Dispersion of light Revision Notes

White light is a mixture of many colours of light, each with a different wavelength. The visible spectrum includes colours such as red, orange, yellow, green, blue, indigo, and violet, arranged in order of decreasing wavelength and increasing frequency.

Each colour corresponds to a specific range of wavelengths, for example, red light has the longest wavelength (~700 nm) and violet the shortest (~400 nm).

• White light contains multiple colours with different wavelengths.
• Visible spectrum ranges approximately from 400 nm (violet) to 700 nm (red).

Refraction is the change in direction of light as it passes from one transparent medium to another with a different optical density, caused by a change in the speed of light.

The refractive index (n) of a medium is defined as n = c/v, where c is the speed of light in vacuum and v is the speed of light in the medium.

When light enters a denser medium (higher refractive index), it slows down and bends towards the normal; when it leaves to a less dense medium, it speeds up and bends away from the normal.

• Refraction occurs due to change in speed of light between media.
• Refractive index n = speed of light in vacuum / speed of light in medium.
• Light bends towards the normal entering a denser medium.

A glass prism is a transparent optical element with flat, polished surfaces that refract light.

When white light enters the prism, each colour component slows down by a different amount because the refractive index of glass varies slightly with wavelength (a phenomenon called dispersion).

Shorter wavelengths (violet, blue) are refracted more than longer wavelengths (red), causing the light to spread out into a spectrum of colours as it emerges from the prism.

• Prism causes refraction at both entry and exit surfaces.
• Refractive index of glass depends on wavelength: n violet > n red.
• Different bending angles separate colours, producing a spectrum.

The dispersed light forms a continuous spectrum with colours arranged from red (least refracted) to violet (most refracted).

The traditional sequence is red, orange, yellow, green, blue, indigo, violet (ROYGBIV).

This sequence corresponds to increasing frequency and decreasing wavelength.

• Red light bends least; violet bends most.
• Spectrum is continuous, showing gradual change in colour.
• Colours are ordered by wavelength and refractive index.

To draw a ray diagram showing dispersion: 1. Draw a triangular prism with labelled faces.

2. Draw an incident ray of white light approaching the first face at an angle to the normal.

3. At the first face, draw refracted rays bending towards the normal inside the prism; separate these into at least two rays representing red and violet light, with violet bending more towards the normal than red due to higher refractive index for violet light (n violet > n red). 4. At the second face, draw the rays emerging from the prism bending away from the normal, again with violet bending more than red, causing the rays to spread apart and form a spectrum. 5. Label the incident ray, refracted rays inside the prism, emergent rays, and the normal lines at each interface.

• Use normal lines at each interface to show angles of incidence and refraction.
• Show violet ray bending more than red at both surfaces.
• Indicate the spread of colours as the emergent rays separate.

The visible spectrum is the portion of the electromagnetic spectrum that can be detected by the human eye. It consists of electromagnetic waves with wavelengths approximately between 400 nm and 700 nm (nanometres). Each wavelength corresponds to a different colour perceived by the eye.

The visible spectrum is traditionally divided into seven distinct colours: red, orange, yellow, green, blue, indigo, and violet. These colours are often remembered by the mnemonic 'ROYGBIV'.

• Visible spectrum wavelength range: about 400 nm to 700 nm.
• Seven traditional colours: red, orange, yellow, green, blue, indigo, violet.
• Each colour corresponds to a specific range of wavelengths and frequencies.

Electromagnetic waves travel at the speed of light (c = 3.0 × 10⁸ m/s) in a vacuum. The wavelength (λ) and frequency (f) of light are related by the equation:

\[ c = f \times \lambda \] where: f is frequency in hertz (Hz), λ is wavelength in metres (m), and c is the speed of light.

Because c is constant, wavelength and frequency are inversely proportional: as wavelength decreases, frequency increases, and vice versa. This means red light has the longest wavelength and lowest frequency, while violet light has the shortest wavelength and highest frequency.

• Speed of light, c = 3.0 × 10⁸ m/s.
• Relationship: c = f × λ.
• Inverse relationship between wavelength and frequency.
• Red: longest wavelength, lowest frequency.
• Violet: shortest wavelength, highest frequency.

The seven colours of the visible spectrum have approximate wavelength and frequency ranges as follows:

Red: wavelength ~ 620–750 nm, frequency ~ 4.0–4.8 × 10¹⁴ Hz

Orange: wavelength ~ 590–620 nm, frequency ~ 4.8–5.1 × 10¹⁴ Hz

• Red: 620–750 nm, 4.0–4.8 × 10¹⁴ Hz
• Orange: 590–620 nm, 4.8–5.1 × 10¹⁴ Hz
• Yellow: 570–590 nm, 5.1–5.3 × 10¹⁴ Hz
• Green: 495–570 nm, 5.3–6.1 × 10¹⁴ Hz
• Blue: 450–495 nm, 6.1–6.7 × 10¹⁴ Hz
• Indigo: 425–450 nm, 6.7–7.1 × 10¹⁴ Hz
• Violet: 400–425 nm, 7.1–7.5 × 10¹⁴ Hz

To draw the visible spectrum, draw a horizontal line representing wavelength decreasing from left to right. Label the left end as approximately 750 nm (red) and the right end as approximately 400 nm (violet).

Divide the line into seven segments, each labelled with one of the seven colours in order: red, orange, yellow, green, blue, indigo, violet.

Alternatively, frequency can be represented on the opposite axis, increasing from left to right, with violet on the right and red on the left.

• Draw horizontal axis labelled 'Wavelength (nm)' decreasing from left (750 nm) to right (400 nm).
• Mark and label seven colour bands in order: red, orange, yellow, green, blue, indigo, violet.
• Optionally, add a frequency axis increasing from left to right.

White light is a mixture of all visible wavelengths. When white light passes through a prism or diffraction grating, it disperses into its component colours because each wavelength refracts (bends) by a different amount.

Longer wavelengths (red) refract less and appear at one end of the spectrum, while shorter wavelengths (violet) refract more and appear at the other end.

This dispersion separates the colours by wavelength and frequency, allowing us to identify the seven traditional colours in order.

• White light contains all visible wavelengths.
• Dispersion separates light into colours by wavelength.
• Longer wavelengths refract less; shorter wavelengths refract more.
• Result: spectrum arranged from red (longest λ) to violet (shortest λ).

Monochromatic light is electromagnetic radiation that has a single frequency and therefore a single wavelength. Since frequency (f) and wavelength (λ) are related by the equation c = fλ, where c is the speed of light in vacuum (approximately 3.0 × 10⁸ m/s), monochromatic light has a precise wavelength and frequency.

Because the frequency is single-valued, the light appears as a pure colour. For example, a laser emitting red light produces monochromatic light with a wavelength around 650 nm.

In contrast, white light is polychromatic, containing a continuous range of frequencies and wavelengths, which combine to produce white.

• Monochromatic light has one frequency (f) and one wavelength (λ).
• Frequency and wavelength are related by c = fλ, where c = 3.0 × 10⁸ m/s.
• Monochromatic light appears as a single pure colour.

Monochromatic light is coherent and has a well-defined phase relationship, especially when produced by lasers. This coherence is important in interference and diffraction experiments.

The energy of photons in monochromatic light is given by E = hf, where h is Planck's constant (6.63 × 10⁻³⁴ J·s) and f is the frequency. Since f is single-valued, all photons have the same energy.

Monochromatic light is ideal for experiments requiring precise measurements of wavelength or frequency, such as diffraction grating experiments or spectroscopy.

• Energy of photons: E = hf, with constant f for monochromatic light.
• Coherence is often associated with monochromatic sources like lasers.
• Used in precise optical measurements and experiments.

Lasers are the most common sources of monochromatic light. They emit light of a single frequency with high intensity and coherence.

Other sources include certain gas discharge lamps (e.g., sodium lamps) that emit light at specific wavelengths, though these are less monochromatic than lasers.

Filters can be used to isolate a narrow band of wavelengths from polychromatic light, approximating monochromatic light for some applications.

• Lasers produce highly monochromatic light.
• Gas discharge lamps emit nearly monochromatic spectral lines.
• Optical filters can select narrow wavelength bands from white light.

Monochromatic light is essential in optical instruments such as interferometers, where precise wavelength control is necessary.

It is used in spectroscopy to identify substances by their absorption or emission lines at specific frequencies.

In telecommunications, monochromatic light from lasers is used in fibre optics for data transmission due to minimal dispersion and signal loss.

• Used in interferometry and diffraction experiments.
• Essential for spectroscopy and chemical analysis.
• Key in fibre optic communications for signal clarity.

Polychromatic light contains multiple frequencies and wavelengths, resulting in a mixture of colours, such as white light from the sun.

When polychromatic light passes through a prism, it disperses into its constituent colours due to different refractive indices for each wavelength.

Monochromatic light does not disperse into multiple colours because it contains only one wavelength.

• Polychromatic light = multiple frequencies; monochromatic = single frequency.
• Dispersion separates polychromatic light into colours.
• Monochromatic light remains a single colour after passing through a prism.