Spectroscopy is a method that analyzes the interaction between matter and electromagnetic radiation to determine material properties or composition.Spectroscopy is like a rainbow that tells the secrets of distant stars. When sunlight passes through a prism, it splits into colors. Scientists look at these colored bands and find out what stars and planets are made of, as if reading their 'fingerprints'. It's similar to how you can tell what animal passed by from tracks in the sand.
The origins of spectroscopy go back to Newton's experiments with a prism (1666). In 1802, William Wollaston observed dark lines in the solar spectrum, but it was Joseph Fraunhofer who described them in detail in 1814. Kirchhoff and Bunsen in 1859 established the link between spectral lines and chemical elements, creating the method of spectral analysis. In 1885, Johann Balmer empirically described a series of hydrogen lines in the visible region. Later, Niels Bohr provided a quantum explanation of the hydrogen spectrum (1913), and the quantum mechanics of Schrödinger and others generalized the theory. Cecilia Payne-Gaposchkin in 1925, using spectroscopy, showed that stars are composed mainly of hydrogen and helium. Modern spectroscopy uses Fourier transform and multichannel detectors.
Atoms and molecules have discrete energy levels. When an electron transitions from a higher level to a lower one, a photon is emitted with energy equal to the difference: ΔE = hν. The frequency ν and wavelength λ determine the position of the spectral line. The set of lines forms a unique 'signature' of an element. In astrophysics, spectroscopy allows measuring radial velocities through the Doppler shift of lines (Doppler effect), and from line broadening — temperature and turbulence. Planck's law of radiation describes the continuous spectrum of heated bodies. Maxwell's equations explain the nature of light as an electromagnetic wave. Quantum mechanics (Schrödinger equation) predicts the exact transition frequencies.
Each chemical element leaves its own unique 'color code' in the spectrum — like a barcode in a store. For example, hydrogen always shows pink, blue, and violet lines. Astronomers use this to find water on distant planets!
| Ω_X | variable | Spectral density of component X — spectral density |
| ρ_tot | variable | Total energy density of the universe — energy density joule per cubic metre |
| ρ_X | variable | Energy density of component X — energy density joule per cubic metre |
| k | variable | Wavenumber (logarithmic scale) — wavenumber per metre |
| d/d ln k | operator | Derivative with respect to the natural logarithm of the wavenumber — logarithmic derivative |
| R | variable | spectral resolution — spectral resolution |
| λ | variable | wavelength of interest — wavelength metre |
| Δλ | variable | smallest resolvable wavelength difference — wavelength difference metre |
















