 2026-05-11

[00:00:04]So welcome to another video. Uh so today I'll teach this smells law analytics. So it is basically kind of uh we incorporating the snails law concept uh like when a light travels from one medium to another we have uh we have a relation and with that we can uh solve the problem even if it is given for multiple mediums. So the same thing uh we'll incorporate into this chamatics and I'll later generalize this problem too and we will also solve a question based on this. Uh so let's go. So here I have uh this distance L is given and I have been told that at like this uh this particle is coming at a velocity V1 at an angle theta 1 with this normal and it is traveling. Okay. And this is the medium. And I want to find uh that the what distance x like this x uh if I turn or I enter this uh medium 2 so that I can reach the point b at the minimum time. Okay. So we we'll calculate that.

[00:01:16]Uh so first of all I'm defining this sin theta1 = to x by this is the theta 1. So this is also theta 1. So sin theta 1= to xy x² + y square. Okay. And sin theta 2= to l - x y^ - x² + y2. Okay. So now time uh required to travel from a to b is a by v1. Okay. A by v1 and ob by v2 o by v2. Okay. So a = roo<unk> x² + y² + y square and = l - x² + y2 square and here okay so for uh minimum time also okay I set this uh for minimum uh time so d a d by dt dx equals to zero so this is our uh differentiation and uh I want to equate it to zero to get the minimum value of x okay So <unk>2 we can cancel it here. So let me rewrite this as x by x² + y² uh into 1x1 - l - x by y2 + l - x² into 1 by <unk>2. Okay. So now uh see one thing sin theta 1 = x by this one.

[00:02:43]Okay. So and here I have just the inverse of sin theta 1 right look it closely I have the uh in sorry not the inverse I have the sin theta 1 only sorry so I can write it as sin theta 1 by v1 minus and this one is what this one is sin theta 2 okay so I can write it as sin theta 2 by 32 = to z so this is our this and I can rewrite it as sin theta 1 by v_sub_1 = to sin theta_2 by v_sub_2 uh okay so this is the condition for traveling from a to b at the minimum time so why I have written like this so I will understand it and I will let you explain so you can explain to yourself too like uh if I want the value of x and I'm given theta 1 theta 2 All these are given. Okay. So with this relation something there will be unknown and from using that value you can calculate x or if x is given so you can calculate the theta one right. So that variations you you know by yourself. So and if I want to generalize this okay for different media remember sin theta that is theta is the angle with the normal angle with the normal by v that is the velocity in that medium okay this will be constant okay So the same as this M's law where we knew that mu sin theta equals to constant same thing the same thing. So okay now let us generalize uh what I meant by generalizing this this is the main condition for generalizing it. Now for different media let me show uh okay so this is one media let this is another media is the boundary.

[00:04:56]Okay. Uh this is a so suppose this is uh so this is the I said the it is coming like this uh and it is traveling like this in this uh this medium and in the next medium uh it is again traveling like something like this. Okay.

[00:05:28]Uh in the next video it's like same as in uh we saw in the case of refraction. Same thing here. So three 1 2 3 2 3.

[00:05:43]So this is the 1. This is 32. This is also two. This is the three. This is the two. And this is the four. And suppose here it is traveling in V_sub_1, here it is in V_sub_2, here in V3 and V_sub_4.

[00:06:03]So in if we want to generalize this one.

[00:06:05]So sin theta by P = constant. So here we can write sin theta 1 by v1 = to sin theta 2 by v2= to sin theta 3 by v3 plus to sin theta 4 by v4.

[00:06:26]So if I want to reach from a to b at the minimum possible time. So this is my condition. Okay. So uh and uh how the question works uh you can modify it accordingly and get the values what you require. Okay. So now let's uh let us solve a question based on this top uh based on this topic.

[00:06:49]So here is the question. So we are told that from a point A on a highway so this is the highway. One has to reach B this B at minimum time. Okay. At what distance from B on the highway should the car turn if the V field equals to V highway by EA like that is the velocity in this like this is the field okay and uh here this is the highway this is the highway so from highway if I turning towards the field my my velocity decreases by ea times okay so we are required to find at what distance x from d okay from d so uh from d if let it be at X uh so I am drawing normal so I have to find this point like this distance X at which if I'm coming from here right so if I turn here I'll reach B so I am required to find this X for which I'll reach B at minimum time okay so uh here I am traveling it's B and here B by I'm taking B is A so I'm coming like this and and this to reach B. Okay.

[00:08:08]Reach B.

[00:08:12]So let this angle be theta and this is 90° you know. So like theta 1= to 90° if I consider highway as medium one and uh field as medium 2 and theta_2 is theta theta I don't know theta 1 to calculate.

[00:08:28]So by the relation that I generalized earlier that is the by the snail's law of chynics.

[00:08:40]Uh okay you can call this as uh snail's law in chynytics also cuz I'm not sure if snail is uh actually built this theorem or not but I am just uh trying to draw analogy. Okay. So, so I have given that sorry uh sin theta 1 by v1 = to sin theta 3 by v_sub_2. So sin theta theta 1 is 90. So this will be 1 and v_sub1 is v and what is v_sub_2? V by theta and sin theta.

[00:09:18]So from here we will get cancel out and sin theta I get as uh 1 by theta. So 1 by theta fine.

[00:09:30]So I get sin theta as this. So if this is theta and this l is given to me and I want this x. So this is theta means this is also theta. Okay. And uh so if I can write then theta = to x by m. So sin theta is this one. So using sin theta I can calculate uh this tan theta. So let us draw the angle. Uh this is theta. So this is 1x theta here. See 1 is the perpendicular and theta is the height.

[00:10:00]So this will be so tan theta = to 1 by 1x 1 square.

[00:10:11]So x = l by e^² - 1.

[00:10:20]Okay. So this is the answer.

[00:10:24]This is what I was asked.

[00:10:28]So this is my answer.

[00:10:34]So that is it for today. Uh I hope you like this topic.

[00:10:39]uh you can also generalize this but actually I I wanted to to know this because if you can remember just this just this so even uh whenever you are asked even if there is multiple medium like this one uh you can do it very easily so subscribe to my channel and for more exciting videos bye-bye