Physics · Lesson 19

Dispersion, colour, EM spectrum & optical instruments

JAMBWAECNECO

What the syllabus asks

JAMB: Dispersion of light and colours: dispersion of white light by a triangular prism, the spectrum, colours of objects, mixing of colours, rainbow; electromagnetic spectrum: description and sources, uses; optical instruments: the eye, correction of defects, camera, microscopes, telescopes, projector

WAEC: Dispersion of white light by a prism, the spectrum, pure spectrum, recombination, rainbow; colours of objects, primary, secondary and complementary colours, mixing coloured lights and pigments, filters; the electromagnetic spectrum: members, order, properties, sources, detection, uses and hazards, c = fλ; optical instruments: the eye and its defects and correction, camera, simple and compound…

NECO: Dispersion of white light by a prism, the spectrum, pure spectrum, recombination, rainbow; colours of objects, primary, secondary and complementary colours, mixing coloured lights and pigments, filters; the electromagnetic spectrum: members, order, properties, sources, detection, uses and hazards, c = fλ; optical instruments: the eye and its defects and correction, camera, simple and compound…

What you will learn

Describe and explain the dispersion of white light by a prism, including how to obtain a pure spectrum and recombine the colours.
Explain the formation of a rainbow.
Explain the colours of objects in white and coloured light, and the effects of filters and pigments.
Name the members of the electromagnetic spectrum in order, with sources, detectors, uses and hazards.
Use c = fλ for electromagnetic waves.
Describe the structure of the eye, its defects and their correction, and calculate lens powers.
Explain the action of the camera, magnifying glass, compound microscope, astronomical telescope and projector, and calculate magnifications.

Key points

A prism disperses white light into ROYGBIV; violet bends most, red least.
A pure spectrum needs a narrow slit, a parallel beam and focusing lenses; a reversed prism recombines the colours.
Rainbow: refraction with dispersion, internal reflection, refraction; red outside, sun behind you.
Primary colours of light: red, green, blue; secondaries: yellow, cyan, magenta; complementary pairs add to white.
Objects show the colours they reflect; under coloured light, colours not present cannot be reflected.
Pigments mix by subtraction: blue + yellow paint = green.
EM spectrum: gamma, X, UV, visible, IR, microwave, radio (increasing λ); all travel at 3 × 10⁸ m/s; c = fλ.
Myopia → diverging lens; hypermetropia → converging lens; P = 1/f (m), unit dioptre.
Magnifier: M = 1 + D/f; compound microscope total = m(objective) × M(eyepiece).
Telescope (normal adjustment): M = f₀/fₑ, length f₀ + fₑ; prisms in binoculars and periscopes use total internal reflection.

Start here: Dispersion of white light

After an afternoon shower in Jos, the sun comes out and a rainbow appears. In 1666, Isaac Newton showed where those colours come from by passing a narrow beam of sunlight through a glass prism: the white light spread into a band of colours. White light is not a single colour; it is a mixture of colours.

The splitting of white light into its colours is called dispersion, and the band of colours is the spectrum. The order, from least bent to most bent, is red, orange, yellow, green, blue, indigo, violet. Remember it as ROYGBIV or “Richard Of York Gave Battle In Vain”.

Why does it happen? All colours travel at the same speed in a vacuum, but in glass they slow down by different amounts. Violet light slows down most, so glass has a higher refractive index for violet than for red, and violet is refracted (bent) most. Red is bent least. So the colours leave the prism in slightly different directions and spread out.

Worked example 19.1

The refractive index of a glass is 1.51 for red light and 1.53 for violet light. Which colour travels faster in the glass?

Refractive index n = speed in vacuum ÷ speed in glass, so speed in glass = c/n.
Red: 3 × 10⁸/1.51 = 1.987 × 10⁸ m/s. Violet: 3 × 10⁸/1.53 = 1.961 × 10⁸ m/s.
Red has the smaller n, so it travels faster and is bent less.

Red (about 1.99 × 10⁸ m/s vs 1.96 × 10⁸ m/s)

Recombination. Newton showed the colours really were in the white light, not added by the glass: a second identical prism placed upside down recombines the spectrum into white light. A spinning Newton’s colour disc, painted in the spectral colours, also looks whitish because the eye blends the colours.

⚠️ Common mistake: saying the prism “adds colour” to light. The prism only separates colours already present in white light.

Try it yourself. Which colour has the greatest deviation through a prism, and why?

Show solution

Violet, because the glass has its largest refractive index for violet, so violet slows down and bends the most.

Continue this lesson in the free app →

Practice questions

1. Arrange in order of increasing wavelength: radio, X-rays, visible, ultraviolet, microwaves.

Show worked answer

X-rays, ultraviolet, visible, microwaves, radio.

2. Find the frequency of orange light of wavelength 600 nm.

Show worked answer

3 × 10⁸/6 × 10⁻⁷ = 5 × 10¹⁴ Hz.

3. A radio station transmits on 200 m. Find its frequency.

Show worked answer

3 × 10⁸/200 = 1.5 × 10⁶ Hz (1.5 MHz).

4. What colour does a green leaf appear in red light? Explain.

Show worked answer

Black: the leaf absorbs red and there is no green light to reflect.

5. A short-sighted student has a far point of 50 cm. Find the focal length and power of the correcting lens.

Show worked answer

Diverging, f = −50 cm, P = −2 D.

Key words

Dispersion: The splitting of white light into its component colours.
Spectrum: The band of colours produced by dispersion.
Pure spectrum: A spectrum in which the colours do not overlap.
Primary colours (light): Red, green and blue: the three colours that mix to make all others.
Secondary colours: Yellow, cyan and magenta, each made by adding two primaries.
Complementary colours: Two colours of light that add to give white, e.g. blue and yellow.
Filter: A transparent material that lets through only certain colours.
Pigment: A coloured substance that absorbs some colours and reflects others.
Electromagnetic wave: A transverse wave of electric and magnetic fields that can travel through a vacuum.
Myopia (short sight): A defect in which near objects are clear but distant ones are blurred.
Hypermetropia (long sight): A defect in which distant objects are clear but near ones are blurred.
Presbyopia: Loss of accommodation with age, making near vision difficult.

Learn Dispersion, colour, EM spectrum & optical instruments step by step, free.
The Cara's Tips app teaches every topic from the very basics, with quick checks, worked examples and exam practice. It works offline.
Open this lesson in the free app Download for Android