E. Physics: Light and Geometric Optics · Light and Geometric Optics

What Is Light? Waves, Energy and the Electromagnetic Spectrum

E3.2 E2.1 A1.12 A1.13About 70 minutes

Learning goals

I can describe light as a form of energy that travels as an electromagnetic wave.
I can label wavelength, amplitude and frequency, and use c = f λ.
I can name the regions of the electromagnetic spectrum in order and identify the visible and invisible regions.
I can give uses and dangers of different kinds of electromagnetic radiation.

Words to know

electromagnetic wave
A wave of changing electric and magnetic fields that carries energy and can travel through a vacuum.

speed of light (c)
3.00 × 10⁸ m/s in a vacuum; the fastest possible speed.

wavelength (λ)
The distance from one crest of a wave to the next, in metres or nanometres.

frequency (f)
The number of waves that pass a point each second, in hertz (Hz).

amplitude
The height of a crest above the rest position; for light, larger amplitude means brighter light.

electromagnetic spectrum
The full range of electromagnetic waves, from radio waves to gamma rays.

visible spectrum
The part of the EM spectrum our eyes detect, about 400 nm (violet) to 700 nm (red).

ray model
Showing light as straight lines with arrows, used in geometric optics.

Light: the fastest thing there is

When you step outside on a sunny winter morning, the sunlight hitting the snow left the Sun about 8 minutes and 20 seconds ago. In that time it crossed about 150 million kilometres of empty space. Nothing travels faster than light.

In this unit you will study light the way physicists and optical engineers do. You will learn what light is, where it comes from, how it reflects off mirrors, how it bends (refracts) in water, glass and lenses, and how we use these properties in cameras, eyeglasses, microscopes, telescopes and the fibre-optic cables that carry the internet.

Remember from earlier grades

In Grade 4 you learned that light is a form of energy, that it travels in straight lines, and that it can be reflected, absorbed or refracted (bent). You also saw a prism split white light into a spectrum of colours. In Grade 9 (the space unit) you met the word electromagnetic spectrum: radiation from radio waves to gamma rays. Grade 10 adds numbers, equations and careful diagrams.

What is light?

Light is a form of energy that travels as a wave. It is called an electromagnetic wave, because it is made of changing electric and magnetic fields.

Three facts make light special:

Light does not need a material (a medium) to travel through. It can cross the vacuum of space. Sound cannot.
In a vacuum, all electromagnetic waves travel at the same speed, the speed of light: c = 3.00 × 10⁸ m/s. That is 300 000 km every second.
Light carries energy. That is why sunlight warms your face and powers solar panels.

Describing a wave

Every wave can be described with a few measurements:

Wavelength (λ, the Greek letter lambda): the distance from one crest to the next crest. Visible light has tiny wavelengths, measured in nanometres (1 nm = 1 × 10⁻⁹ m).
Frequency (f): how many waves pass a point each second, measured in hertz (Hz). 1 Hz = 1 wave per second.
Amplitude: the height of a crest above the rest position. For light, a bigger amplitude means brighter light.

One wave, labelled. The wavelength is measured from crest to crest (or trough to trough). The amplitude is measured from the rest position to a crest.

The wave equation

Speed, frequency and wavelength are linked by the universal wave equation:

v = f λ

For light in a vacuum (or in air, which is almost the same), v = c, so c = f λ. Since c is fixed, frequency and wavelength are inversely related: if one goes up, the other goes down. Long-wavelength light has a low frequency. Short-wavelength light has a high frequency.

Energy also depends on frequency: the higher the frequency, the more energy each bit of light carries. That is why ultraviolet light can damage skin cells but radio waves pass harmlessly through you.

Red and violet light drawn with their true 7 : 4 ratio of wavelengths. Violet light has the shorter wavelength, so more waves pass each second: it has the higher frequency and more energy.

Worked example

Example 1: The frequency of red light

Red light has a wavelength of 700 nm. What is its frequency?

Write what you know: λ = 700 nm = 700 × 10⁻⁹ m = 7.00 × 10⁻⁷ m, and c = 3.00 × 10⁸ m/s.
Rearrange c = f λ to get f = c ÷ λ.
f = (3.00 × 10⁸ m/s) ÷ (7.00 × 10⁻⁷ m)
f = 4.29 × 10¹⁴ Hz (three significant digits, to match the data).

f = 4.29 × 10¹⁴ Hz. That is about 429 trillion waves passing every second.

Worked example

Example 2: The wavelength of an FM radio station

An FM radio station broadcasts at 99.9 MHz (1 MHz = 1 × 10⁶ Hz). What is the wavelength of its radio waves?

f = 99.9 × 10⁶ Hz = 9.99 × 10⁷ Hz.
λ = c ÷ f = (3.00 × 10⁸ m/s) ÷ (9.99 × 10⁷ Hz)
λ = 3.00 m

λ = 3.00 m, about the length of a car. Radio waves are still light-speed electromagnetic waves; our eyes just cannot detect them.

The electromagnetic spectrum

Visible light is only a small part of a much larger family. The electromagnetic (EM) spectrum is the full range of electromagnetic waves, arranged by wavelength or frequency. From longest wavelength (lowest frequency, lowest energy) to shortest wavelength (highest frequency, highest energy):

radio waves → microwaves → infrared → visible light → ultraviolet → X-rays → gamma rays

A memory trick: Rabbits Mate In Very Unusual eXpensive Gardens.

Inside the visible region, the colours run red, orange, yellow, green, blue, violet. Red has the longest wavelength (about 700 nm) and violet the shortest (about 400 nm). White light, like sunlight, is a mixture of all the colours.

The electromagnetic spectrum (the band widths are not to scale). Frequency and energy increase to the right; wavelength increases to the left. The visible part is a tiny slice, expanded below.

Region	Typical wavelength	Some uses	Cautions
Radio waves	metres to kilometres	radio, TV, cell signals, MRI scanners	low energy
Microwaves	about 1 mm to 1 m	microwave ovens, radar, Wi-Fi, GPS	can heat tissue at high power
Infrared (IR)	about 700 nm to 1 mm	TV remotes, thermal cameras, heat lamps	we feel strong IR as heat
Visible	about 400 nm to 700 nm	seeing, photography, plant growth	very bright light can damage eyes
Ultraviolet (UV)	about 10 nm to 400 nm	vitamin D production in skin, sterilizing water, fluorescent lights	sunburn, skin cancer, eye damage
X-rays	about 0.01 nm to 10 nm	medical and dental images, airport security	can damage cells; exposure is limited
Gamma rays	less than about 0.01 nm	cancer treatment, sterilizing medical tools	highest energy; very damaging to cells

The boundaries between regions are approximate; neighbouring regions overlap.

Worked example

Example 3: How long does moonlight take to reach us?

The Moon is about 3.84 × 10⁸ m from Earth. How long does light reflected from the Moon take to reach your eyes?

Light travels at constant speed, so use v = d ÷ t, rearranged to t = d ÷ v.
t = (3.84 × 10⁸ m) ÷ (3.00 × 10⁸ m/s)
t = 1.28 s

t = 1.28 s. You always see the Moon as it was a little more than a second ago.

Sunlight takes about 500 seconds to reach Earth: t = (1.50 × 10¹¹ m) ÷ (3.00 × 10⁸ m/s) = 500 s, which is 8 minutes and 20 seconds.

Two models of light

Physicists use different models for different jobs. The wave model explains colour and the EM spectrum. For the rest of this unit you will mostly use the ray model: light is drawn as straight lines called rays, with arrows showing the direction of travel. Studying light with rays is called geometric optics.

Just for fun

Why did the photon get through airport security so quickly?

It was travelling light.

Hands-on activity

Make a spectrum and spot invisible light

You need: a clear glass of water, a sunny window (or a bright flashlight), a sheet of white paper, an old CD or DVD (optional), a TV remote and a phone camera.

Water-glass spectrum. Put the glass of water on a sunny windowsill so that sunlight shines through it onto white paper on the floor. Move the paper until you see a small band of colours. Record the order of the colours. Which colour is bent the most?
CD spectrum. Tilt the shiny side of a CD under a lamp. The tiny tracks split white light into colours.
Invisible infrared. Point a TV remote at a phone camera and press a button while watching the phone screen. Many phone cameras show a flickering light from the remote's infrared LED, even though your eyes see nothing. (If one camera does not show it, try the other camera on the phone.)
Write a short conclusion: what do your observations tell you about white light and about light our eyes cannot detect?

What to look for: red at one edge of the spectrum and violet at the other, always in the order red, orange, yellow, green, blue, violet; violet is bent the most. The remote's IR shows up on many cameras as a white or purple flicker.

Safety (grown-up note): Never look directly at the Sun, even through water or a CD.

Your turn

List the regions of the electromagnetic spectrum from lowest to highest frequency.

Which has the longer wavelength, red light or blue light? Which has the higher frequency?

Green light has a wavelength of 530 nm. Calculate its frequency.

Which carries more energy: ultraviolet or infrared? Explain.

Explain why we can see the Sun but could never hear it, even if it made a loud sound.

What is meant by "white light"?

More practice: warm-up

State the speed of light in a vacuum, with units.

What is the unit of frequency?

Which invisible region lies just beyond violet light?

Which region does a TV remote use?

Put these colours in order of increasing wavelength: green, red, violet, yellow.

More practice: on your own

A microwave oven uses waves with a frequency of 2.45 × 10⁹ Hz. Find their wavelength in centimetres.

An X-ray has a frequency of 3.0 × 10¹⁸ Hz. Find its wavelength in metres and in nanometres.

Red light from a laser pointer has a wavelength of 650 nm. Write this in metres and find the frequency.

Rank from lowest to highest frequency: gamma rays, radio waves, infrared, visible light.

Why do sunscreen labels talk about UV, but not about infrared or radio waves?

Challenge

A light-year is the distance light travels in one year. Calculate it in metres (use 365.25 days).

An AM radio station broadcasts at 680 kHz and an FM station at 100 MHz. Find both wavelengths. Which wave is longer, and by about how many times?

Use c = f λ to explain what happens to the wavelength of light if its frequency is doubled.

Check your understanding

Quiz

Which list is in order of increasing wavelength?

What is the speed of light in a vacuum?

Which colour of visible light has the highest frequency?

Light with a wavelength of 6.00 × 10⁻⁷ m has a frequency of:

Which statement about light is true?

Which region of the EM spectrum is used by thermal (heat-sensing) cameras?

For parents and teachers

Big idea: Light is electromagnetic energy that travels at 3.00 × 10⁸ m/s in a vacuum. Visible light is one small region of the electromagnetic spectrum (expectation E3.2). The wave equation c = f λ links frequency and wavelength.

Common difficulties:

Scientific notation and nanometres. Practise converting: 500 nm = 500 × 10⁻⁹ m = 5.00 × 10⁻⁷ m. Most calculators use an EE or EXP key for "× 10 to the power".
Inverse relationship. Teens often think "bigger wavelength = bigger everything". Remind them: longer wavelength means lower frequency and lower energy.
Order of the spectrum. The memory sentence helps; so does remembering that "ultraviolet" means beyond violet and "infrared" means below red.

How to help: Ask your teen to point out EM waves around the house (Wi-Fi router, microwave oven, remote control, light bulbs) and name the region each one uses. Do the spectrum activity together on a sunny day, and remind them never to look directly at the Sun.