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Home/Optics & Light/Chromatic Aberration

Chromatic Aberration

Chromatic aberration arises from the fundamental property of dispersion: the refractive index of a transparent material depends on the wavelength of light passing through it. This simulator visualizes the effect of dispersion on image formation by a simple converging lens. It models the refractive index using Cauchy's equation, an empirical formula given by n(λ) = A + B/λ², where A and B are material-specific constants and λ is the wavelength. This relationship shows that shorter wavelengths (e.g., blue light) experience a higher refractive index than longer wavelengths (e.g., red light). The lensmaker's equation for a thin lens in air, 1/f = (n - 1)(1/R₁ - 1/R₂), then dictates that the focal length f is a function of n, and therefore of λ. Consequently, a single lens has multiple focal points—one for each color. The simulator traces paraxial rays of three distinct wavelengths (representing red, green, and blue) from an on-axis object point through the lens. Students observe how these rays, initially parallel, refract at different angles due to dispersion and converge at different axial positions, creating a longitudinal chromatic aberration. The primary simplification is the use of paraxial (small-angle) ray tracing, which ignores spherical aberration and other higher-order imperfections. The model also treats the lens as infinitely thin and uses a simplified three-color spectrum. By interacting with this simulation, learners directly connect the abstract concept of dispersion, quantified by Cauchy's equation, to the tangible optical defect of chromatic blurring. They can explore how changing the lens curvature or material constants alters the separation of the color foci, reinforcing the relationship between material properties, geometry, and optical performance.

Who it's for: Undergraduate physics and engineering students studying wave optics, optical design, or aberrations in geometrical optics.

Key terms

  • Chromatic Aberration
  • Dispersion (optics)
  • Refractive Index
  • Cauchy's Equation
  • Lensmaker's Equation
  • Focal Length
  • Paraxial Approximation
  • Wavelength

Live graphs

Glass model (Cauchy)

1.52
0.0042

Lens scale

140 mm

n(λ) decreases as λ increases (normal dispersion), so (n−1) is larger for blue → shorter focal length. Red focuses farther than blue along the axis.

Measured values

n (650 nm)1.5299
n (550 nm)1.5339
n (450 nm)1.5407
f_R (≈)141.04mm
f_B (≈)138.22mm

How it works

A simple lens has focal length set by the refractive index. Because n(λ) varies with wavelength (dispersion), different colors focus at slightly different distances along the optical axis — longitudinal chromatic aberration. This page uses a Cauchy n(λ) and thin-lens scaling f ∝ 1/(n−1) with f fixed at green for calibration.

Key equations

n(λ) = n₀ + B / λ_µm²
1/f ∝ (n(λ) − 1) (same lens shape)

Frequently asked questions

Why does blue light bend more than red light in the lens?
For most transparent materials like glass, the refractive index is higher for shorter wavelengths (blue light) than for longer ones (red light). This property is called normal dispersion. Since the bending angle of light at an interface depends on the refractive index (via Snell's Law), blue light experiences a stronger refraction, leading to a shorter focal length.
Is chromatic aberration only a problem for lenses? What about mirrors?
Chromatic aberration is a refractive effect, caused by wavelength-dependent refraction. Mirrors operate on the principle of reflection, where the angle of reflection equals the angle of incidence for all wavelengths. Therefore, a simple mirror does not suffer from chromatic aberration, which is why reflective telescopes are often used to avoid color fringing.
What is the main simplification in this simulator, and how does it differ from a real lens?
This simulator uses the paraxial approximation, tracing rays very close to the optical axis at small angles. Real lenses have finite apertures, so rays hitting the edges cause spherical aberration and other defects. Furthermore, real white light contains a continuous spectrum, not just three discrete colors, and the Cauchy equation is an approximation that works best in the visible range away from absorption bands.
How do lens designers correct for chromatic aberration in real devices like camera lenses?
Designers create achromatic doublets by combining two lenses made of different types of glass (e.g., crown and flint) with different dispersion properties. The lenses are shaped so that the dispersion of one largely cancels out the dispersion of the other, bringing two specific wavelengths (often red and blue) to a common focus, dramatically reducing color fringing.