A-Level Physics: Waves and Optics

The principles of waves and optics are not just abstract concepts confined to a textbook; they are the foundational physics behind the technologies that define our modern world. From the fibre optic cables delivering high-speed internet to the LCD screen you're reading this on, a clear understanding of polarisation, total internal reflection, and photon interactions is essential.

Polarisation: Filtering Wave Oscillations

Polarisation is a property unique to transverse waves, where the oscillations are perpendicular to the direction of energy transfer. Light is a transverse electromagnetic wave, and its electric field vector can vibrate in any direction perpendicular to its travel. Unpolarised light, like that from the sun or a light bulb, has its electric field vibrating in all these possible directions simultaneously.

A Polaroid filter works by only allowing oscillations in one specific plane to pass through. You can imagine it as a picket fence: only the waves whose vibration aligns with the gaps can get through. When unpolarised light passes through a polariser, it emerges plane-polarised. If this polarised light then encounters a second polariser (an analyser) rotated at 90° to the first, no light is transmitted—this is known as crossed polarisers. The intensity of transmitted light follows Malus's Law: $I=I_0{\cos }^2\theta$, where $I_0$ is the initial intensity and $\theta$ is the angle between the polarisation direction of the light and the axis of the analyser.

A key application is in LCD screens. Each pixel contains a liquid crystal sandwiched between two polarising filters. By applying an electric voltage, the liquid crystal twists the plane of polarisation of the light passing through it. This controls how much light from the backlight is blocked by the second polariser, creating the dark and light areas that form the image on your screen.

Optical Fibres and Signal Degradation

Optical fibres are thin strands of glass or plastic that guide light over long distances using the principle of total internal reflection (TIR). For TIR to occur, two conditions must be met: light must travel from a denser medium to a less dense medium (e.g., glass to air), and the angle of incidence must be greater than the critical angle. The critical angle, $c$, is found using Snell's Law: $n_1\sin c=n_2\sin 90^{\circ }$, which simplifies to $\sin c=n_2/n_1$, where $n_1$ is the refractive index of the core and $n_2$ is the refractive index of the cladding ($n_1>n_2$).

While TIR is highly efficient, real-world fibre optic communication faces the challenge of pulse broadening, which leads to signal degradation. This occurs primarily through two types of dispersion:

1. Modal Dispersion: In a multi-mode fibre (with a relatively wide core), light can travel along many different paths (modes). Rays taking a longer, zig-zag path arrive at the end of the fibre later than those taking a more direct path. This difference in travel time spreads out a sharp input pulse, limiting the rate at which pulses can be sent without overlapping.
2. Material Dispersion: Even in a single-mode fibre, different wavelengths (colours) of light travel at slightly different speeds within the glass material. A practical light source, like an LED or laser, emits a narrow but not single wavelength. The slight range of wavelengths will thus arrive at different times, broadening the pulse. This is a key reason why monochromatic lasers are preferred for long-distance, high-data-rate communication.

Engineers minimise these effects by using single-mode fibres (to eliminate modal dispersion) and carefully chosen light sources and wavelengths to reduce material dispersion, ensuring clear, high-bandwidth signals.

The Electromagnetic Spectrum and Photon Interactions

Light is part of the continuous electromagnetic spectrum, which ranges from radio waves to gamma rays. All electromagnetic waves travel at the same speed in a vacuum ($c=3.00\times 10^8,{\text{m s}}^{-1}$) and are differentiated by their wavelength, $\lambda$, and frequency, $f$, related by $c=f\lambda$. The quantum of electromagnetic energy is the photon. The energy $E$ of a single photon is directly proportional to its frequency: $E=hf$, where $h$ is Planck's constant ($6.63\times 10^{-34},\text{J s}$). You can also express this as $E=hc/\lambda$.

This quantised energy leads to the phenomena of absorption and emission spectra. When a photon collides with an atom, it can be absorbed only if its energy exactly matches the difference between two of the atom's discrete electron energy levels. This removes specific wavelengths from a continuous spectrum, creating dark lines known as an absorption spectrum. Conversely, when an excited electron falls to a lower energy level, it emits a photon of that specific energy. A collection of these emitted photons produces bright lines on a dark background—an emission spectrum.

For example, the unique spectral lines of sodium or hydrogen act as a "fingerprint" for those elements. This principle allows astronomers to determine the composition of distant stars and is the basis for techniques like flame tests in chemistry.

Common Pitfalls

1. Confusing Polarisation with Other Wave Properties: Remember that only transverse waves can be polarised. Longitudinal waves, like sound, cannot. Do not confuse polarisation (restriction of oscillation direction) with colour/frequency (which determines photon energy) or intensity (which is related to the amplitude squared and number of photons).
2. Misapplying the Critical Angle Formula: A common error is to invert the ratio in $\sin c=n_2/n_1$. Always remember that $n_1$ is the refractive index of the material you are in (the denser medium, e.g., the fibre core), and $n_2$ is the refractive index of the material you are going into (the less dense cladding).
3. Mixing Up Photon Energy and Intensity: Increasing the intensity of light means increasing the number of photons per second, not the energy of each individual photon. The energy per photon is determined solely by its frequency ($E=hf$). A dim blue light has higher-energy photons than a very bright red light.
4. Confusing Absorption and Emission Spectra: It's easy to get the visual patterns backwards. An absorption spectrum has dark lines on a bright continuous background (like the Fraunhofer lines from the sun). An emission spectrum has bright coloured lines on a dark background (like a neon sign).

Summary

• Polarisation demonstrates the transverse nature of light. Polaroid filters transmit only oscillations in one plane, a principle utilised in technologies like LCD screens and sunglasses to reduce glare.
• Optical fibres use total internal reflection to guide light. Signal quality is degraded by pulse broadening due to modal dispersion (different path lengths) and material dispersion (different speeds for different wavelengths).
• Light is part of the electromagnetic spectrum. The energy of a photon is quantised and given by $E=hf$. Atoms absorb and emit photons of specific energies, producing unique absorption and emission spectra that are vital tools for identifying elements.