1: Nature of Light
- Page ID
- 128435
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\(\newcommand{\avec}{\mathbf a}\) \(\newcommand{\bvec}{\mathbf b}\) \(\newcommand{\cvec}{\mathbf c}\) \(\newcommand{\dvec}{\mathbf d}\) \(\newcommand{\dtil}{\widetilde{\mathbf d}}\) \(\newcommand{\evec}{\mathbf e}\) \(\newcommand{\fvec}{\mathbf f}\) \(\newcommand{\nvec}{\mathbf n}\) \(\newcommand{\pvec}{\mathbf p}\) \(\newcommand{\qvec}{\mathbf q}\) \(\newcommand{\svec}{\mathbf s}\) \(\newcommand{\tvec}{\mathbf t}\) \(\newcommand{\uvec}{\mathbf u}\) \(\newcommand{\vvec}{\mathbf v}\) \(\newcommand{\wvec}{\mathbf w}\) \(\newcommand{\xvec}{\mathbf x}\) \(\newcommand{\yvec}{\mathbf y}\) \(\newcommand{\zvec}{\mathbf z}\) \(\newcommand{\rvec}{\mathbf r}\) \(\newcommand{\mvec}{\mathbf m}\) \(\newcommand{\zerovec}{\mathbf 0}\) \(\newcommand{\onevec}{\mathbf 1}\) \(\newcommand{\real}{\mathbb R}\) \(\newcommand{\twovec}[2]{\left[\begin{array}{r}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\ctwovec}[2]{\left[\begin{array}{c}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\threevec}[3]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\cthreevec}[3]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\fourvec}[4]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\cfourvec}[4]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\fivevec}[5]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\cfivevec}[5]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\mattwo}[4]{\left[\begin{array}{rr}#1 \amp #2 \\ #3 \amp #4 \\ \end{array}\right]}\) \(\newcommand{\laspan}[1]{\text{Span}\{#1\}}\) \(\newcommand{\bcal}{\cal B}\) \(\newcommand{\ccal}{\cal C}\) \(\newcommand{\scal}{\cal S}\) \(\newcommand{\wcal}{\cal W}\) \(\newcommand{\ecal}{\cal E}\) \(\newcommand{\coords}[2]{\left\{#1\right\}_{#2}}\) \(\newcommand{\gray}[1]{\color{gray}{#1}}\) \(\newcommand{\lgray}[1]{\color{lightgray}{#1}}\) \(\newcommand{\rank}{\operatorname{rank}}\) \(\newcommand{\row}{\text{Row}}\) \(\newcommand{\col}{\text{Col}}\) \(\renewcommand{\row}{\text{Row}}\) \(\newcommand{\nul}{\text{Nul}}\) \(\newcommand{\var}{\text{Var}}\) \(\newcommand{\corr}{\text{corr}}\) \(\newcommand{\len}[1]{\left|#1\right|}\) \(\newcommand{\bbar}{\overline{\bvec}}\) \(\newcommand{\bhat}{\widehat{\bvec}}\) \(\newcommand{\bperp}{\bvec^\perp}\) \(\newcommand{\xhat}{\widehat{\xvec}}\) \(\newcommand{\vhat}{\widehat{\vvec}}\) \(\newcommand{\uhat}{\widehat{\uvec}}\) \(\newcommand{\what}{\widehat{\wvec}}\) \(\newcommand{\Sighat}{\widehat{\Sigma}}\) \(\newcommand{\lt}{<}\) \(\newcommand{\gt}{>}\) \(\newcommand{\amp}{&}\) \(\definecolor{fillinmathshade}{gray}{0.9}\)- 1.1: Light and coulour
- This page introduces light, briefly previewing ideas that are discussed in detail in later chapters. It starts with Newton’s prism experiment: a beam of white light is refracted by a prism and the white light is dispersed into the visible spectrum. A second prism recombines the colours back into white light.
- 1.2: Wavelengths and spectrum
- This page introduces the spectrum of electromagnetic radiation: radio, microwaves, infrared, visible, ultraviolet, X rays, gamma rays. Visible light has wavelengths from about 400 to 700 nm, or less than an octave in frequency. At shorter wavelengths (and higher frequencies) come successively ultraviolet, X rays and gamma rays. At longer wavelengths come infrared (which we feel as warmth), microwave, and the different frequency bands of radio.
- 1.3: Speed of light
- We measure the speed of visible light directly with a time-of-flight measurement using ultra short light pulses (as are used to transmit data in optical waveguides). The speed of light, , which is the same as the speed of electromagnetic waves. This equality led Maxwell to propose that light was electromagnetic. The Système International of units defines the value of c; this then defines the metre in terms of the second.
- 1.4: Electromagnetic waves
- Using UHF radio waves, we measure c using standing waves; we transmit UHF waves in the vertical direction and reflect the downwards-going waves with a conducting plane on the ground. We map the resulting electric field with a moveable receiving antenna. We show that the electric field is at right angles to the direction of propagation, which defines the plane of polarisation. Interference of incident and reflected waves gives the wavelength, and with the oscillator frequency this gives c.
- 1.5: Waves, particles, rays
- If the wavelength is much longer than the size of objects, then those objects cast clear shadows and we can describe the behaviour of light with ray optics. A ray is an idealised narrow beam of light. In a later chapter, we use ray diagrams (geometrical optics) to show the operation of lenses, telescopes and microscopes. In contrast, if the wavelength is comparable with or greater than the size of objects, waves diffract around the objects and we can observe interference. We meet interference in
- 1.7: Transverse or longitudinal?
- We show that mechanical waves can be transverse or longitudinal, if the particle displacement is respectively at right angles to or parallel to the direction of propagation. In space or an isotropic medium, the electric and magnetic fields of EM radiation are at right angles to each other and to the direction of propagation. When the electric field is in just one direction, the wave is polarised. The direction of propagation and of the electric field define the plane of polarisation.
- 1.8: Quanta and photons
- There is more to light than waves. On the small scale, we find that the energy transmitted by light is not infinitesimally divisible – the energy is quantised and each quantum of energy is . A quantum of energy is conveyed by a single photon. The photons can sometimes display properties associated with particles, including localisation and momentum. An ultraviolet photon has more energy than a visible photon, which has more energy than an infrared photon.
- 1.9: Summary
- Light is a transverse electromagnetic wave. Visible light covers only a small part of the vast EM spectrum. In the visible spectrum, colour corresponds to frequency or wavelength. When wavelength is small and objects large, radiation is illustrated by rays. When wavelengths are small or objects large, diffraction results and interference is often observed. Energy in EM radiation is quantised.
- 1.10: Appendix
- 1.10.1: Why vision?
- 1.10.1.1: Why light? Why vision?
- 1.10.1.2: Vision vs hearing
- 1.10.2: Colour mixing
- 1.10.3: Electromagnetic transverse waves
- 1.10.4: Molecules and photons
- 1.10.5: Newton's prisms
- 1.10.6: Shadows-particles and waves
- 1.10.7: Speed of light
- 1.10.8: Speed of Radio Waves
- 1.10.9: Young's experiment
- 1.10.10: Experiments with mixing colour
- 1.10.10.1: Introduction
- 1.10.10.2: Additive mixing of light
- 1.10.10.3: Partitive mixing of light in time
- 1.10.10.4: Partitive mixing in space for light
- 1.10.10.5: Subtractive mixing