Dispersion of light

1. Overview

Dispersion is the process where white light is split into its individual component colours. This occurs because white light is a mixture of different frequencies, and each frequency refracts by a different amount when passing through a material like glass.

Key Definitions

• Dispersion: The separation of white light into its constituent colours (the visible spectrum).
• Visible Spectrum: The range of seven colours that make up white light: Red, Orange, Yellow, Green, Blue, Indigo, and Violet.
• Refraction: The change in direction of light as it changes speed when moving from one medium to another.
• Monochromatic Light: Light of a single frequency or a single wavelength (and therefore a single colour).

Core Content

Dispersion by a Glass Prism

When white light enters a triangular glass prism, it is refracted. Because white light is a mixture of different colours, and each colour travels at a different speed in glass, each colour bends by a different angle.

1. Entry: As light enters the glass, it slows down and bends towards the normal. Dispersion begins the moment the light enters the glass.
2. Exit: As light leaves the glass and enters the air, it speeds up and bends away from the normal. This further increases the separation of the colours.
3. Deviation: The light always bends towards the base (the thickest part) of the prism, never towards the apex (the top point).

The Visible Spectrum

You must know the seven colours in order. A common mnemonic is ROY G. BIV.

Order by Wavelength (Longest to Shortest):

1. Red (Longest $\lambda$)
2. Orange
3. Yellow
4. Green
5. Blue
6. Indigo
7. Violet (Shortest $\lambda$)

Order by Frequency (Lowest to Highest):

1. Red (Lowest $f$)
2. Orange
3. Yellow
4. Green
5. Blue
6. Indigo
7. Violet (Highest $f$)

The Bending Rule:

• Red is Relaxed: It has the longest wavelength and is slowed down the least by the glass, so it bends the least.
• Violet is Violent: It has the shortest wavelength and is slowed down the most by the glass, so it bends the most.

Extended Content (Extended Curriculum Only)

Monochromatic Light

In the exam, you may be asked about light of a single frequency.

• Definition: Light that consists of only one frequency is called monochromatic.
• Properties: Monochromatic light cannot be dispersed into other colours. If you shine a monochromatic red laser through a prism, it will bend (refract), but it will stay as a single red beam.

Why Dispersion Happens (Advanced)

Different frequencies of light travel at the same speed in a vacuum ($3.0 \times 10^8$ m/s). However, in a medium like glass, the speed of light depends on its frequency. Since the refractive index ($n$) is linked to the speed of light in the medium, different colours experience different refractive indices. Violet light "sees" a higher refractive index than red light, which is why it deviates more.

Key Equations

While dispersion is mostly descriptive, it relies on the wave equation and refractive index:

• $v = f\lambda$
  • $v$ = speed (m/s)
  • $f$ = frequency (Hz)
  • $\lambda$ = wavelength (m)
• $n = \frac{c}{v}$
  • $n$ = refractive index (no units)
  • $c$ = speed of light in a vacuum ($3.0 \times 10^8$ m/s)
  • $v$ = speed of light in the medium (m/s)

Common Mistakes to Avoid

• ❌ Wrong: Suggesting that dispersion only starts when the light exits the glass.
  • ✓ Right: Separation begins the moment light enters the first surface of the prism.
• ❌ Wrong: Placing Red at the bottom of the spectrum.
  • ✓ Right: Red deviates the least, so it is always at the top of the spectrum exiting a prism (unless the prism is upside down!).
• ❌ Wrong: Drawing the ray through a prism bending upwards towards the apex.
  • ✓ Right: Light always refracts towards the wider base of the prism.
• ❌ Wrong: Thinking Red has the highest frequency.
  • ✓ Right: Red has the lowest frequency and the longest wavelength.

Exam Tips

1. Drawing Diagrams: When asked to complete a diagram of dispersion, ensure your rays bend at both boundaries (entry and exit) and that the "fan" of colours gets wider as it leaves the prism.
2. Frequency vs. Wavelength: Examiners often switch between asking for the order of frequency and the order of wavelength. Read the question carefully!
3. Labeling: If asked to label "the spectrum," make sure you indicate which end is Red and which end is Violet based on the amount of bending shown.