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.

nonexist

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...

kye

Might be helpful for you all: https://math.stackexchange.com/questions/188490/why-is-the-differential-solid-angle-have-a-sin-theta-term-in-integration-in-s

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: https://math.stackexchange.com/questions/188490/why-is-the-differential-solid-angle-have-a-sin-theta-term-in-integration-in-s