The inverse square law has significant implications in astrophotography, particularly in terms of exposure and image brightness. When photographing celestial objects, understanding how light intensity decreases with distance is crucial for determining the correct exposure settings. This law helps astrophotographers calculate the amount of light that reaches the camera sensor from a distant star or galaxy. As celestial objects are often at vast distances, the light received is extremely faint, requiring long exposure times to collect enough light for a clear image. The law also explains why photographs of objects at different distances require different exposures; for example, photographing a nearby planet versus a distant galaxy. Additionally, in processing astrophotographs, understanding the inverse square law assists in adjusting brightness and contrast to reveal details of celestial objects, compensating for the decreased intensity of light received from these distant sources.

Yes, the inverse square law also applies to gravitational forces. It states that the gravitational force between two objects is inversely proportional to the square of the distance between their centres. This law is a fundamental principle in Newtonian gravity, expressed by Newton's law of universal gravitation. The formula is F = G(m1*m2)/r², where F is the gravitational force, G is the gravitational constant, m1 and m2 are the masses of the two objects, and r is the distance between the centres of the two objects. This principle explains why gravitational forces weaken significantly with distance, which is crucial in understanding planetary orbits, the behaviour of satellites, and astronomical phenomena. The inverse square nature of gravity is fundamental to the calculations that predict the motion of celestial bodies and the structure of the universe on large scales.

The inverse square law is essential in radiation safety, particularly in protecting against exposure from radioactive sources. Understanding this law helps in determining safe distances from radiation sources and in designing shielding and safety protocols. For instance, in medical applications like X-rays or radiation therapy, knowing how radiation intensity decreases with distance helps in positioning patients and staff to minimise exposure. In nuclear power plants, this law is crucial for calculating safe distances for workers and for designing containment structures. The law underscores the principle that increasing distance from a radiation source is an effective means of reducing exposure, as the intensity of radiation decreases rapidly with distance. However, it's also important to note that the type of radiation (alpha, beta, gamma, or neutron) and the medium through which it travels can affect how rapidly its intensity decreases, necessitating additional protective measures beyond just distance.

Using the inverse square law for light intensity in water requires adjustments because water absorbs and scatters light, which affects the light's propagation. In clear water, light diminishes not only due to the spreading out of light waves but also because of absorption and scattering by water molecules and any suspended particles. The absorption varies with the wavelength of light; for instance, red light is absorbed more quickly than blue light, which is why underwater environments tend to have a blueish tint. To accurately calculate light intensity in water, one must consider the absorption and scattering coefficients of water for the specific light wavelength. These coefficients indicate how much light is absorbed and scattered per unit distance. This complexity means that while the inverse square law provides a starting point, more sophisticated models are required for precise calculations in aquatic environments.

The inverse square law applies to sound intensity in a manner similar to light. Sound intensity decreases with the square of the distance from the source. This is because sound energy, like light, spreads out as it travels from its source. As the distance from the source increases, the same amount of sound energy must fill a larger area, leading to a decrease in sound intensity. For example, if you move twice as far from a sound source, the intensity of the sound becomes one-fourth of its original value. However, this application assumes an ideal condition where the sound propagates in a free field without any reflections or absorption. In real-world scenarios, factors like air absorption, environmental noise, and reflections from surfaces can alter the way sound intensity decreases with distance. Therefore, while the inverse square law provides a basic understanding of how sound intensity diminishes, real-world applications often require additional considerations.