IIT JEE , AIEEE Forum - Physics , General

Tushar3078

Solid angle has a unit called strandiene

i didn't understand solid angle is dimensionless

edison

Yes solid angle is dimensionless. infact any angle is dimensionless be it 2D angle subtended between two lines or solid angle subtended at some point by some surface.

The solid angle, ?, that an object subtends at a point is a measure of how big that object appears to an observer at that point. For instance, a small object nearby could subtend the same solid angle as a large object far away. The solid angle is proportional to the surface area, S, of a projection of that object onto a sphere centered at that point, divided by the square of the sphere's radius, R. (Symbolically, ? = k S/R², where k is the proportionality constant.) A solid angle is related to the surface area of a sphere in the same way an ordinary angle is related to the circumference of a circle.

If the proportionality constant is chosen to be 1, the units of solid angle will be the SI steradian (abbreviated sr). Thus the solid angle of a sphere measured at its center is 4? sr, and the solid angle subtended at the center of a cube by one of its sides is one-sixth of that, or 2?/3 sr. Solid angles can also be measured (for k = (180/?)²) in square degrees or (for k = 1/4?) in fractions of the sphere (i.e., fractional area).

edison

In the above explanation read '?' as

which is solid angle.

Furter i have mentioned above that solid angle is calulated as

= k S/R², where k is dimensionless proportionality constant and thus

is dimensionless as it is ratio of two quantities S(cm²) and R² (cm²) having same dimensions.

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