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A wave is a disturbance that travels through a material, transferring energy without causing the medium itself to move to a new location. Instead, the particles of the medium vibrate in place. Waves can occur as a single event, known as a wave pulse, or as a series of repeated, identical disturbances, referred to as a continuous wave.

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Waves can be transverse or longitudinal. In transverse waves, particles move perpendicular to the wave’s direction, as seen in water or string waves. In longitudinal waves, particles move parallel to the wave’s direction, like in sound or some earthquake waves.

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Mechanical waves require three things to exist: a source to start the disturbance, a medium for the wave to travel through, and a mechanism to transmit the disturbance between parts of the medium. This transmission can occur through physical connection, collisions, or coordinated movement within the medium.

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A continuous wave has four key characteristics. Its amplitude and frequency are determined by the source, amplitude relates to energy, and frequency, which is measured in Hertz, shows how often vibrations occur per second. Speed depends only on the medium, not the source. Wavelength depends on both frequency and speed, following the equation: wavelength = speed ÷ frequency.

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While some waves, like those on a string, move in one dimension, others spread out in two or three dimensions. Surface water waves move in 2D, and sound waves travel in 3D. These waves can be represented using wavefront diagrams, which show the position of wave peaks and the direction of wave movement.

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Reflection occurs when waves hit a barrier and bounce back. This barrier can be a solid object or a change in the medium. In one-dimensional waves, the wave simply reverses direction. In 2D or 3D waves, the reflected wave leaves the boundary at the same angle it arrived, following the law of reflection.

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Refraction happens when a wave passes into a different part of a medium where its speed changes. This causes a change in wavelength, but not frequency. If the wave crosses the boundary at an angle, it also changes direction, bending due to the speed difference across the wavefront.

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Interference happens when two or more waves overlap in within the same space. Their amplitudes will combine if both are at a maximum and they add together, but if one is at a maximum and the other at a minimum, they can cancel each other out, resulting in no movement at that spot.

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Standing waves form from the interference of incoming and reflected waves, creating points called nodes that stay still. On a string fixed at both ends, standing waves only occur at certain frequencies that fit whole numbers of half-wavelengths. Instruments use this principle to produce specific musical notes by adjusting string tension or air column length.

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Light ray diagrams use straight arrows to represent how light travels from a source. Light spreads out in all directions unless blocked, so multiple rays are drawn to show this. To see a light source, light must enter the observer’s eye. These diagrams help visualize how light moves and interacts with objects.

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When light from a point source passes through a pinhole, it continues in a straight line and creates a single dot on a screen directly in line with the ray. If multiple point sources are used, each creates its own dot. For continuous sources, like a light bulb, each point acts as a point source, and the resulting image on the screen appears upside down. The size of the image can be predicted by tracing rays from the top and bottom of the source.

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Shadows are formed when light from a point source is blocked by an object, preventing it from reaching a screen behind the object. The shadow has the same shape as the blocker. Its position and size can be predicted by drawing boundary rays from the top and bottom of the light source that just pass the edges of the blocker.

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When light reflects off a shiny surface, like a mirror, it follows the law of reflection: the angle of incidence equals the angle of reflection. These angles are measured relative to a normal line, which is drawn perpendicular to the surface at the point where the light strikes. A minor concept related to this is the use of sightlines, by tracing sightlines backward from the eye, we can locate the apparent position of an image in a mirror.

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When light reflects off a non-shiny surface, like paper, it scatters in many directions. Unlike shiny surfaces that reflect light in specific directions, rough surfaces reflect rays diffusely. This scattered reflection allows light to enter the eyes of observers from various angles, making the surface visible from different viewpoints.

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Refraction occurs when light passes from one transparent material into another, causing it to change direction. The angle of the light ray becomes smaller in denser materials and larger in less dense materials. If light travels from a dense to a less dense material and the angle is large enough (about 50° or more), total internal reflection can occur, where all the light is reflected back inside. This principle is what makes technologies like fiber optics possible.

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The visible color spectrum includes a range of colors, commonly identified as Red, Orange, Yellow, Green, Blue, and Violet. For understanding human vision, this spectrum is simplified into three broad color bands: Red (R), Green (G), and Blue (B). These correspond to the three types of light-sensitive cells in the human eye, each tuned to one of these bands. The colors we perceive depend on how these three bands are combined in the light entering our eyes.

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Color addition refers to how we perceive different colors when multiple light bands enter the eye at the same time. Light mixes differently than paint, combining all colors of light results in white.

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Color subtraction explains why objects appear a certain color. Objects absorb some parts of the light spectrum and reflect the rest, what’s reflected is what we see. For example, a yellow object absorbs blue light and reflects red and green, which combine to appear yellow. This principle also applies to color filters, inks, and dyes, which block certain wavelengths and allow others to pass or reflect.