Define plane angle and solid angle

Answer: A plane angle (θ) is formed between two straight lines that meet at a point in the same plane. It is a two-dimensional angle and is measured in radians (rad). A solid angle (Ω) is formed when three or more planes or surfaces meet at a single point in space, like the tip of a cone or the corner of a room.

Complete Answer: 

When light spreads from a single point, it goes in all directions. To understand and measure how it spreads, two types of angles are used: plane angle and solid angle.

How to define plane angle and solid angle?

Plane Angle (θ): A plane angle is formed when two straight lines meet at a point on the same flat surface (plane). For example, the angle between the hands of a clock or the corners of a triangle are plane angles. This kind of angle lies in two dimensions, and its SI unit is radian (rad). One radian is the angle formed at the center of a circle when the arc length is equal to the radius of the circle.

• It is measured in radians (rad).
• One radian is the angle made at the center of a circle when the arc length equals the radius.
• Formula: θ = l/r, where l is arc length and r is the radius.
• A full circle contains 2π radians.

Source: ChatGPT

Solid Angle (Ω): A solid angle, on the other hand, is formed when three or more planes meet at a single point in space, such as the tip of a cone or the corner where three walls of a room meet. It shows how much surface is seen from a particular point, like how big the Moon or the Sun looks from Earth. This is a three-dimensional concept, and the SI unit of solid angle is steradian (sr). One steradian is the solid angle that cuts out a portion of a sphere’s surface equal to the square of the sphere’s radius.

• It is measured in steradians (sr).
• One steradian is the solid angle that cuts out a portion of a sphere’s surface equal to the square of the radius.
• Formula: Ω = A/r²
  where A is the area of the curved surface on the sphere and r is the radius.
• A full sphere contains 4π steradians.

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