Eli5, what is the definition of a solid angle in physics?
In: Physics
Imagine a sphere around you, a certain distance away. As if you were trapped inside a giant ball.
The solid angle tells you how much of that ball is covered by the thing you are measuring.
So if an object covered half the ball it would have a solid angle of 2π (as 4π is the whole sphere – we’re in radians, because maths). If it only covered a quarter of the sphere it would be just π.
It tells you how much of your theoretical maximum field of view (if you could see forever in all directions) is blocked by something.
Here’s a topical example: the solar eclipse.
It’s a remarkable coincidence that the moon is just about the perfect size to almost completely cover the sun when it passes in front of it.
Of course, the sun and the moon are not the same size. The sun is much larger, but it’s much further away. You could also pick up a coin and hold it up at the correct length to cover up the sun, and it is much smaller still. But all three of these take up approximately the same amount of space in your field of view. That is their “solid angle.”
To put it another way: you can measure a two-dimensional angle by imagining a unit circle and measuring what length of arc the angle covers, which we call “radians.” You can measure a three-dimensional solid angle by imagining a unit sphere and measuring how much surface area the angle covers, which is called “steradians.”
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