Light and Spectroscopy | Tale of Space
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Light and Spectroscopy

From the wave nature of light to the chemical interpretation of the universe, a journey through the electromagnetic spectrum

1600-1900 - Optical Revolution

Light is both a wave and a particle, a cosmic messenger and a tool for investigation. Spectroscopy, born from Newton's decomposition of white light, now allows us to analyze the chemical composition of stars billions of light-years away and understand the evolution of the universe.

The Visible Electromagnetic Spectrum

Visible light represents only a tiny portion of the electromagnetic spectrum, between 380 and 750 nanometers. Each color corresponds to a specific wavelength.

380nm
Violet 450nm
Blue 520nm
Green 580nm
Yellow 650nm
Red 750nm
IR
E = h × f = h × c / λ

The energy of a photon is inversely proportional to its wavelength.

Nature of Light

Electromagnetic waves and particles

An electromagnetic wave

Light is a coupled oscillation of an electric field and a magnetic field that propagates in a vacuum at 299,792 km/s. Unlike sound, it does not require any material medium to travel.

Fundamental properties

  • Constant speed in a vacuum: c = 299,792,458 m/s
  • Can be reflected, refracted, diffracted
  • Transportation of energy and information
  • Wave-particle duality (photons)

Maxwell's equations

Light is a solution to Maxwell's equations in a vacuum, describing the coupled propagation of electric and magnetic fields.

Electromagnetic wave equation: ∇²E - (1/c²) · ∂²E/∂t² = 0 ∇²B - (1/c²) · ∂²B/∂t² = 0 where c = 1/√(ε₀μ₀) = 299,792,458 m/s Energy-frequency relation (Planck): E = h × f = ℏ × ω where h = 6.626 × 10⁻³⁴ J·s

Full electromagnetic spectrum

  • Radio waves: λ > 1 mm (radio broadcasting, WiFi)
  • Microwave: 1 mm - 1 m (radar, oven)
  • Infrared: 750 nm - 1 mm (heat, night vision)
  • Visible: 380-750 nm (perceptible light)
  • Ultraviolet: 10-380 nm (tanning, sterilization)
  • X-rays: 0.01-10 nm (medical imaging)
  • Gamma rays: λ < 0.01 nm (radioactivity, astrophysics)

Refraction and Dispersion

Why prisms create rainbows

n₁ × sin(θ₁) = n₂ × sin(θ₂)

Snell-Descartes law: relationship between angles of incidence and refraction

Refraction

When light passes from one medium to another (air → glass, for example), it changes direction. This phenomenon is called refraction and is due to the change in the speed of light in different materials.

Dispersion

Dispersion is the fact that different colors (wavelengths) are deflected differently. Blue is deflected more than red, which explains why white light is broken down into a rainbow by a prism.

Application: The rainbow

A rainbow forms when sunlight enters water droplets, refracts, reflects inside, and then exits while dispersing. Each droplet reflects only one color back to your eye, but millions of droplets create the full spectrum.

Refractive index

Definition of the index: n = c / v where v is the speed of light in the medium Snell-Descartes law: n₁ sin(θ₁) = n₂ sin(θ₂) Critical angle (total reflection): sin(θ_c) = n₂/n₁ (if n₁ > n₂)

Chromatic dispersion

The refractive index depends on the wavelength. This dependence can be approximated by Cauchy's formula:

n(λ) = A + B/λ² + C/λ⁴ + ... Examples of indices (λ = 589 nm, sodium D line): - Vacuum: n = 1 (by definition) - Air: n = 1.000293 - Water: n = 1.333 - Crown glass: n = 1.52 - Diamond: n = 2.42

Interference and Diffraction

Proof of wave nature

Interference

When two light waves meet, they can add together (constructive interference → more intense light) or cancel each other out (destructive interference → darkness). This is proof that light is a wave.

Diffraction

Diffraction is the ability of light to bend around obstacles. When a wave passes through a narrow opening, it spreads out in a semicircular pattern. This phenomenon limits the resolution of telescopes and microscopes.

Young's double-slit experiment (1801)

Condition for constructive interference: δ = d × sin(θ) = k × λ (k integer) Interfringe (distance between bright fringes): i = λ × D / d where D = screen-slit distance, d = slit spacing

Rayleigh criterion (resolution)

θ_min = 1.22 × λ / D where D is the diameter of the aperture (telescope, eye) For the human eye (D = 5 mm, λ = 550 nm): θ_min = 1.3 × 10⁻⁴ rad ≈ 27 arc seconds For the Hubble telescope (D = 2.4 m): θ_min = 2.8 × 10⁻⁷ rad ≈ 0.06 arc seconds

Applications

  • Holography: Recording of 3D interference patterns
  • Interferometry: Detection of gravitational waves (LIGO)
  • Diffraction gratings: High-resolution spectroscopy

Astronomical Spectroscopy

Reading the chemical composition of the universe

Spectral lines

Each chemical element absorbs and emits light at very specific wavelengths, like a fingerprint. By analyzing the light from a star, we can determine its chemical composition, temperature, velocity, and even its magnetic field.

Types of spectra

  • Continuous spectrum: Hot body emitting all wavelengths
  • Emission spectrum: Bright lines (hot gas)
  • Absorption spectrum: Dark lines (cold gas in front of a hot source)

Spectroscopic Doppler effect

If a star moves away, its spectral lines shift toward the red (redshift). If it moves closer, they shift toward the blue (blueshift). This is how we discovered the expansion of the universe and how we detect exoplanets.

Bohr model (energy levels)

Energy of hydrogen levels: E_n = -13.6 eV / n² Transition between levels: ΔE = E_f - E_i = h × f = h × c / λ Rydberg formula (hydrogen lines): 1/λ = R_H × (1/n₁² - 1/n₂²) with R_H = 1.097 × 10⁷ m⁻¹ (Rydberg constant) Hydrogen spectral series: - Lyman (UV): n₁ = 1, n₂ = 2,3,4... - Balmer (visible): n₁ = 2, n₂ = 3,4,5... - Paschen (IR): n₁ = 3, n₂ = 4,5,6...

Doppler-Fizeau effect

Décalage en longueur d'onde : Δλ/λ₀ = v/c (pour v << c) Redshift z (cosmologie) : z = (λ_obs - λ_em) / λ_em = Δλ/λ₀ Loi de Hubble-Lemaître : v = H₀ × d où H₀ = 70 km/s/Mpc (constante de Hubble)

Applications in astrophysics

  • Chemical composition: Identification of elements in stars
  • Temperature: Wien's law, line width
  • Radial velocity: Doppler effect, exoplanet detection
  • Density: Collisional broadening of lines
  • Magnetic field: Zeeman effect (line splitting)

Spectroscopy in Astronomy

Spectroscopy is the most powerful tool in modern astrophysics. Here is what it allows us to discover:

Composition of stars

Each spectral line reveals the presence of a chemical element. We know, for example, that the Sun is composed of 73% hydrogen and 25% helium.

Stellar temperature

The dominant color and relative intensity of the lines make it possible to determine the surface temperature of a star with an accuracy of a few degrees.

Speed and distance

The Doppler effect measures radial velocity. Combined with Hubble's law, it allows us to estimate the distance of the most distant galaxies.

Detection of exoplanets

Periodic oscillations in a star's spectral lines reveal the presence of an orbiting planet through the Doppler effect (radial velocity method).

Modern Applications

Light and spectroscopy are at the heart of many contemporary technologies.

Optical fibers

Modern telecommunications rely on the propagation of light in glass fibers, enabling data transfer rates of several terabits per second.

Medical spectroscopy

Spectral analysis can be used to identify molecules in the blood, detect cancer using fluorescence, and perform laser surgery.

Satellite remote sensing

Satellites analyze the spectrum of light reflected by the Earth to monitor crops, detect pollution, and map resources.

Screens and display

LED, OLED, and LCD screens exploit the properties of light to create millions of colors from three primary sources.

Holography

Recording light interference makes it possible to create three-dimensional images and secure official documents.

Raman spectroscopy

A molecular analysis technique used in chemistry, biology, and archaeology to identify substances without destroying them.