The solid angle between two intersecting planes

Question

Is there a solid angle between two intersecting planes? I assumed that there is one and found that this will be equal to 2A where A is the angle between the planes.However my friends disagree .They say that a solid angle exist in case of cones and other similar figures.Our textbook does not give much information on solid angles. Thus who is correct ; me or my friends?

Answer 1

Interesting question!

Solid angle, as it's normally defined, is from a point. Two planes cannot intersect at only one point. They can only be coincident, parallel, or intersect at some (infinite) line.

What you can talk about, though, is a hybrid solid-angle-like angular measure that extends over all space from that line of intersection. There would be $2\pi$ of these things, and it would look like a wedge of a circular disk along the line of symmetry. The angular measure would cover all of the space away from the line ("r", if you will) and all of the space along the line ("z", if you will).

So if the angle between the two planes is $A$, then the space in between the planes where $A$ is included would cover the fraction $A/2\pi$ of all space.

What you have, I think, is a solid angular measure, but it definitely is different than the solid angle your friends are likely talking about.