Solid Angle Tutorial

Solid angle explained using integral calculus.
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#SolidAngle

[@owen7185]

Dr Remillard you're an excellent teacher, thank you

[@jatingarg1375]

thank u so much sir love you too much.. ☺️☺️
after visiting so many videos and searches on google I got what i wanted to know about solid angle..
Love from india thank u much sir again ...🇮🇳🇮🇳🇮🇳

[@stephenremillard1]

Thank you. That's very encouraging for me to hear.

[@timothynguyen4305]

Thanks for the clear explanation!

[@guitarttimman]

R d(theta) is the arc. It can also be derived using the Jacobean to convert from rectilinear to polar coordinates. Oh!

[@evolforever7448]

thank you so much !

[@guitarttimman]

This is great, but I have a question for you: Is this analogous to using double integration with surface area in rectilinear coordinates and then transposing it to polar coordinates? I am thinking of surface integrals where, when the function is equal to one, you get the surface area of a swept out patch.

[@stephenremillard1]

Along the lines of what you just described, solid angle is what you get when you integrate the area element without a function, or rather with the function equal to unity, and then divide the result by the radius of curvature, Omega=[Int(dA)]/R^2.
As for rectilinear versus polar, since the area that Int(dA) gives is part of a sphere, it is considerably easier to work in spherical polar coordinates when finding solid angle. If you integrate in rectilinear coordinates, then the integral probably isn't being evaluated on the surface of a sphere. (Ah, good, I just saw your 2nd post and see that you made an additional comment about converting to spherical before integrating. Great point!)