Lecture

Introduction: what does optics study?

Optics is the branch of physics that studies the nature of light, the laws of its propagation and its interaction with matter. In the narrow sense, light means visible radiation (wavelengths of roughly 380–760 nm); in the broad sense optics also covers infrared (up to ≈1 mm) and ultraviolet (down to ≈10 nm) radiation. We receive 80–90 percent of the information about the world around us through vision, which is why optics is one of the oldest and most practical sciences: from spectacles and the microscope to the optical fibres that carry the internet and laser surgery.

In this lecture we answer the questions: how did ideas about light evolve? Why does light show both wave and particle properties? How is optics connected with other branches of physics and with the natural sciences?

Branches of optics

Geometrical optics follows from wave optics as the limiting case in which the wavelength $\lambda$ is much smaller than the size of the objects ($\lambda \to 0$).

History of optics

Antiquity and the medieval East

Greek scholars knew that light travels in straight lines and knew the law of reflection: Euclid (3rd century BC) stated in his «Catoptrics» that the angle of incidence equals the angle of reflection. Hero of Alexandria showed that a reflected ray follows the shortest path, and Ptolemy (2nd century AD) compiled tables of refraction angles.

In the 9th–11th centuries optics flourished in the East. Ibn Sahl (984) wrote the law of refraction in its correct form. Ibn al-Haytham (Alhazen), in his «Book of Optics» (≈1021), established the correct theory of vision — light comes from the object into the eye — used experiment as a scientific method and studied the camera obscura and lenses. Abu Rayhan al-Biruni and Ibn Sina (Avicenna) argued that the speed of light is finite and incomparably greater than the speed of sound.

The 17th century: geometrical optics and two theories

W. Snellius (1621) and R. Descartes (1637) formulated the law of refraction as $n_1 \sin\alpha = n_2 \sin\beta$. P. Fermat (1662) stated the principle that light travels between two points along the path that takes the least time. F. Grimaldi discovered diffraction. I. Newton (1666) used a prism to show that white light splits into a spectrum (dispersion) and developed the corpuscular theory: light is a stream of tiny particles. C. Huygens (1690) proposed the wave theory: every point of a wavefront is a source of secondary wavelets. In 1676 O. Rømer made the first estimate of the speed of light from the delays of the eclipses of Jupiter's moon Io.

The 19th century: the triumph of wave optics

T. Young (1801) observed interference in the double-slit experiment, A. Fresnel (1818) created the wave theory of diffraction, and E. Malus (1808) discovered polarization by reflection; polarization proved that light waves are transverse. J. Fraunhofer studied the dark lines in the solar spectrum, and G. Kirchhoff and R. Bunsen (1859) founded spectral analysis. A. Fizeau (1849) measured the speed of light on Earth, and L. Foucault (1850) showed that light travels more slowly in water than in air — which contradicted the corpuscular theory. J. Maxwell (1865) showed theoretically that light is an electromagnetic wave:

$$c = \frac{1}{\sqrt{\varepsilon_0 \mu_0}} \approx 3.00\times 10^{8}\ \text{m/s},$$

where $\varepsilon_0 = 8.85\times10^{-12}\ \text{F/m}$ is the electric constant and $\mu_0 = 4\pi\times10^{-7}\ \text{H/m}$ is the magnetic constant. H. Hertz (1888) produced electromagnetic waves experimentally, and P. N. Lebedev (1900) measured the pressure of light.

The 20th century: quantum optics and lasers

M. Planck (1900) introduced the hypothesis that energy is emitted in portions in order to explain thermal radiation, and A. Einstein (1905) explained the photoelectric effect using light quanta (photons):

$$\varepsilon = h\nu = \frac{hc}{\lambda}, \qquad p = \frac{h}{\lambda},$$ where $h = 6.63\times10^{-34}\ \text{J}\cdot \text{s}$ is Planck's constant, $\nu$ is the frequency, $\lambda$ is the wavelength and $p$ is the photon momentum.

Thus light has wave–particle duality: in propagation (interference, diffraction) it behaves as a wave, and in interaction with matter (photoelectric effect, Compton effect) as a particle. In 1928 C. Raman, and independently L. I. Mandelstam and G. S. Landsberg, discovered combination (Raman) scattering; in 1960 T. Maiman built the first (ruby) laser (theoretical foundations by C. Townes, N. G. Basov and A. M. Prokhorov). D. Gabor proposed holography (1948), and C. Kao proposed optical-fibre communication (1966).

Measuring the speed of light

In Fizeau's method light passes between the teeth of a wheel with $N$ teeth and is reflected by a mirror at a distance $L$. For the returning light to be blocked for the first time at rotation frequency $\nu$, the wheel must turn by half a tooth period: $t = \dfrac{1}{2N\nu}$. During this time light travels the distance $2L$, therefore

$$c = \frac{2L}{t} = 4LN\nu.$$

Today the speed of light in vacuum has an exact value: $c = 299\,792\,458\ \text{m/s}$ (since 1983 the metre has been defined through it). In a medium the speed of light is $v = c/n$, where $n$ is the absolute refractive index of the medium.

Example

In Fizeau's experiment $L = 8633\ \text{m}$, $N = 720$, and light was first blocked at $\nu = 12.6\ \text{rev/s}$. Find the speed of light.

Solution: $c = 4LN\nu = 4\cdot 8633\cdot 720\cdot 12.6 \approx 3.13\times10^{8}\ \text{m/s}$. The result differs from the modern value by only ~4% — excellent accuracy for the mid-19th century.

Follow the time axis in the interactive model: the key discoveries in the history of optics appear one after another. Try to decide which theory — corpuscular or wave — each discovery supported.

Connections of optics with other sciences and its role

• Electrodynamics: light is a particular case of electromagnetic waves; Maxwell's equations are the theoretical foundation of optics.
• Atomic and quantum physics: line spectra led to Bohr's theory and the birth of quantum mechanics; the problem of thermal radiation gave rise to the concept of the quantum.
• Molecular physics and thermodynamics: laws of thermal radiation, optical pyrometry.
• Astronomy: telescopes; spectral analysis reveals the composition, temperature and velocity of stars (Doppler shift).
• Chemistry, biology, medicine, geology: spectral analysis, microscopy, endoscopy, laser surgery, remote sensing.
• Information technology: fibre-optic communication, laser recording and reading, photonics.

Difficulties in studying the course and methodological guidance

The main difficulties in studying optics are: understanding the dual nature of light; the fact that wave fields cannot be seen with the eye; and the need to use vector algebra, complex numbers and differential equations. Recommendations: in each topic, first observe the phenomenon in the interactive model, then write down the law and the formula; work out the physical meaning and unit of every quantity in a formula; solve problems independently in the practical classes; and learn to estimate measurement errors in the laboratory work.

Objectives of the course

1. To give coherent knowledge of the nature of light and the laws of its propagation.
2. To teach the quantitative description of optical phenomena (interference, diffraction, polarization, dispersion, radiation).
3. To introduce the operating principles of optical instruments and modern optical technologies.
4. To develop skills in experimentation and data processing and to shape a scientific worldview.