In this article, we’ll look at the Nature of Light module and the new physics that studying light led to at the start of the 20th century.
Are all the formulas making you ‘Light’-headed?
In Year 11, you learned that light is an electromagnetic (EM) wave, composed of oscillating electric and magnetic fields. Understanding light as a wave allows us to explain many of its behaviours, including reflection, refraction, diffraction and interference.
However, there are some things light does that cannot be explained in these terms.
Experiments at the turn of the 20th century produced results that contradicted the recently established EM wave model. As scientists developed new theories about the nature of light, it led to unexpected major changes in our understanding of the universe.
The first field to emerge was quantum physics. The basis of this branch of science is that there are quantities which can only take certain (‘quantised’) values, as opposed to classical physics where every quantity has values along a continuum.
Another major development was Special Relativity. When Einstein formulated the idea that the speed of light would be the same for all observers, regardless of their own motion, he realised that the consequences included observers disagreeing on measurements of space and time!
Therefore, studying the nature of light is not just interesting for its own sake – it is a window into modern physics.
The Nature of Light Module can be divided into three main topics:
Early scientific models of light included both wave and particle explanations for its behaviour.
Initially, these scientists both explained reflection and refraction given the limited knowledge of the time. However, more experiments were conducted and the diffraction, interference and polarisation of light were investigated, as was the speed at which it travelled.
Diffraction is the spreading out of wavefronts that occurs when a wave passes through a gap or around an obstacle whose size is comparable to the wavelength. Diffraction of light was thus only explained by the wave model.
If diffraction of these incoming parallel wavefronts occurs at multiple slits, the outgoing wavefronts will superimpose and interfere with each other, providing further evidence for the wave nature of light. The interference will produce bright regions (due to increased amplitude resulting from constructive interference) and darker regions (decreased amplitude due to destructive interference).
The equation which predicts where the bright regions will form is:
\(d \sin θ=mλ\)The fact that light can be polarised tells us that it is a transverse wave. We define its polarisation by the orientation of the electric field oscillations. Malus’ Law allows us to predict what fraction of polarised light intensity will pass through a polariser at some arbitrary angle.
\(I=I_{\text{max}} \cos^2 θ\)Note that Malus’ Law only works if the incoming light is polarised. If unpolarised light (a beam of light consisting of large numbers of randomly polarised beams) is incident on a polariser, the throughput is always 50% and the emerging beam’s polarisation is aligned with the polariser.
Various scientists also measured the speed of light using a variety of techniques, including astronomical measurements and measurements involving timing light travelling to and from a mirror. Apart from determining that the speed of light was \(3 \times 10^8 \text{ ms}^{-1}\), they showed that light slowed down in a denser medium (like water) compared to a less dense medium (like air). This was an important differentiator between Newton’s and Huygens’ original models – this observation agreed with Huygens’ predictions but contradicted Newton’s.
All this evidence led to the conclusion that light behaved as a transverse wave. However, it was not until the 19th century that the type of wave was identified.
In Module 6, you learned that electric and magnetic fields are related through, for example, induction. In the late 19th century James Maxwell unified electricity and magnetism into electromagnetism and showed that they are two aspects of the one phenomenon. A consequence of Maxwell’s theory was the prediction that a changing electric field could create a changing magnetic field, and vice versa which led to the concept of a self-sustaining electromagnetic wave.
Maxwell realised that EM waves would travel at \(3 \times 10^8 \text{ ms}^{-1}\) (sound familiar?) and had other properties as were known for light, thus he proposed that light is an electromagnetic wave. Shortly after this Heinrich Hertz produce radio-frequency EM waves and showed their properties were the same as light, differing only in their frequency and wavelength. This confirmed that light is indeed an electromagnetic wave. Except that…
The first piece of evidence that our understanding of light was incomplete came from analysing black body spectra. A black body is a theoretical object (but one which is closely approximated by some real systems) which absorbs any frequency of radiation that falls on it and re-radiates it with a spectrum that depends only on its temperature.
Scientists found that the spectra were continuous with a peak intensity at a wavelength which depended on temperature. The hotter the object, the shorter the wavelength, as expressed by Wien’s Law:
\(λ_{max}=\frac{b}{T}\)
Black body spectra also showed a cut-off at short wavelengths/high frequencies, beyond which no radiation was emitted. The cut-off would vary with temperature but was always present.
They tried to explain the shape of the spectra using what they knew about radiation from Maxwell’s theory. However, this led to a result that not only contradicted experimental results but was physically impossible: the black body was predicted to emit light at an infinite number of frequencies, resulting in an infinite amount of total energy.
Max Planck resolved this by proposing the emission of light from a black body occurred in fixed amounts of energy – in discrete packets or ‘quanta’. He stated that the amount of energy emitted each time depended on the frequency of the light by:
\(E=hf\)
This allowed Planck to explain the features of the spectrum. A black body would not emit frequencies above a certain cut-off, as this would require large amounts of energy to be emitted at once, and no individual particle within the object would have enough energy to do this. At different temperatures, certain energy transitions would be more likely than others, resulting in that frequency being the brightest in the spectrum.
Planck did not make any claims about the nature of the light being emitted, but he was the first to suggest that light energy was quantised rather than continuous – it could only be emitted in multiples of some small value.
More support for this idea came in analysing experiments on the photoelectric effect. Scientists discovered that it was possible for electrons to be emitted from a metal surface when light was shone on it, but only if the light was above a certain frequency. Beyond this threshold frequency, increasing the frequency of the light increased the maximum kinetic energy of the electrons. Increasing the intensity increased the number of electrons emitted but had no effect on their energy.
This could not be explained in terms of classical electromagnetic waves. Instead, Albert Einstein used Planck’s theory to suggest that light travels in particle-like packets called photons, each one having an energy \(E=hf\). When a photon hits the metal nothing will happen if its energy (and frequency) are too low to release an electron. If the photon does have the minimum energy required, the energy is transferred to a single electron. The electron uses an amount of energy \(ϕ\) to escape the metal, and any energy leftover becomes the kinetic energy of the free-electron:
\(K_{max}=hf-ϕ\)
The explanations of the black body spectrum and of the photoelectric effect established the photon model (particle model) of light.
Both the wave and particle models of light are needed to explain light’s behaviour, so light is said to have a ‘dual nature’. It can act as a wave or a particle depending on the situation, but never both at the same time.
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The Special Theory of Relativity addresses another aspect of light: its speed as measured relative to different reference frames. Special Relativity consists of two postulates:
Inertial frames of references are those which are not accelerating: for example, a car travelling at constant velocity. Any experiment you do in any inertial frame will have the same result, as according to the first postulate, the laws of physics are always the same. The most important consequence of this is that an observer in an inertial frame can never detect the frame’s motion: being in a car on a smooth ride feels the same as sitting in it when it is stationary. All the observer can say for sure is that they are moving relative to something else.
In Year 11, you learned to solve problems about relative motion. For example, if someone is sitting in a train moving at \(v_{TG}\) relative to the ground, and throws a ball forwards at \(v_{BT}\) relative to the train, an observer outside the train sees the ball moving at a velocity \(v_{BG}\) relative to the ground:
\(v_{BG}=v_{BT}+v_{TG}\)
Einstein’s Special Relativity proposed that light does not behave this way:
According to the second postulate, the speed of light is the same for all observers regardless of their motion.
If the train passenger switched on a torch, he would observe the beam to travel at a speed of \(3 \times 10^8 \text{ ms}^{-1}\). Regardless of how fast the train was travelling, the observer outside the train would also see the beam travelling at the same speed. For this to happen, both observers must disagree on the measurements of distance, time, momentum and mass.
Time dilation is a phenomenon where observers in motion relative to each other will disagree on the time that passes between two events. The observer who sees both events happen in the same location measures the proper time, \(t_0\) (this is the shortest possible time). An observer moving with speed \(v \) relative to the first will instead measure the dilated time interval:
\(t=\frac{t_0}{\sqrt{\left(1-\frac{v^2}{c^2}\right)}}\)
An important thing to remember is that because all inertial frames are equivalent, neither person is more ‘correct’ than the other. It is not a valid question to ask what the ‘real’ time interval is. All we can do is state what each observer measures.
Length contraction is simpler. If you are in the same reference frame as an object, you will measure its rest length or proper length \(l_0\). Anyone in motion at a speed \(v \) relative to this object will observe it to be shorter and will measure its contracted length:
\(l=l_0\sqrt{\left(1-\frac{v^2}{c^2}\right)}\)
The last effect we are interested in is how relativity affects momentum and mass. In classical physics, the momentum of an object is \(p=mv\). Under relativity, the value diverges from this at high speeds and is calculated by:
\(p_v=\frac{m_0 v}{\sqrt{\left(1-\frac{v^2}{c^2}\right)}}\)
One way to interpret this is that an object’s mass effectively increases as it reaches these high speeds: it increases from the rest mass \(m_0\) to the relativistic mass
\(m_v=\frac{m_0}{\sqrt{\left(1-\frac{v^2}{c^2}\right)}}\)
The increased mass means we need additional force to provide further acceleration, eventually requiring an infinite amount of force. This is why no object can ever reach the speed of light – it would take an infinite amount of work.
At speeds approaching the speed of light, doing additional work on an object will increase its mass rather than its speed. To reconcile this with the conservation of energy Einstein realised that mass must be a form of energy
\(E=mc^2\)
meaning that mass can be converted into other forms of energy and vice versa.
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