Question

Define the plane angle and solid angle.

Answer 1

Hint: The light is spread in all directions from the origin, and it is not restricted to a particular plane; now we define the plane angle and solid angle. When two straight lines lie on the same plane, they will be the angle between the lines at a joining point. This angle is a plane angle. Moreover, the Plane angle is expressed in radians. The solid angle has defined an angle that is made at a point in place by an area.

Complete answer:
A plane angle is a measurement around a point in $2D$ object, whereas solid angles are for $3D$ objects. The angle of a triangle is a plane angle, whereas the angle made by the corner of a room is solid. The plane angle and solid angle iis shown below:

A plane angle is made between the crossing of two straight lines or the junction of two planes. The SI unit of plane angle is radian, and it is expressed as 'rad,' where 'radian' is the angle made at the centre of a circle by an arc whose length is equivalent to the radius of the circle because it has two dimensions. Radians are used for measuring angles.
Solid angle is an angle made by three or more planes joining at a common point and identified as 'angle formed at the cone's vertex. The solid angle's SI unit is steradian, and it is expressed as 'sr' where 'steradian' is the solid angle at the centre of a sphere made by a portion whose surface area is equivalent to the radius square of the sphere because it has three dimensions. Solid angle is utilized to estimate the amount of the field view from some special point that an object covers.

Note:
If the surface includes the entire sphere, then the number of steradians is 4π. If we recognize the solid angle $\mathrm{\Omega }$ in steradians, we can estimate the corresponding area of the sphere's surface from the expression
$S=R^2\mathrm{\Omega }$
where R is the sphere's radius.