Your question is why I squared (AD/BC)=(1/R). First of all as I explained in the video, the solid angle is similar to a surface and we also have a surface dS which is receiving the radiation from point P. So, our aim is to get a ratio of these two surface areas and to do that we have to obtain the expression of area of a circle with radius 1 unit and R unit which is Pi*(1)^2 and Pi*(R)^2. The surfaces are circle in the present case because we are considering these surface on the sphere surface. Its like if you switch ON a torch light on the surface of a football, then you will see it forms a circle. So, even if you directly write Area of circle with radius 1 unit divided by Area of circle with radius R units, we get dOmega/dS= Pi*1^2/Pi*R^2 dOmega/dS = 1/R^2 Now, to establish the ratio of these areas, I started with the similarity of two triangles PAD and PBC. So, (AD/BC)= (1/R). To keep the ratio constant, we squared both sides and then multiplied Pi on LHS to show that LHS is actually a ratio of areas of surface representing solid angle (domega) and receiving surface area dS. Finally, we get the expression domega/dS = 1/R^2. I hope it gets clear now. If you have any doubts you can write it.
@@Spirit365 This is because the maximum possible solid angle of a sphere is 4pi. Also you might be aware that the area of a sphere is 4*Pi*r^2. So, if we calculate the domega over a complete sphere, it will be equal to sphere surface area and will only come to be 4Pi only if sphere radius is 1 unit. That is why I took the radius 1 unit for the sphere which had the solid angle as domega. Also, the unit steradian is defined as the solid angle subtended at the centre of a unit sphere by a unit area on its surface.
@@salma-kc6jt No. Small r symbol just represents radius. It is not equal to capital R. For unit sphere, radius is 1 unit. So, r=1. And for bigger sphere, radius is R. So, it is written r=R. I hope it gets clear now.
@@ENGINEERINGSTREAMLINED i've been thought everything i currently know in french and even if i understand english, in scientific subjects like these i get confused, so with "radius is 1 unit" u mean a trigonometric circle? thats the circle i know we use in trigonometry which has the radius of 1, if it im right than there is no problem. but i have another question, u multiplied by pi, i assumed it was to create a surface right? but shouldnt u multiply by 2pi? like in orther to get a full surface of a circle because dS and dOMEGA are circles.
@@salma-kc6jt Yes, dS and domega are circle. I multiplied Pi with AD^2 and BC^2 because area of a circle is given by Pi × r^2. If you use 2 × Pi × r then you will get the circumference of the circle.
@@salma-kc6jt In the video, triangle PAD is similar to triangle PBC. Now, The ratio of any pair of corresponding sides of similar triangles is the same. So, we can write the ratio of sides AD/BC equal to some constant say k. Now, ratio of sides PA/PB is also equal to the constant k. Thus, AD/BC = PA/PB. PA is equal to the radius of unit sphere, so PA =1. And PB is the radius of the bigger sphere, so PB =R. Finally, we substitute the values of PA/PB = 1/R.
Thanks that was very easy to understand
I am glad it was helpful for you.
👏👏👏👏👏👏👏👏👏👏👏Take a bow sir 🙂
Thanks for the appreciation
amazing brother please keep it up🤗
@@MBKaka.mhdbilalkhan Thanks for the appreciation
but the question is why you squared it ..?
Your question is why I squared (AD/BC)=(1/R). First of all as I explained in the video, the solid angle is similar to a surface and we also have a surface dS which is receiving the radiation from point P. So, our aim is to get a ratio of these two surface areas and to do that we have to obtain the expression of area of a circle with radius 1 unit and R unit which is Pi*(1)^2 and Pi*(R)^2. The surfaces are circle in the present case because we are considering these surface on the sphere surface. Its like if you switch ON a torch light on the surface of a football, then you will see it forms a circle. So, even if you directly write Area of circle with radius 1 unit divided by Area of circle with radius R units, we get
dOmega/dS= Pi*1^2/Pi*R^2
dOmega/dS = 1/R^2
Now, to establish the ratio of these areas, I started with the similarity of two triangles PAD and PBC. So, (AD/BC)= (1/R). To keep the ratio constant, we squared both sides and then multiplied Pi on LHS to show that LHS is actually a ratio of areas of surface representing solid angle (domega) and receiving surface area dS. Finally, we get the expression domega/dS = 1/R^2.
I hope it gets clear now. If you have any doubts you can write it.
@@ENGINEERINGSTREAMLINED why have you taken only 1 unit of radius ? why not 2 units ?
@@Spirit365 This is because the maximum possible solid angle of a sphere is 4pi. Also you might be aware that the area of a sphere is 4*Pi*r^2. So, if we calculate the domega over a complete sphere, it will be equal to sphere surface area and will only come to be 4Pi only if sphere radius is 1 unit. That is why I took the radius 1 unit for the sphere which had the solid angle as domega. Also, the unit steradian is defined as the solid angle subtended at the centre of a unit sphere by a unit area on its surface.
@@ENGINEERINGSTREAMLINED so where Omega max is something like a balloon filled with gas is covered with another balloon...?
@@Spirit365 Yes, you can say that.
Really good videos
Thanks for your appreciation.
how come R=r even if R>r?
@@salma-kc6jt No. Small r symbol just represents radius. It is not equal to capital R. For unit sphere, radius is 1 unit. So, r=1. And for bigger sphere, radius is R. So, it is written r=R. I hope it gets clear now.
@@ENGINEERINGSTREAMLINED i've been thought everything i currently know in french and even if i understand english, in scientific subjects like these i get confused, so with "radius is 1 unit" u mean a trigonometric circle? thats the circle i know we use in trigonometry which has the radius of 1, if it im right than there is no problem. but i have another question, u multiplied by pi, i assumed it was to create a surface right? but shouldnt u multiply by 2pi? like in orther to get a full surface of a circle because dS and dOMEGA are circles.
@@salma-kc6jt Yes, dS and domega are circle. I multiplied Pi with AD^2 and BC^2 because area of a circle is given by Pi × r^2. If you use 2 × Pi × r then you will get the circumference of the circle.
@@ENGINEERINGSTREAMLINED ohh true i forgot about that, but one more thing how come we went from PA\PB to 1\R
@@salma-kc6jt In the video, triangle PAD is similar to triangle PBC. Now, The ratio of any pair of corresponding sides of similar triangles is the same. So, we can write the ratio of sides AD/BC equal to some constant say k. Now, ratio of sides PA/PB is also equal to the constant k. Thus, AD/BC = PA/PB. PA is equal to the radius of unit sphere, so PA =1. And PB is the radius of the bigger sphere, so PB =R. Finally, we substitute the values of PA/PB = 1/R.
Amazing video, keep posting more ones like this
Thanks for the appreciation
красавчик
@@qqq-z9m Which language is this? I don't understand your comment.
@@ENGINEERINGSTREAMLINED this language is quite popular...
@@luftmaxsa ok