Dispersion in Instruments: Spectra, Spectrometers, and Colour Fringes

A continuous spectrum contains a smooth spread of many wavelengths with no gaps. It often comes from dense hot sources like incandescent solids or dense gases.

A line spectrum consists of discrete wavelengths produced by specific atomic transitions. Because only certain energy differences are allowed, only certain colours appear.

A spectrometer separates light into wavelengths and allows measurement of spectral features. This helps identify substances, temperatures, or motion through shifts in lines.

Chromatic aberration occurs when a lens fails to focus all colors of light at the same point, leading to a distortion in the image. This is particularly noticeable at the edges of the lens, where different wavelengths of light are refracted by varying amounts. As a result, colored fringes appear around the edges of objects in the image, creating a rainbow-like effect. These fringes are a visual indication of the lens's inability to properly converge all colors, highlighting the imperfections in the optical design.

Refractive index depends on wavelength, so a lens bends colours by different amounts. That difference shifts the focus for each colour and creates fringing.

A prism separates colours mainly through wavelength-dependent refraction. An ideal mirror reflects without the same wavelength-dependent bending, so it doesn’t spread white light into a spectrum like a prism.

Achromatic lenses combine elements made from materials with different dispersion. They are designed so at least two colours focus more closely together, reducing visible colour fringes.

Larger apertures allow more peripheral rays, which can worsen visible colour fringing and blur. Stopping down reduces those rays, while achromats and mirrors tend to reduce chromatic problems.

Each element produces unique sets of emission lines at specific wavelengths. Dispersion separates those wavelengths so the pattern can be observed and matched to the element.

Cooler gas atoms absorb specific wavelengths from a continuous background. This removes those wavelengths from the transmitted light, creating dark lines in the spectrum.

A prism separates colors due to the phenomenon of refraction, which occurs when light passes through different media. The refractive index of a material varies with the wavelength of light; shorter wavelengths (like blue) refract more than longer wavelengths (like red). This difference in bending causes the light to spread out into its constituent colors, creating a spectrum. Thus, the separation of colors in a prism is fundamentally linked to how each wavelength interacts differently with the material of the prism.

Shorter wavelengths generally have slightly larger refractive index in common glass. Higher n means slower speed and usually greater bending for violet than red.

By dispersing light into a spectrum, astronomers can locate known spectral lines precisely. Comparing observed positions to expected wavelengths reveals shifts linked to motion.

A shift to longer wavelength means the light is 'stretched' compared to its rest wavelength. In the usual interpretation, that corresponds to recession along the line of sight.

A rainbow and prism output show light spread by wavelength into colours, and gas discharge tubes show discrete line spectra. A shadow is simply blocked light, not a wavelength-separated distribution.

Since different colours refract at different angles, they travel in different directions after passing through a prism. Over distance, those angles become a visible spatial spread.

Each wavelength experiences a different refractive index, leading to different refracted angles. That angle difference is what spreads the colours apart.

A grating separates wavelengths because different wavelengths interfere constructively at different angles. This is a different mechanism from prism dispersion, but the result is still a spectrum.

Prisms separate light via dispersion (n depends on wavelength). Gratings separate light via interference, but both spread wavelengths into distinct directions.

Dispersion allows light to be separated by wavelength, enabling spectroscopy and identification of spectral lines. The same wavelength dependence also explains why lenses can create colour fringes.