Light · Model
Light travels
A flash and a bang leave the same hillside at the same instant and arrive six seconds apart. One of them needed air to get to you. The other did not need anything.
Start here
You see the strike. You wait for the bang.
Lightning hits a hillside two kilometres away. The flash is instant. The thunder takes about six seconds. It was one event: the flash and the bang left the same place at the same moment.
Why does one of them get to you six seconds before the other?
One event, two messengers, wildly different speeds. Light covers two kilometres in about seven millionths of a second; sound in air needs about six seconds for the same trip. Counting the gap is a real method: every three seconds between flash and bang is roughly one kilometre.
Light is a wave, and much of what you know about waves on water and about sound carries straight over. It has a wavelength and an amplitude, it carries energy from one place to another without carrying material with it, it reflects off surfaces and it can be absorbed. Like a water wave and unlike sound, it is transverse.
Two things about it are genuinely different, and both matter. First, light needs no medium. Sound is particles shoving their neighbours, so it stops dead in a vacuum; light crosses empty space perfectly well, which is why the Sun warms a planet 150 million kilometres away across nothing at all. Second, light is very much faster. In a vacuum it travels at 300 000 000 metres every second — close to a million times the speed of sound in air — and it is the fastest anything can go.
Light does travel in straight lines through anything even and unchanging, which is why shadows have sharp edges and why a ray drawn with a ruler is a good enough model for most of what light does.
At the bench · a flash and a bang, set off together
Same start. Two arrivals.
Change a control to begin
A lamp and a starting pistol fire at the same instant, and two detectors at the far end record when each arrives. Set how far away they are, and set what is in between.
Commit first. The same flash and bang are set off on the Moon, where there is no air. What do the two detectors record?
What is in between
—
The gap
—
—
The light arrives after
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at 300 000 000 m/s
The bang arrives after
—
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Which wins, and by how much
—
The figure
Light beside the waves you can see
| Waves on water | Sound | Light | |
|---|---|---|---|
| Carries energy without carrying material | Yes | Yes | Yes |
| Has a wavelength and an amplitude | Yes | Yes | Yes |
| Reflects, and can be absorbed | Yes | Yes | Yes |
| Transverse or longitudinal | Transverse | Longitudinal | Transverse |
| Needs a material to travel through | Yes — water | Yes — any solid, liquid or gas | No — crosses a vacuum |
| How fast | A few m/s | About 340 m/s in air | 300 000 000 m/s in a vacuum |
Three rows the same, three rows different. The row that does the most work is the fifth: needing a material is what makes sound a wave in matter and light a wave that does not care.
Writing it down · the shape of this relationship
Distance = speed of light × time
The triangle
Cover the one you want
d = c × t
c = d ÷ t
t = d ÷ c
Two things side by side means multiply. One thing over another means divide.
d · distance the light travels · m
c · speed of light in a vacuum · m/s
t · time it takes · s
The speed is the one for a vacuum, and air is close enough to make no difference at this scale.
Worked example · one step at a time
Light from the Sun takes 500 s to reach the Earth. Light travels at 300 000 000 m/s. How far away is the Sun?
Step 0 of 5
Convert
300 000 000 m/s stays as it is · 500 s stays 500 s
The speed is in metres per second and the time is in seconds, so there is nothing to convert.
Formula
distance = speed of light × time
Cover d on the triangle: c and t sit side by side, so you multiply.
Insert
distance = 300 000 000 m/s × 500 s
The speed is the one for a vacuum, and space is very close to one.
Fine-tune
300 000 000 × 500 = 150 000 000 000
Metres per second multiplied by seconds leaves metres.
Answer
distance = 150 000 000 000 m
A hundred and fifty billion metres, which is 150 million kilometres.
Worked example · one step at a time
Light takes 8.0 minutes to reach us from the Sun. How far away is it?
Step 0 of 5
Convert
8.0 min × 60 = 480 s
The speed is metres per second, so the time has to be in seconds before it can multiply.
Formula
distance = speed of light × time
Cover d on the triangle: c and t sit side by side, so you multiply.
Insert
distance = 300 000 000 m/s × 480 s
The converted time goes in. The 8.0 never does.
Fine-tune
300 000 000 × 480 = 144 000 000 000
Metres per second multiplied by seconds leaves metres.
Answer
distance = 144 000 000 000 m
Insert 8.0 instead of 480 and the Sun comes out 2.4 billion metres away — sixty times too close.
Your turn · the same five steps
Your gap: 1.0 km, which is 1000 m.
Write each line out yourself — starting by deciding whether anything needs converting. Then check your working and tick the lines you had.
The five lines · tick what you had
Convert
the speed is in m/s · the time is already in seconds
Metres per second multiplied by seconds gives metres, so there is nothing to convert.
Formula
t = d ÷ c
Cover t on the triangle: d sits over c, so you divide.
Insert
t = 1000 m ÷ 300 000 000 m/s
The gap comes from your slider; the speed is light in a vacuum, and air is close enough to make no difference here.
Fine-tune
1000 ÷ 300 000 000 = 3.33e-6
Metres divided by metres per second leaves seconds.
Answer
t = 3.33 millionths of a second
Over the same gap the bang would take 2.94 s through air.
The five lines above give 3.33 millionths of a second for the light across 1.0 km.
Light from the Moon reaches the Earth in 1300 ms. How far away is the Moon?
Write each line out yourself — starting by deciding whether anything needs converting. Then check your working and tick the lines you had.
The five lines · tick what you had
Convert
1300 ms ÷ 1000 = 1.3 s
The speed is metres per second, and a millisecond is a thousandth of a second.
Formula
distance = speed of light × time
Cover d on the triangle: c and t sit side by side, so you multiply.
Insert
distance = 300 000 000 m/s × 1.3 s
The converted time goes in. The 1300 never does.
Fine-tune
300 000 000 × 1.3 = 390 000 000
Metres per second multiplied by seconds leaves metres.
Answer
distance = 390 000 000 m
Insert 1300 instead of 1.3 and the Moon comes out a thousand times further away than the Sun.
The five lines give 390 000 000 m — 390 000 km, which is close to the real figure.
Key fact
Light is a transverse wave that needs no material to travel through, and in a vacuum it moves at 300 000 000 m/s — close to a million times the speed of sound in air. Like every wave it carries energy without carrying material, and it reflects and can be absorbed. Distance = speed of light × time.
Think again
“Light is instant — it takes no time at all.”
It is fast, not instant, and over a room the difference is undetectable. Over a distance it matters a great deal: the Moon is 1.3 seconds away, the Sun 8 minutes and 20 seconds, and a radio command to a spacecraft at Mars takes several minutes to arrive, which is why they cannot be flown by joystick. Because nothing beats the speed of light, looking at anything far away is looking into the past — the Sun you can see is the Sun of eight minutes ago, and if it went out you would have no way of knowing for eight minutes.
“Space is empty, so light has nothing to travel in and must be slowed down by it.”
Empty is exactly the condition light likes. Sound needs particles because it is particles shoving their neighbours; light is not made of pushed material at all, and a material is something for it to be slowed and absorbed by rather than something it needs. Light is fastest in a vacuum and slower in glass or water, which is the opposite of the pattern for sound.
Mastery ladder
Not started yet.
Rungs 3 and 4 you mark yourself.
Rung 1 · Calculate
The Moon is about 384 000 000 m away. Light travels at 300 000 000 m/s. How long does light from the Moon take to reach us?
Rung 2 · The one that catches people
A student says light must be slower in space than in air, because space is empty and there is nothing to carry it. Which statement is right?
Rung 3 · Explain
Lightning strikes two kilometres away. Explain why you see the flash almost at once but wait about six seconds for the thunder, naming the speed of each.
Rung 4 · Take it somewhere new
A rover on Mars is being driven from Earth. At its closest, Mars is about 55 000 000 000 m away. Work out how long a command takes to reach it, then explain why the rover has to be able to stop itself rather than being steered live.
Key note
Light is a transverse wave. Like waves on water and like sound it carries energy without carrying material, has a wavelength and an amplitude, reflects and can be absorbed. Unlike sound, it needs no material at all and crosses a vacuum, which is how sunlight reaches the Earth. In a vacuum it travels at 300 000 000 m/s, close to a million times the speed of sound in air, and distance = speed of light × time.
Going further
Because light takes time, every telescope is a time machine. Looking at the Moon is looking 1.3 seconds into the past, at the Sun about eight minutes, and at the nearest star beyond the Sun about four years. Some of the galaxies photographed by the largest telescopes are seen as they were before the Earth existed, and a few of the stars visible tonight may already have died — the news is still in transit.
The number 300 000 000 m/s is a rounded one, and the exact figure is stranger than it looks. Since 1983 the metre has been defined as the distance light travels in 1/299 792 458 of a second, which makes the speed of light exactly 299 792 458 m/s by definition rather than by measurement. It cannot be measured more accurately, because measuring it more accurately would only make the metre more accurate.
Before this lesson
Connects to
At GCSE this becomes
- The electromagnetic spectrum, the wave equation applied to light, and light-years as a unit of astronomical distance.
Where to next
- Next: Reflection: mirrors and scattering
- Previous: Ultrasound at work
Waves and sound
Ask Mr Badmus AI
Got a distance and want to know how long light takes to cross it?
The bench is a teaching model. The speed of light is taken as 300 000 000 m/s, a rounded value; the exact figure in a vacuum is 299 792 458 m/s, and light in air is very slightly slower than that. The speed of sound is taken as about 340 m/s, its value in air at around 20 degrees Celsius. The distance axis multiplies by ten at every mark because the two travel times are about a million times apart and a ruler scale could not show both. Neither wave is drawn losing any strength with distance, which real light and real sound both do.
Lesson content © MrBadmusAI.