Dispersion of Light and Spectrum: Prism Colours Explained
White sunlight looks colourless, but a prism reveals it is a mixture of colours. Dispersion is the splitting of light into its spectrum because glass bends each colour by a slightly different amount. The result is the familiar rainbow band from red to violet.
This effect explains rainbows, the colours from diamond, and how spectroscopes identify elements by their light. Newton first showed with prisms that colours are inherent to light, not created by glass.
Key Concepts
Spectrum: Ordered band of colours: violet, indigo, blue, green, yellow, orange, red (VIBGYOR) from most to least deviation.
Dispersion cause: Refractive index n depends on wavelength: n higher for violet (short wavelength) than red (long). Called normal dispersion, approximated by Cauchy relation.
Angular dispersion: Difference in deviation between violet and red, delta_v minus delta_r, in degrees.
- Violet deviates most, velocity slowest in glass
- Red deviates least, velocity fastest among visible
- Dispersion zero in vacuum – all colours travel at c
Formulas
Deviation for colour: D approx (n minus 1) A for thin prism (small A in radians). For thick prism use prism formulas with n_colour.
Dispersive power ω = (n_violet minus n_red) divided by (n_yellow minus 1). Dimensionless, characterises material. Higher ω means wider spectrum.
Angular dispersion = (n_v minus n_r) times A for thin prism, A in radians or degrees consistently. n values dimensionless.
Worked Example
For crown glass n_red = 1.51, n_yellow = 1.52, n_violet = 1.54. Thin prism angle 6 degrees. Find angular dispersion and dispersive power.
- Angular dispersion = (n_v minus n_r) times A = (1.54 minus 1.51) times 6 degrees = 0.03 times 6 = 0.18 degrees.
- Mean deviation for yellow approx (n_y minus 1) A = 0.52 times 6 = 3.12 degrees.
- Dispersive power ω = (1.54 minus 1.51) divided by (1.52 minus 1) = 0.03 divided by 0.52 = 0.0577.
Spectrum spreads only 0.18 degrees, small but visible. Flint glass has higher ω about 0.09 giving wider spectrum, preferred for spectroscopes.
Common Misconceptions
- Prism adds colour: Newton recombination experiment showed second inverted prism recombines spectrum to white. Colours pre-exist.
- All materials disperse equally: Dispersive power varies: flint glass disperses more than crown. Vacuum disperses none.
- Dispersion and scattering same: Scattering (blue sky) is by particles, dispersion is refraction wavelength dependence. Different mechanisms.
Real-World Applications
- Spectroscopes split starlight to find element composition and Doppler shifts
- Rainbows form by dispersion plus internal reflection inside raindrops
- Chromatic aberration in lenses is unwanted dispersion, corrected with achromatic doublets
- Diamond fire is high dispersion 0.044 giving colourful flashes
Dispersion reveals white light as mixture because n varies with colour. Violet bends most, red least, creating spectrum measured by dispersive power.