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.

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Exam-Style Questions

Practice these original exam-style questions to test your understanding. Each question mirrors the style, structure, and mark allocation of real Cambridge 0625 Theory papers.

Exam-Style Question 1 — Short Answer [5 marks]

Question:

(a) Define the term dispersion in the context of light. [2]

(b) State the order of the three colours of the visible spectrum with the shortest wavelengths. [3]

Worked Solution:

(a)

1. Dispersion is the separation of white light into its constituent colours. [Definition of dispersion]

How to earn full marks:

• State that dispersion involves the separation of light.
• State that the separation produces different colours.

(b)

1. The colour with the shortest wavelength is violet. [Correct colour]

2. The next colour is blue. [Correct colour]

3. And then green. [Correct colour]

$\boxed{\text{Violet, Blue, Green}}$

How to earn full marks:

• State all three colours in the correct order (violet, then blue, then green).
• No marks are deducted for spelling errors as long as the intent is clear.
• Award 1 mark for each correctly identified colour in the correct order.

Common Pitfall: Many students struggle to remember the order of colours in the visible spectrum. A helpful mnemonic is ROYGBIV (Red, Orange, Yellow, Green, Blue, Indigo, Violet), remembering that violet has the shortest wavelength and highest frequency.

Exam-Style Question 2 — Short Answer [6 marks]

Question:

A beam of white light is shone through a triangular glass prism.

(a) Describe what happens to the white light as it passes through the prism. [3]

(b) Explain why the different colours of light are separated by the prism. [3]

Worked Solution:

(a)

1. The white light is refracted as it enters the prism. [Light bends at the air-glass interface]
2. The white light is dispersed into its constituent colours, forming a spectrum. [Dispersion into colours]
3. The colours emerge from the prism at different angles. [Different angles of refraction]

How to earn full marks:

• Mention refraction.
• Mention the formation of a spectrum or colours.
• Mention the different angles (or amounts) of refraction.

(b)

1. Different colours of light have different wavelengths (or frequencies). [Wavelength differences]
2. The refractive index of the glass is slightly different for each wavelength (or frequency). [Refractive index variation]
3. Therefore, each colour is refracted by a slightly different amount. [Different amounts of bending]

How to earn full marks:

• Relate colour to wavelength/frequency.
• State that the refractive index depends on wavelength/frequency.
• Explain that this leads to different amounts of refraction.

Common Pitfall: A common mistake is thinking that dispersion only happens when the light leaves the prism. Remember that the different colours start to separate as soon as the white light enters the prism due to the wavelength-dependent refractive index.

Exam-Style Question 3 — Extended Response [8 marks]

Question:

A student sets up an experiment to investigate the dispersion of light using a prism and a screen. The student shines a narrow beam of white light onto one face of the prism.

(a)

Draw a diagram showing the path of the white light through the prism and onto the screen. Label the incident ray, the prism, the screen, and the approximate positions of the red and violet light on the screen. [4]

(b) The student measures the angle of deviation for both red light and violet light. The angle of deviation for red light is $41.2^\circ$, and the angle of deviation for violet light is $42.8^\circ$. Calculate the difference in the angles of deviation between the red and violet light. [2]

(c) Suggest one way to improve the experiment to obtain more accurate measurements of the angles of deviation. [2]

Worked Solution:

(a)

1. The diagram shows a prism with a white light ray entering. [Prism and incident ray]
2. The ray is refracted at the first surface. [Refraction at entry]
3. The ray is dispersed into red and violet, with violet deviated more. [Dispersion and different deviations]
4. The red and violet light are shown hitting the screen in different locations. [Spectrum on screen]

How to earn full marks:

• Correctly draw the prism and the path of the white light entering.
• Show refraction at the first surface.
• Show dispersion into red and violet, with violet deviated more.
• Label the red and violet light on the screen in the correct relative positions.

(b)

1. The difference in angles is the violet angle minus the red angle. [Recognise subtraction is needed]
2. $\text{Difference} = 42.8^\circ - 41.2^\circ = 1.6^\circ$ [Subtract and get answer]

$\boxed{1.6^\circ}$

How to earn full marks:

• Correctly subtract the two angles.
• State the correct answer with the correct units.

(c)

1. Use a narrower beam of white light. [Reasonable improvement]
2. This would produce sharper lines on the screen. [Justification]

How to earn full marks:

• Suggest a valid improvement to the experimental setup (e.g., narrower beam, protractor with finer divisions).
• Explain how the improvement would lead to more accurate measurements (e.g., sharper lines, smaller uncertainty).

Common Pitfall: When drawing the diagram, many students forget that violet light bends more than red light. Make sure your diagram clearly shows the violet ray deviating further from the original path of the white light than the red ray.

Exam-Style Question 4 — Extended Response [9 marks]

Question:

A ray of white light is incident on a glass prism, resulting in the dispersion of light into its constituent colours. The refractive index of the glass is slightly different for each colour. The refractive index for red light is $1.51$ and for violet light is $1.53$.

(a) Define the term refractive index. [2]

(b) Calculate the speed of red light inside the glass prism. The speed of light in a vacuum is $3.0 \times 10^8 \text{ m/s}$. [3]

(c) Explain why violet light is refracted more than red light when passing through the prism. [4]

Worked Solution:

(a)

1. The refractive index of a material is the ratio of the speed of light in a vacuum to the speed of light in that material. [Definition of refractive index]

How to earn full marks:

• State that refractive index is a ratio of speeds of light.
• Correctly identify the two speeds being compared (vacuum and material).

(b)

1. The refractive index, $n$, is given by $n = \frac{c}{v}$, where $c$ is the speed of light in a vacuum and $v$ is the speed of light in the material. [State formula]
2. $v = \frac{c}{n} = \frac{3.0 \times 10^8 \text{ m/s}}{1.51}$ [Rearrange and substitute]
3. $v = 1.99 \times 10^8 \text{ m/s}$

$\boxed{1.99 \times 10^8 \text{ m/s}}$

How to earn full marks:

• State the correct formula for refractive index.
• Correctly substitute the given values into the formula.
• Calculate the correct answer with the correct units.

(c)

1. The refractive index of the glass is higher for violet light than for red light. [State refractive index difference]
2. This means that violet light slows down more than red light when entering the glass. [Relate refractive index to speed]
3. Since a higher refractive index means a greater change in direction, violet light is refracted more. [Relate refractive index to angle of refraction]
4. Therefore, violet light bends more towards the normal than red light. [Conclusion about bending]

How to earn full marks:

• State the difference in refractive index between red and violet light.
• Explain that this means violet light slows down more.
• Relate the higher refractive index to a greater change in direction.
• Conclude that violet light bends more towards the normal.

Common Pitfall: Students often forget the link between refractive index and the amount of bending. A higher refractive index means the light slows down more, and therefore bends more towards the normal. Don't just state the refractive index difference; explain its effect on the speed and direction of the light.