Angular Dispersion & Dispersive Power
How much a material spreads the colours compared with how much it bends them.
Lesson at a glanceShow the key points
- Overall deviation is measured by yellow light (δᵧ); angular dispersion is δᵥ − δᵣ.
- Thin prism (or small angles): δ = (μ − 1)A, so δᵥ − δᵣ = (μᵥ − μᵣ)A and δᵧ = (μᵧ − 1)A.
- Dispersive power ω = angular dispersion / mean deviation = (μᵥ − μᵣ)/(μᵧ − 1) (20.1), a property of the material.
- From a thin lens: 1/f ∝ (μ − 1), so ω = (1/fᵥ − 1/fᵣ)/(1/fᵧ).
A prism does two things to white light: it bends the beam as a whole, and it spreads the colours. Different glasses do these in different proportions, and that ratio is what lens designers care about.
Mean deviation and angular dispersion
By convention the overall deviation of a white beam is measured by yellow light, whose wavelength is roughly in the middle of the visible range: the mean deviation δᵧ. If violet and red are deviated by δᵥ and δᵣ, the beam’s angular spread δᵥ − δᵣ is the angular dispersion.
For a thin prism (or small angles), each colour is deviated by δ = (μ − 1)A, so
Dispersive power
A dense flint glass has refractive indices 1.649 (red), 1.655 (yellow) and 1.668 (violet). Find its dispersive power, and the angular dispersion of a 4° prism of it.
Dispersive power from a lens
A thin lens has 1/f = (μ − 1)K, where K = 1/R₁ − 1/R₂ depends only on its shape. So μ − 1 ∝ 1/f for each colour, and
A thin lens has focal length 60.0 cm for red light and 58.0 cm for violet. Estimate the dispersive power of its glass.
- 1Mean deviation is measured with yellow light; angular dispersion is δᵥ − δᵣ.
- 2Thin prism: δ = (μ − 1)A for each colour.
- 3Dispersive power ω = (μᵥ − μᵣ)/(μᵧ − 1), a property of the material.
Check yourself
Keep exploring
Hand-picked videos, simulations and readings that explain this idea from a different angle.