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I can see geometrically that $dw = sin(\theta)(d\theta)(\phi)$, and I know that $dA = r^{2}dw$, but I don't fully get why this is correct / what $dA$ is measuring. My instinct says that $dA$ should relate a solid angle to an area, i.e. $dA = 4\pi r^{2} dw$, but that constant factor isn't typically used. I'm probably just missing something obvious.


I am a little confused about concept of dA. I can see how dA is derived but intuitively, if light is isotropic, shouldn't dA is the same in each direction either? Got trouble here...


Might be helpful for you all: