Describe the dispersion of light as illustrated by the refraction of white light by a glass prism

3.2.3 Thin Lenses – Dispersion of Light

Learning Objective

Describe the dispersion of light as illustrated by the refraction of white light by a glass prism.

Key Concepts

• White light is a mixture of all visible wavelengths (colours).
• When light passes from one medium to another, its speed changes, causing refraction.
• The refractive index \$n\$ of a material depends on the wavelength \$\lambda\$ of the light; this is called dispersion.
• Shorter wavelengths (blue/violet) are slowed more than longer wavelengths (red), so they are bent more sharply.
• A prism separates white light into a spectrum because each colour is refracted by a different amount.

How a Prism Produces a Spectrum

1. White light enters the first face of the prism at an angle of incidence \$i\$.
2. Each component wavelength \$\lambda\$ experiences a different refractive index \$n(\lambda)\$, so the angle of refraction \$r_1\$ varies with colour.
3. The light travels through the glass and reaches the second face, where it is refracted again. The total deviation \$\delta\$ for each colour is given by:

   \$\delta = i + e - A\$

   where \$e\$ is the angle of emergence and \$A\$ is the prism angle.

4. Because \$n(\lambda)\$ is larger for blue light than for red light, \$\delta{\text{blue}} > \delta{\text{red}}\$, spreading the colours into a spectrum.

Refractive Index vs. Wavelength

The relationship can be approximated by Cauchy’s equation, but for IGCSE level a simple table is sufficient.

Important Relationships

• Snell’s Law: \$n1\sin i = n2\sin r\$
• Dispersion leads to angular separation \$\Delta\theta\$ between two colours:

  \$\Delta\theta \approx (n{\text{blue}} - n{\text{red}})\,\sin A\$

• For a thin prism, the deviation is approximately proportional to \$(n-1)A\$.

Common Misconceptions

• All colours travel at the same speed in glass. – Incorrect; speed \$v = c/n\$ varies with \$\lambda\$.
• The prism creates new colours. – Incorrect; it merely separates the colours already present in white light.
• Dispersion only occurs in prisms. – Incorrect; any medium where \$n\$ varies with \$\lambda\$ (e.g., lenses, rain droplets) shows dispersion.

Link to Thin Lenses

Because the refractive index of glass depends on wavelength, a thin lens focuses different colours at slightly different points – a phenomenon known as chromatic aberration. Understanding prism dispersion helps explain why lenses are often coated or made from low‑dispersion glass.

Summary Checklist

1. State that white light consists of a continuous range of wavelengths.
2. Explain that \$n\$ varies with \$\lambda\$, causing different refraction angles.
3. Describe the path of light through a prism and how the deviation angle depends on \$n(\lambda)\$.
4. Identify the observable result – a spectrum from red (least deviated) to violet (most deviated).
5. Connect dispersion to practical effects in lenses (chromatic aberration).