Waves in matter Revision Notes

The Nature of Light and Colour

White light is a mixture of all the colours of the visible spectrum, often remembered by the acronym ROYGBIV (Red, Orange, Yellow, Green, Blue, Indigo, Violet). When light interacts with an object, it can be absorbed, transmitted, or reflected. The specific interaction depends on the object's material properties and the wavelength (colour) of the incident light. Our eyes perceive colour based on the light that reaches them after these interactions. Understanding these processes is key to explaining why objects have the colours we see.

How Opaque Objects Get Their Colour

For opaque objects, two main processes determine their observed colour: absorption and reflection. When white light strikes an opaque object, certain wavelengths (colours) of light are absorbed by the object's surface molecules, converting the light energy into thermal energy. The colours that are not absorbed are reflected. The reflected colour is the one we see. For example, a blue cover absorbs all colours except blue, which it reflects. A black object absorbs almost all colours and reflects very little, while a white object reflects almost all colours equally.

How Transparent/Translucent Objects Get Their Colour

For transparent or translucent objects, the process of transmission is also crucial, alongside absorption. These materials allow light to pass through them. Their perceived colour is determined by the specific wavelengths of light that are transmitted through the material. Any colours that are not transmitted are absorbed. For example, a red filter appears red because it allows red light to pass through it, while absorbing most other colours like blue and green. If you shine green light through a red filter, very little light would pass through, making it appear dark or black, as the red filter would absorb the green light.

The Effect of Different Coloured Lights

The perceived colour of an object can change depending on the colour of the light illuminating it. An object can only reflect or transmit colours that are present in the incident light. For instance, a red apple under green light would appear black because the apple only reflects red light, but there is no red light in the green illumination for it to reflect. The green light would be absorbed by the apple. Similarly, a white object will appear the colour of the light shining on it because a white object reflects all colours that strike it.

Amplitude and Energy in Waves

Amplitude is defined as the maximum displacement of a point on a wave from its equilibrium (rest) position. For transverse waves, this is the height from the equilibrium line to a crest or the depth from the equilibrium line to a trough. For longitudinal waves, it relates to the maximum compression or rarefaction from the normal density. A larger amplitude indicates that the wave carries more energy. For instance, a louder sound wave has a larger amplitude, and a brighter light wave also has a larger amplitude.

Wavelength (λ) as Spatial Repetition

Wavelength, symbolised by the Greek letter lambda (λ), is the distance between two consecutive corresponding points on a wave. This is most commonly measured from one crest to the next crest, or from one trough to the next trough. It can also be measured from any point on a wave to the identical point on the next cycle of the wave. Wavelength is a measure of the spatial extent of a single cycle of a wave.

Frequency (f) and Period (T): Time-Based Wave Characteristics

Frequency (f) is the number of complete oscillations or cycles that a wave makes in one second. It is measured in Hertz (Hz), where 1 Hz means one cycle per second. Period (T) is the time taken for one complete wave cycle to pass a fixed point. It is measured in seconds (s). Frequency and period are inversely related through the formula: f = 1/T, or equivalently, T = 1/f. This means that if a wave has a high frequency, it will have a short period, and vice-versa.

Basic Interactions of Electromagnetic Waves (Higher)

Electromagnetic (EM) waves, such as visible light, radio waves, or X-rays, interact with matter in four primary ways: absorption, transmission, reflection, and refraction. These interactions are fundamental to how we perceive the world and how various technologies function. Absorption involves the transfer of energy from the EM wave to the material, often increasing its internal energy. Transmission is the passage of the wave through the material without significant interaction. Reflection is the bouncing back of the wave from a surface. Refraction is the bending of the wave as it passes from one medium to another due to a change in speed. The crucial aspect to remember at Higher tier is that these interactions are not constant for all EM waves; they depend significantly on the properties of the substance and, critically, on the wavelength of the EM wave.

Wavelength Dependence of Absorption (Higher)

The degree to which a substance absorbs an electromagnetic wave is highly dependent on the wave's wavelength. For instance, water molecules strongly absorb microwaves, which is why microwave ovens are effective at heating food containing water. In contrast, water is largely transparent to visible light, allowing aquatic life to receive sunlight. Dark-coloured objects absorb more visible light and infrared radiation than light-coloured objects, leading to a greater temperature increase. Different materials are designed to absorb specific wavelengths; for example, the ozone layer in Earth's atmosphere preferentially absorbs harmful ultraviolet radiation, protecting life on the surface, while being transparent to most visible light.

Wavelength Dependence of Transmission and Reflection (Higher)

Just as absorption varies with wavelength, so do transmission and reflection. Clear glass, for example, effectively transmits visible light but absorbs most ultraviolet (UV) radiation and infrared (IR). This is why you can see through a window, but you can still get sunburnt through certain types of glass over time, or feel less heat from the Sun through glass. Different materials are designed to either transmit or reflect specific wavelengths. Materials used in radio telescopes are designed to reflect radio waves, while allowing other wavelengths to pass through. Metallic surfaces reflect a broad range of EM waves, including radio waves and visible light. The choice of material for specific applications, such as satellite dishes or stealth aircraft, depends on carefully selected wavelength-dependent reflection and transmission properties.

Wavelength Dependence of Refraction (Higher)

Refraction, the bending of a wave as it passes from one medium to another, also depends on wavelength. This phenomenon is known as dispersion. When white light, which is composed of a spectrum of colours (different wavelengths), passes through a dispersive medium like a prism or a water droplet, it splits into its constituent colours. This happens because the refractive index of the material is slightly different for each wavelength. Shorter wavelengths (like violet light) are typically refracted more than longer wavelengths (like red light) in many common media. This explains why rainbows form, as water droplets act as tiny prisms, separating sunlight into its colour spectrum. Understanding dispersion is crucial in optics, particularly in the design of lenses to correct chromatic aberration.

The Electromagnetic Spectrum

The electromagnetic (EM) spectrum is a continuous range of all types of electromagnetic waves. These waves are arranged in order of increasing frequency and decreasing wavelength. From longest wavelength to shortest, the spectrum includes radio waves, microwaves, infrared radiation, visible light, ultraviolet radiation, X-rays, and gamma rays. All electromagnetic waves travel at the same speed in a vacuum, which is the speed of light, approximately 300,000,000 metres per second (3 x 10^8 m/s). They differ in their energy, with higher frequency waves carrying more energy. Understanding the EM spectrum is crucial because each part has distinct properties and uses, from communication with radio waves to medical imaging with X-rays.

Visible Light: Our Limited View

Our eyes can only detect a very small portion of the vast electromagnetic spectrum. This narrow band is known as visible light. Visible light is responsible for our sense of sight and is composed of different colours, which we perceive as red, orange, yellow, green, blue, indigo, and violet (ROYGBIV). Red light has the longest wavelength and lowest frequency within the visible spectrum, while violet light has the shortest wavelength and highest frequency. Waves outside this visible range, such as infrared (longer wavelength than red) and ultraviolet (shorter wavelength than violet), are invisible to human eyes. This limitation means we cannot directly see phenomena that rely on these other types of electromagnetic radiation.

Invisibility of Other EM Waves

Waves like radio waves, microwaves, infrared, ultraviolet, X-rays, and gamma rays are all forms of electromagnetic radiation, just like visible light. However, human eyes are not equipped to detect them. For example, while bats use ultrasound for navigation, and some insects can see ultraviolet light, our sensory organs are tuned primarily to the visible spectrum. Infrared radiation is often felt as heat but not seen. Ultraviolet light from the sun can cause sunburn and skin damage, yet it remains unseen. This fundamental biological constraint means we rely on specialised instruments and experiments to study and utilise these 'invisible' parts of the electromagnetic spectrum, such as night vision cameras for infrared or telescopes for radio waves.