Magnetism and magnetic fields Study Guide

Electromagnetic waves, such as light, travel at a constant speed in a vacuum, approximately 3.0 x 10^8 meters per second. However, when these waves pass through different substances, their speed changes. This change in speed is the fundamental cause of refraction, which is the bending of light as it passes from one medium to another. Different substances have different optical densities; a higher optical density means that the electromagnetic waves interact more with the particles of the substance, causing them to slow down. The extent to which an electromagnetic wave slows down in a material is quantified by the material's refractive index. A higher refractive index indicates a greater reduction in the wave's velocity within that medium. When an electromagnetic wave enters a new medium at an angle (other than perpendicular), one side of the wavefront enters the new medium and changes speed before the other side. This differential in speed across the wavefront causes the wave to change direction, or refract. For example, when light passes from air into water, it slows down and bends towards the normal. Conversely, when it passes from water into air, it speeds up and bends away from the normal. This phenomenon explains why objects underwater appear to be in a different position than they actually are, and why lenses can focus or diverge light. The specific amount of bending depends on the change in velocity and the angle at which the wave strikes the interface between the two substances.

Radioactive decay is a entirely random process, meaning it is impossible to predict when an individual unstable nucleus will decay. However, for a very large number of identical unstable nuclei, the average rate of decay can be measured and is consistent. This leads to the concept of half-life. The half-life of a radioactive isotope is defined as the time taken for half of the unstable nuclei in a sample to decay, or alternatively, the time taken for the activity of a radioactive source to halve. Because decay is random, we cannot say exactly when a specific atom will decay, but we can predict that after one half-life, approximately half of a large sample will have decayed. After two half-lives, half of the remaining half will have decayed, leaving one-quarter of the original unstable nuclei. This exponential decrease means the activity of a source also halves over each successive half-life period. Different radioactive isotopes have vastly different half-lives, ranging from fractions of a second to billions of years, depending on the stability of their nuclei. This characteristic property makes half-life a crucial concept for understanding and applying radioactive materials in various fields, such as carbon dating, medical imaging, and nuclear power.