Optical Dispersion
Optical dispersion is the phenomenon in which the refractive index of a medium varies with the wavelength (frequency) of light, causing different colours to refract by different amounts and thereby separate from one another when passing through a dispersive medium such as a glass prism or water droplet. Shorter wavelengths (violet) are refracted more than longer wavelengths (red) in normal dispersion. Dispersion is responsible for the formation of rainbows, chromatic aberration in lenses, and the spectral analysis of light sources.
Key Formula
V = (n_d − 1) / (n_F − n_C) (Abbe number)
LaTeX: V = \frac{n_d - 1}{n_F - n_C}
| Symbol | Meaning | Unit |
|---|---|---|
| V | Abbe number (higher V = less dispersion) | dimensionless |
| n_d | Refractive index at yellow d-line (589 nm) | dimensionless |
| n_F | Refractive index at blue F-line (486 nm) | dimensionless |
| n_C | Refractive index at red C-line (656 nm) | dimensionless |
Worked Example
Problem
Crown glass has refractive indices n_F = 1.5224, n_d = 1.5179, n_C = 1.5145. Calculate its Abbe number and comment on its dispersive power.
Solution
Step 1: Apply Abbe number formula: V = (n_d − 1) / (n_F − n_C) Step 2: Numerator: 1.5179 − 1 = 0.5179 Step 3: Denominator: 1.5224 − 1.5145 = 0.0079 Step 4: V = 0.5179 / 0.0079 ≈ 65.6
Answer
Abbe number V ≈ 65.6 (high value indicates low dispersion — crown glass is suitable for achromatic doublets)
Visible Light Spectrum: Colour, Wavelength, and Approximate Refractive Index in Crown Glass
| Colour | Wavelength (nm) | n in Crown Glass | Deflection (relative) |
|---|---|---|---|
| Violet | 380–450 | 1.528 | Most (highest bending) |
| Blue | 450–495 | 1.524 | High |
| Green | 495–570 | 1.520 | Medium |
| Yellow | 570–590 | 1.518 | Medium–low |
| Orange | 590–620 | 1.516 | Low |
| Red | 620–750 | 1.514 | Least (lowest bending) |
Interactive Tools
PhET Bending Light – Prism
Shine white light through a prism and observe spectral dispersion in real time.
Open ToolWolframAlpha – Dispersion
Plot refractive index as a function of wavelength for common optical materials.
Open ToolKhan Academy – Dispersion of Light
Video explaining how dispersion produces rainbows and splits white light into a spectrum.
Open Tool
Wikimedia Commons, CC BY-SA
Related Terms
Light Refraction
Light refraction is the bending of a light ray as it passes from one transparent medium into another of different optical density, caused by a change in the wave's speed. The greater the difference in refractive indices between the two media, the more the ray bends toward or away from the normal. Refraction is responsible for phenomena such as the apparent bending of a straw in water, the formation of rainbows, and the focusing action of lenses.
Snell's Law
Snell's Law (also called the law of refraction) states that the product of the refractive index and the sine of the angle of incidence is constant across the interface between two media: n₁ sin θ₁ = n₂ sin θ₂. It quantitatively describes how a light ray changes direction when it transitions between media of different optical densities. Snell's Law is the cornerstone of lens design, fibre optic engineering, and the correction of refractive vision errors.
Total Internal Reflection
Total Internal Reflection (TIR) occurs when a light ray travelling through a denser medium strikes the boundary with a less dense medium at an angle greater than the critical angle, causing the ray to be completely reflected back into the denser medium rather than refracted out. The critical angle θ_c is defined as sin θ_c = n₂/n₁, where n₁ > n₂. TIR is the operating principle behind optical fibres, diamonds' brilliance, and binocular prisms.
From Latin "dispersio" meaning "a scattering" (dis- = apart, spargere = to scatter). Isaac Newton coined the optical sense of the term in his 1672 paper "New Theory about Light and Colors" and systematically investigated it in "Opticks" (1704), showing that white light is composed of all spectral colours. The Abbe number is named after Ernst Karl Abbe (1840–1905).