 Alright, so let us move to next try solving this, okay, so this is also a straight forward question if your concepts are proper, so we have ray of light that is passing through four transparent media, their refractive indexes are different. The surfaces are parallel, if the emergent ray CD is parallel to AB then what should be the relation? So if AB is parallel to CD then you know if this is a normal then this angle should be equal to that angle, right? So this angle which is angle in refractive index mu1 should be equal to that angle which is angle in refractive index mu4, right? So Snell's law says that refractive index into sin of the angle in that medium which is this should be equal to mu2 into sin of angle here, mu3 into sin of angle there is equal to mu4 into sin of angle there, which should be equal to this because these two rays are parallel, so mu1 will come out to be equal to mu4, okay, right? In case you have any doubts please type in, I will move to the next one, you will be able to see an object only when the light from that point reaches your eye, okay? So use that, should I solve? Okay, let me solve it now, beaker is filled with a liquid up to a height of 2H, so up to this height let us say it is filled with liquid, okay? Now he can see the lower end of the rod. Now he will be able to see the lower end of the rod only when light from the lower end reaches the eye, okay? So light has to follow this path then only this guy will be able to see it, right? We need to find refractive index of the liquid. Now we know that this is the normal, okay? So if I apply Snell's law over here, let us say this is angle i and then this has to be r, fine? So we have refractive index over here is mu, so mu into sin of i has to be equal to 1 which is refractive index of air into sin of r. Now you will notice here that the value of r is 45 degrees, how? Because this length from here to here, this length is h and even that length is h and this is a 90 degree triangle. This angle is 45, so even that is 45 because complete should be 90 degrees, okay? So angle r is 45 degrees, okay? Now if you look at angle i, for that if you do a small construction, drop a perpendicular like this, okay? You will see that, are you guys able to hear me? Okay, let me share it again. Now so tan i is 1 by 2, so from here you will get sin of i as 1 by root 5, okay? So you will have mu into sin of 5 which is 1 by root 5 equals to 1 into sin of 45 which is 1 by root 2, okay? So you will get mu to be equal to under root of 5 by 2, so that is an option number, 2 is correct over here. How do you know that the light is meeting at the water level at its midpoint? Very good question, okay? Now let us imagine, all of you understood, right? How root 5 by 2 is coming? Now Amog is asking, how do we know that light is meeting the water level at its midpoint, okay? That is what the question is. Now suppose it doesn't meet here, it goes there, then what will happen? It will bend away from the normal, okay? So this angle, alright? This angle will be more than that angle as in what I am trying to say, this is the midpoint let us say, okay? So this is the midpoint which is such a way that the light ray is able to reach the person's eye, okay? If assume that is a condition, then if light ray is going from right hand side of this surface, okay? Then what will happen here is that this angle of incidence, since it is more than this one, so this is I1 and this is I2. Since I2 is more than I1, it will bend further away, okay? So what is given here is that he can see the lower end of the rod when the liquid is being filled up to a height of 2H, okay? So this guy is just able to see it. Now if I talk about a point over here, alright? Let us say I talk about point over there, then this angle of incidence is less, okay? Now in order for it to, you know, let us say the eye is over here, okay? This is the eye which is seeing through this slit, okay? So eye, the ray will has to travel from the eye, the ray has to go in this direction only because you can see that there is this opening, right? There is this kind of opening. It is already fixed, the direction is already fixed, the light has to enter this. It's not just a hole like this. It's a slit like that and the eye is seeing through the slit. So when you say that light is going through and through of that slit, then the red line is already fixed, isn't it? And this red line is passing through the center only because this, when you draw like this, this is angle 45 degrees, okay? This length is equal to that length. Now no matter up to what height you move the water level up to, this line, the perpendicular will always hit the center line. Are you able to understand what I'm trying to say here? Or you can understand like this also, that the light has to travel this path, all of you agree this? Light has to travel 1 to 2 if it has to reach the eye. If light has to travel through 1 to 2, if it has to reach the eye, there is no other choice, okay? One has to be the midpoint because the angle is 45 degrees. So I did not went into all that discussion because then unnecessarily you will start thinking in various other directions. So I wanted to keep it a little simple, but then anyways it is a very good question. Let's move to next question, question number 30. Should I do it? If intensity of the central maxima remains unchanged, which is what? I is equal to 4I0 cos square phi by 2, right? So in that intensity formula if you keep I1 is equal to I2 is equal to I0, you will arrive at this relation, okay? So at maxima intensity should be 4I0, okay? So whether it is central maxima or any other maxima, in double slit experiment all have same intensity, all the maximas, okay? So cos of phi by 2 should be equal to plus minus 1 or phi should be equal to 2n pi, okay? Or you can say that the path difference should be integer times lambda. So all that you can consider here. We need to find the minimum thickness of the glass plate over here. Now if glass plate has a thickness t at the location where central maxima is there, okay? Let's say this is the location where central maxima is there, okay? Here the actual path difference is 0, okay? The only path difference is coming because of the slit, sorry because of the glass plate and because of the glass plate we know that path difference has to be equal to mu minus 1 into t, right? So when this is equal to n lambda then concept interference will happen or the same intensity as that of central maxima was there, that will be there. So t will be equal to n lambda by mu minus 1, right? So minimum thickness t minimum will be lambda divided by mu minus 1, okay? Lambda is what? Oh lambda, in terms of lambda we need to find out. So lambda divided by mu is 1.5, so 1.5 minus 1. So you will get 2 times of lambda as the answer. So option 1 is correct over here, okay? You guys are making a lot of silly errors, okay? It's not good, you have to be careful, these are like sitters, you have to get it right. You can't afford to be wrong in such easy questions, alright? So let's move to the next one, this one, should I do it? See here you will have this angle as 30 degree because of reflection. So like that you will get this angle to be 60 degrees and similarly you can get this angle to be 60. And then this will also become 60, so you will get equilateral triangle. So every time you will get equilateral triangle only, fine? Every time you will get equilateral triangle. So you can see that each equilateral triangle is occupying this much length, okay? Which is how much? Which is equal to the side length of the equilateral triangle. Which how will you find? I have this length, this length I have to be equal to 0.2. So in this right angle triangle, I can get the side of the equilateral triangle which is this to be equal to 0.2 divided by cos of 30, this is the side length, okay? So A will come out to be 0.2 divided by root 3 by 2, so this is 0.4 divided by root 3. Is this thing clear? Okay? Now let's calculate number of equilateral triangles. So in 2 root 3 meters, number of equilateral triangles will be equal to 2 root 3 divided by 0.4 divided by root 3, okay? This will be 6 divided by 0.4, okay? So 5 and this is 3. So you will have 15 equilateral triangles, fine? You will have 15 equilateral triangles and every equilateral triangle, you will see that every edge of it represents one reflection, okay? So if there are 15 equilateral triangles, then you may tend to think that 15 into 3 as in 45 reflections are there. But then you will see that this reflection, this one, this one, all these reflections are counted twice, okay? So if you just count two reflections, as in suppose this equilateral triangle, you count only 1 and 2, then this equilateral triangle, you just count 3 and 4. So per equilateral triangle, if you count just two reflections, then you will be covering all the reflections, okay? So hence, number of reflections will be equal to 15 into 2, which is 30, okay? That is an option number, 2 is correct over here, all right? Now you may see that towards the end, this will be the situation where the last equilateral triangle, this one will be one of the possible reflection, okay, where it will get reflected and go away, all right? So answer is actually 30 or 31, but then 31 is not in the option, so that is why option 2 is correct. Any doubt, guys? Anything? This is more of, I think, geometry question or more of mathematics question than the physics one. In case you have any doubts, please type in.