☰ Contents · Physics

Measuring with a grating and dispersion

Lessons 26–27 · 2 lessons · N. Sh. Turdiyev, K. A. Tursunmetov, A. G. Ganiyev, K. T. Suyarov, J. E. Usarov, A. K. Avliyoqulov. Physics Grade 11, 1st edition. Niso Poligraf Publishing House, Tashkent, 2018
27

Dispersion of light. Spectral analysis

Textbook: pp. 98–102
GoalExplain dispersion of light, the dependence of n on λ, the kinds of spectra (continuous, band, line, absorption) and the essence of spectral analysis.
New words
dispersion · dispersiyacontinuous spectrum · tutash spektrline spectrum · chiziqli spektrspectral analysis · spektral analiz
Explanation

In 1666 Newton used a prism to show that white sunlight splits into seven colours (red, orange, yellow, green, light blue, blue, violet) and with a second prism recombined them into white light; this is the dispersion of light. The cause: the refractive index n of a substance depends on wavelength (frequency); since n = c/v, rays of different colours travel at different speeds in a medium: red fastest and violet slowest, which is why red is refracted least and violet most. Visible light has wavelengths from about 380 nm (violet) to 760 nm (red). In vacuum all rays travel at the same speed, so there is no dispersion. Spectra: continuous (hot solids and liquids, an incandescent lamp, the Sun), band (molecules) and line (individual atoms in rarefied gases); an absorption spectrum has dark lines on a continuous background because a gas absorbs the frequencies it emits when heated. Each chemical element has its own line spectrum, a kind of «fingerprint», so determining the composition of a substance from its spectrum, spectral analysis, is very sensitive and also gives the composition of the Sun and stars. Helium was first found in the solar spectrum.

Worked examples
In glass n_red = 1.51 and n_violet = 1.53. v = c/n: v_red = 3·10⁸/1.51 ≈ 1.99·10⁸ m/s and v_violet = 3·10⁸/1.53 ≈ 1.96·10⁸ m/s: red light is faster.
Light with λ = 600 nm in air has frequency ν = c/λ = 3·10⁸/6·10⁻⁷ = 5·10¹⁴ Hz. In glass with n = 1.5 the frequency is unchanged and λ' = λ/n = 400 nm.
Class activity

At home: fill a clear glass with water, place it in the light from a window and look for rainbow colours on the wall; or make a spectrum from a lamp on a CD surface. Do not look at the Sun, and never look at the Sun through a prism or binoculars. Observing a salt flame spectrum must be done only under adult supervision in suitable conditions.

Practice
1
Which coloured ray is refracted least and which most in a prism?
2
In air λ = 600 nm. What is the frequency in units of 10¹⁴ Hz? (c = 3·10⁸ m/s)
3
The speed of light in glass is 2·10⁸ m/s. What is the refractive index?
4
What do the dark lines in the solar spectrum show?