Physic Labs

Optics

Dispersion of light and spectra

Because refractive index depends on wavelength, white light separates into colors; in ordinary dispersive glass, a prism typically deviates violet more than red.

Because refractive index depends on wavelength, white light separates into colors; in ordinary dispersive glass, a prism typically deviates violet more than red.

n=cv,n=n(λ)n=\frac{c}{v},\qquad n=n(\lambda)

Definition: Dispersion and spectra

The refractive index n = c/v describes light speed v in a medium and generally depends on wavelength λ in transparent materials. In ordinary dispersion, n is usually larger at shorter visible wavelengths, so refraction and deviation are greater for violet than red. A spectrometer maps wavelength to position or detector signal to study continuum, emission-line, and absorption-line spectra.

Compare red, green, blue, and violet rays deviated by a prism; adjust incidence angle and dispersion to compare paths.

Model and quantities

The refractive index n = c/v describes light speed v in a medium and generally depends on wavelength λ in transparent materials. In ordinary dispersion, n is usually larger at shorter visible wavelengths, so refraction and deviation are greater for violet than red. A spectrometer maps wavelength to position or detector signal to study continuum, emission-line, and absorption-line spectra.

Example: A prism and color deviation

In a spectral band, glass has n_violet = 1.532 and n_red = 1.514. Which color has the larger refraction angle when entering glass from air at the same incidence angle?

Solution

Snell’s law gives sinθ₂ = sinθ₁/n (n_air ≈ 1). The smaller n for red gives a larger sinθ₂ and θ₂. Violet refracts closer to the normal and is usually deviated more overall by a prism.

Quick check

In a prism, the refractive index varies slightly with wavelength, so each colour bends by a different amount; ordinary glass bends violet more than red. White light therefore spreads into a continuous band of colours. Water droplets can refract sunlight, reflect it internally, and refract it again to produce a rainbow. An element’s emission or absorption line spectrum contains characteristic wavelengths, like a fingerprint, allowing astronomers to identify gases in stars.

In ordinarily dispersive glass, violet light usually has a refractive index that is:

A prism produces a color spectrum from white light mainly because:

References

  1. Eugene Hecht (2017). Optics