Intensity of radiation varies with the:

Explanation:

Intensity of Radiation and the Inverse Square Law

Definition: The intensity of radiation refers to the amount of energy radiated per unit area per unit time. It is a fundamental concept in physics, particularly in the study of electromagnetic waves and thermal radiation.

Correct Option: Inverse Square Law

The correct answer to the statement "Intensity of radiation varies with the:" is option 1, which states that the intensity of radiation varies with the inverse square of the distance. This principle is known as the inverse square law.

Inverse Square Law:

The inverse square law is a physical principle that describes how the intensity of a physical quantity (such as radiation, light, sound, etc.) decreases as the distance from the source increases. According to this law, the intensity of radiation is inversely proportional to the square of the distance from the source. Mathematically, it can be expressed as:

I ∝ 1/d²

Where:

• I = Intensity of radiation
• d = Distance from the radiation source

This means that if the distance from the source is doubled, the intensity of radiation becomes one-fourth. Similarly, if the distance is tripled, the intensity becomes one-ninth, and so on.

Derivation and Explanation:

The inverse square law can be derived from the geometry of how radiation spreads out from a point source. Imagine a point source emitting radiation uniformly in all directions. The radiation travels outward in spherical waves. As the distance from the source increases, the surface area of the sphere over which the radiation is spread increases.

The surface area of a sphere is given by the formula:
A = 4πd²

Where:

• A = Surface area of the sphere
• d = Radius of the sphere (distance from the source)

As the radiation travels outward, its energy is distributed over the surface area of the sphere. Since the surface area increases with the square of the distance, the intensity of radiation (energy per unit area) decreases with the square of the distance. Therefore, the intensity of radiation at distance d is inversely proportional to d².

Applications of the Inverse Square Law:

• Astronomy: The inverse square law is crucial in astronomy for understanding the brightness of stars and other celestial objects. The apparent brightness of a star decreases with the square of the distance from the observer.
• Radiation Safety: In radiation safety, the inverse square law is used to determine safe distances from radiation sources to minimize exposure. By increasing the distance from a radiation source, the intensity of exposure decreases significantly.
• Acoustics: In acoustics, the inverse square law explains how the intensity of sound decreases as the distance from the sound source increases. This principle is important in designing audio systems and soundproofing environments.
• Lighting: In lighting design, the inverse square law helps in calculating the illumination levels from light sources at different distances. It is essential for setting up proper lighting in various environments.