Waves in matter Study Guide

Ray diagrams are indispensable tools in optics for visualising how light behaves when it interacts with different surfaces and media. When light encounters a smooth surface, like a mirror, it undergoes reflection. The law of reflection states that the angle of incidence (the angle between the incoming ray and the normal to the surface) is equal to the angle of reflection (the angle between the reflected ray and the normal). Both the incident ray, the reflected ray, and the normal lie in the same plane. Ray diagrams for reflection typically show light rays bouncing off a surface, with arrows indicating the direction of light travel.

Refraction occurs when light passes from one transparent medium to another, for example, from air to water or from air to a glass lens. This change in medium causes the light to change speed and direction, resulting in the bending of the light ray. The amount of bending depends on the refractive indices of the two media and the angle at which the light strikes the interface. When drawing ray diagrams for refraction, the light ray changes direction at the boundary between the two media. If light moves from a less dense medium (like air) to a more dense medium (like glass), it bends towards the normal. If it moves from a more dense medium to a less dense medium, it bends away from the normal.

Lenses are optical devices that manipulate light through refraction. There are two primary types of lenses: convex and concave. A convex lens, also known as a converging lens, is thicker in the middle and thinner at the edges. When parallel rays of light pass through a convex lens, they converge to a single point called the principal focus (or focal point). This property is used in magnifiers and cameras. A concave lens, also known as a diverging lens, is thinner in the middle and thicker at the edges. When parallel rays of light pass through a concave lens, they diverge as if originating from a single point on the same side of the lens as the incident light, known as the principal focus. Ray diagrams for lenses involve drawing rays incident on the lens and then showing their path after refracting through both surfaces. For convex lenses, an object placed beyond the focal point forms a real, inverted image. For concave lenses, the image formed is always virtual, upright, and diminished, regardless of the object's position.

Electromagnetic (EM) waves, such as light, consist of oscillating electric and magnetic fields. When an EM wave travels from one transparent medium to another, its speed changes. This change in speed is the fundamental cause of refraction, the bending of the wave. The optical density of a material determines how much it slows down EM waves; a higher optical density means a slower wave speed. The refractive index (n) of a medium is a measure of its optical density, defined as the ratio of the speed of light in a vacuum (c) to the speed of light in the medium (v), i.e., n = c/v. Since c is constant, a higher refractive index implies a lower speed of light in that medium.

When an EM wave enters a new medium at an angle other than 90 degrees to the surface, the part of the wavefront that enters first changes speed while the other part is still in the original medium. This differential change in speed causes the wavefront to pivot or bend. For example, if light goes from a less optically dense medium (higher speed) to a more optically dense medium (lower speed), the wave bends towards the normal. Conversely, if it goes from a more optically dense medium to a less optically dense medium, it bends away from the normal. This phenomenon accounts for various effects, including the formation of rainbows, the operation of lenses in spectacles and cameras, and the ability of optical fibres to transmit data over long distances through total internal reflection.