PhysicsICSE Class 10 · Spectrum and Scattering of Light

Scattering of Light: Why the Sky Is Blue and the Sunset Red (ICSE Class 10)

Updated 15 October 2026 · Fact-checked

Scattering is the sending of light in all directions by tiny particles such as air molecules. Particles much smaller than the wavelength scatter short wavelengths far more, as 1/λ⁴. Blue light is scattered about four times as much as red, so the sky looks blue, while the Sun looks red at sunrise and sunset.

Understand Scattering of Light: Blue Sky and Red Sunset

What scattering is. When light meets very small particles (air molecules, fine dust, tiny droplets), each particle absorbs a little of the light and re-emits it in all directions. This is scattering of light. It is why a beam of sunlight entering a dusty room through a gap becomes visible from the side: the dust scatters some light towards your eye.

How much is scattered: the wavelength rule. For particles much smaller than the wavelength of light (such as the nitrogen and oxygen molecules of air), the intensity of scattered light is inversely proportional to the fourth power of the wavelength:

$I \propto \frac{1}{λ ^{4}} .$

So shorter wavelengths are scattered much more. Halving the wavelength increases scattering $2^{4} = 16$ times. Red light (about 680 nm) has roughly 1.45 times the wavelength of blue (about 470 nm), so blue is scattered about $1.4 5^{4} \approx 4.4$ times as much as red.

Size of the particle matters. The $\frac{1}{λ ^{4}}$ rule holds only for particles much smaller than the wavelength. Large particles (water droplets in clouds, big dust grains) scatter all colours nearly equally, so the scattered light looks white.

Applications (the ones examiners ask).
1. Blue sky. Sunlight passing through the air has its blue part scattered strongly in all directions by air molecules. Wherever you look in the sky, scattered blue light reaches your eye. Violet is scattered even more, but sunlight contains less violet and our eyes are less sensitive to it, so the sky looks blue rather than violet.
2. Red Sun at sunrise and sunset. Near the horizon, sunlight crosses a much longer path through the atmosphere. Most of the blue and violet is scattered out of the direct beam on the way, and the light that reaches you directly is mainly red and orange. At noon the path is short, little blue is lost, and the Sun looks white.
3. White clouds. Cloud droplets are large compared with the wavelength of light, so they scatter all colours almost equally; the mixture looks white.
4. Red danger signals. Red has the longest wavelength in the visible spectrum, so it is scattered least by air, fog and dust. A red light keeps its intensity and colour over long distances and can be seen from far away. (It is the least scattering, not refraction or brightness, that is the reason.)
5. Black sky in space. On the Moon, or for astronauts above the atmosphere, there is no air to scatter sunlight, so the sky looks black even when the Sun is up. At very high altitude (high-flying aircraft) the sky looks dark blue to black because the air is very thin.

Scattering across the spectrum. The same rule compares any two electromagnetic radiations passing through the same tiny particles: ultraviolet (shorter wavelength) is scattered far more than infrared or microwaves (longer wavelengths). This is why infrared cameras can 'see' through light haze better than ordinary cameras.

Scattering is not refraction. Refraction is the bending of a beam at a boundary between two media; scattering sends light off in all directions from tiny particles within one medium. Dispersion (a prism splitting white light) depends on refraction, not scattering.

Scattering of Light: Blue Sky and Red Sunset: formulas and key facts

Rayleigh's law of scattering (small particles): $I \propto \frac{1}{λ ^{4}}$; Valid when the particles are much smaller than the wavelength (air molecules).
Comparing two wavelengths: $\frac{I _{1}}{I _{2}} = (\frac{λ _{2}}{λ _{1}})^{4}$; The shorter wavelength is scattered more; note the ratio is turned upside down.
Applications of scattering: Blue sky air molecules scatter blue most
Red Sun at sunrise and sunset long path removes blue from the direct beam
White clouds large droplets scatter all colours equally
Red danger signals red is scattered least
Black sky on the Moon no air, no scattering; State the reason, not just the effect.

Blue sky	air molecules scatter blue most
Red Sun at sunrise and sunset	long path removes blue from the direct beam
White clouds	large droplets scatter all colours equally
Red danger signals	red is scattered least
Black sky on the Moon	no air, no scattering

How to solve Scattering of Light: Blue Sky and Red Sunset questions

Scattering questions are either an explanation of an everyday observation or a calculation with the fourth-power law.

1For an explanation, name the scatterers (air molecules, dust, droplets) and say whether they are small or large compared with the wavelength.
2Small scatterers: state that shorter wavelengths are scattered more ( $I \propto \frac{1}{λ ^{4}}$ ) and say which colour that favours.
3For sunrise or sunset, add the long path through the atmosphere; for space or the Moon, add that there is no air.
4For a calculation, write $\frac{I _{short}}{I _{long}} = (\frac{λ _{long}}{λ _{short}})^{4}$ and evaluate; the answer must be greater than 1 for the shorter wavelength.
5To find a wavelength from a scattering ratio $k$ , take the fourth root: $λ_{short} = \frac{λ _{long}}{k ^{1/4}}$ .

Scattering of Light: Blue Sky and Red Sunset in real life

Each concept, met in an everyday situation. Read the situation, try the problem, then check the solution. The one-line hook is what to remember.

Choosing a colour for a hilltop warning lamp

Suppose a telecom company must fit a warning lamp to the top of a tall mobile tower on a hill that is often misty. The engineer can choose a blue, a green or a red lamp.

Which should she choose, and why?

Try it first, then show the solutionSolution

Mist and dust scatter light out of the beam; the shorter the wavelength, the more is scattered.
Red has the longest wavelength of the three, so it is scattered least and still reaches distant pilots and drivers brightly.

Answer: Red, because it is scattered least and can be seen from the greatest distance.

Memory hook: Red runs far; blue gets lost on the way.

An astronaut's sky

Imagine an astronaut standing on the Moon at local noon, with the Sun high overhead.

What colour is the sky above her, and why is it different from Earth's sky at noon?

Try it first, then show the solutionSolution

The Moon has no atmosphere, so there are no particles to scatter sunlight towards her eyes from other directions.
Light reaches her only directly from the Sun (and from bright objects); the rest of the sky sends no light.

Answer: Black: without air there is no scattering, so the sky stays dark even at noon.

Memory hook: No air, no blue.

Tricks to remember Scattering of Light: Blue Sky and Red Sunset

Short memory aids. Say each one aloud once, then use it on a question the same day.

Fourth power, short wins
'Small waves scatter, big waves travel': short λ scatters much more (to the power four), long λ goes straight on.
Use it when: Any 'which is scattered more' question.
Sky blue, Sun red: the same blue
The blue that is taken out of the sunset beam is the blue you see in the sky.
Use it when: Linking the blue sky and the red sunset in one explanation.
Big drops, no favourites
Large droplets scatter every colour equally, so clouds and mist look white or grey.
Use it when: Cloud and fog questions.
Halve λ, sixteen times
2 × 2 × 2 × 2 = 16: halving the wavelength gives 16 times the scattering.
Use it when: Quick ratio calculations.

Scattering of Light: Blue Sky and Red Sunset: solved examples

Ordered from board level to HOTS. Try each one before you open the solution.

Example 1: Colour scattered least · 1 mark · MCQBoard level

Of the following colours, the one scattered least by air molecules is:
(a) violet
(b) blue
(c) yellow
(d) red

Try it first, then show the solutionSolution

Scattering falls rapidly as wavelength increases; red has the longest wavelength here.

Answer: (d) red

Example 2: Sky and clouds · 3 marks · Short answerBoard level

(a) Name the phenomenon responsible for the blue colour of the clear sky. (b) Explain why the sky is blue. (c) Why are clouds white, although they are in the same sky?

Try it first, then show the solutionSolution

(a) Scattering of light. (1)
(b) Air molecules are much smaller than the wavelength of light and scatter shorter wavelengths far more ( $I \propto \frac{1}{λ ^{4}}$ ); blue is scattered strongly in all directions and reaches the eye from every part of the sky. (1)
(c) Cloud droplets are large compared with the wavelength, so they scatter all colours nearly equally; the mixture appears white. (1)

Answer: (a) Scattering (b) Air molecules scatter blue most (c) Large droplets scatter all colours equally

Example 3: Blue against red · 2 marks · Short answerHarder board level

Compare the intensity of scattering by air of blue light of wavelength 470 nm with that of red light of wavelength 680 nm.

Try it first, then show the solutionSolution

$\frac{I _{blue}}{I _{red}} = (\frac{680}{470})^{4}$ . (1)
$= (1.447)^{4} \approx 4.38$ , so blue is scattered about 4.4 times as much as red. (1)

Answer: Blue is scattered about 4.4 times as strongly as red

Example 4: Effect of changing the wavelength · 2 marks · Short answerHarder board level

By what factor does the scattered intensity change if the wavelength of light is (a) halved, (b) reduced by 10%?

Try it first, then show the solutionSolution

(a) $(\frac{1}{0.5})^{4} = 16$ : the scattering becomes 16 times. (1)
(b) $(\frac{1}{0.9})^{4} \approx 1.52$ : the scattering increases by about 52%. (1)

Answer: (a) 16 times (b) About 1.52 times (52% more)

Example 5: Finding a wavelength from a scattering ratio · 3 marks · Short answerHOTS / competency

Radiation X is scattered by air 81 times as strongly as infrared radiation of wavelength 960 nm. (a) Find the wavelength of X. (b) Name the region of the spectrum to which X belongs.

Try it first, then show the solutionSolution

(a) $(\frac{960}{λ _{X}})^{4} = 81$ , so $\frac{960}{λ _{X}} = 8 1^{1/4} = 3$ . (1)
$λ_{X} = \frac{960}{3} = 320$ nm. (1)
(b) 320 nm is shorter than violet (about 400 nm): ultraviolet. (1)

Answer: (a) 320 nm (b) Ultraviolet

Example 6: Ultraviolet against microwaves · 3 marks · Short answerHOTS / competency

Ultraviolet radiation of wavelength 200 nm and microwaves of wavelength 2 cm pass through the same air. (a) Which of the two does the air scatter more strongly? (b) Work out the factor. (c) Use your answer to judge this statement: 'Microwaves are scattered more because their wavelength is longer.'

Try it first, then show the solutionSolution

(a) Ultraviolet, the shorter wavelength. (1)
(b) $\frac{I _{U V}}{I _{micro}} = (\frac{2 \times 1 0 ^{- 2}}{2 \times 1 0 ^{- 7}})^{4} = (1 0^{5})^{4} = 1 0^{20}$ . (1)
(c) False: a longer wavelength means much less scattering; that is why microwaves can be used for radar and satellite links through the atmosphere. (1)

Answer: (a) Ultraviolet (b) $1 0^{20}$ times (c) The statement is false

Example 7: Case study: colours of the day · 4 marks · Case-basedHOTS / competency

A student photographs the same scene at sunrise, at noon and just after sunset.
(a) Why does the Sun look reddish at sunrise?
(b) Why does it look nearly white at noon?
(c) Why does the sky overhead stay blue for some time after sunset, even though the Sun is below the horizon?
(d) Would an astronaut in orbit, looking away from the Earth, see a blue sky? Explain.

Try it first, then show the solutionSolution

(a) At sunrise sunlight crosses a long path through the atmosphere; most blue is scattered out of the direct beam, so mainly red and orange reach the camera. (1)
(b) At noon the path through the air is short, little blue is removed and all colours arrive together. (1)
(c) The upper atmosphere is still lit by the Sun; its air molecules scatter blue light down towards the ground. (1)
(d) No: above the atmosphere there is no air to scatter light, so space looks black. (1)

Answer: (a) Long path removes blue (b) Short path, little loss (c) Sunlit upper air still scatters blue (d) No, space is black

Where students lose marks in Scattering of Light: Blue Sky and Red Sunset

The slips examiners see most often, and what to write instead.

Mistake: Explaining red danger signals by refraction or brightness
The examiner wants the property of red light that matters in air: it is scattered least.
Wrong working
'Red light is refracted least' or 'red is bright and can be seen from far'.
Right working
'Red has the longest wavelength, so it is scattered least by air and fog, and is visible from a long distance.'
Do this: Always name scattering and give the wavelength reason.
Usually costs: Reported by CISCE examiners for 2024 Q4(iii)(a).
Mistake: Not linking scattering to wavelength in assertion–reason items
Scattering by small particles depends on $\frac{1}{λ ^{4}}$ : shorter wavelength, more scattering.
Wrong working
Marking 'both true' for a reason that says the more scattered radiation has the longer wavelength.
Right working
Check the wavelength order first; the more scattered radiation must have the shorter wavelength.
Do this: Write the spectrum order and the 1/λ⁴ rule before choosing an option.
Usually costs: Reported by CISCE examiners for 2024 Q1(v).
Mistake: Missing the chain bending → wavelength → scattering
A ray that bends more in glass has a larger μ, hence a shorter wavelength, hence is scattered more by air.
Wrong working
Saying the ray that bends more is scattered less.
Right working
'It bends more, so it has a shorter wavelength and is scattered more.'
Do this: Link refraction and scattering through the wavelength.
Usually costs: Reported by CISCE examiners for 2025 Q5(ii).
Mistake: Inverting the ratio
Scattering is inversely proportional to $λ^{4}$ , so the longer wavelength goes on top.
Wrong working
$\frac{I _{blue}}{I _{red}} = (\frac{470}{680})^{4} \approx 0.23$ .
Right working
$\frac{I _{blue}}{I _{red}} = (\frac{680}{470})^{4} \approx 4.38$ .
Do this: Check that the shorter wavelength gives the larger number.
Usually costs: The calculation mark.

Exam tips

Learn the statement: the intensity of scattered light is inversely proportional to the fourth power of its wavelength, for particles much smaller than the wavelength.
For the red Sun at sunrise, mention both the longer path through the atmosphere and the scattering of blue out of the direct beam.
For 'why not violet' questions, give both reasons: less violet in sunlight and the eye's lower sensitivity to violet.
Keep scattering, refraction and dispersion separate: use the right word for each phenomenon.

Practice questions on Scattering of Light: Blue Sky and Red Sunset

Write each answer on paper first. Open the hint only if you are stuck, and the answer only when you have finished.

Q1 · 1 mark · Assertion-reasonBoard level
Assertion (A): The Sun appears red at sunset.
Reason (R): At sunset light travels a shorter distance through the atmosphere.
(a) (A) is true and (R) is false.
(b) (A) is false and (R) is true.
(c) Both (A) and (R) are true, and (R) is the correct explanation for (A).
(d) Both (A) and (R) are true, but (R) is not the correct explanation for (A).
Hint
Is the path shorter or longer near the horizon?
Answer
(a) (A) is true; (R) is false, because the path through the atmosphere is longer at sunset.
Q2 · 1 mark · Very short answerBoard level
Why does the sky appear black to an astronaut on the Moon?
Hint
What scatters sunlight on Earth?
Answer
The Moon has no atmosphere, so there is nothing to scatter sunlight into the observer's eyes.
Q3 · 2 marks · Short answerHarder board level
Compare the scattering of violet light (400 nm) with that of blue light (480 nm).
Hint
Ratio of the wavelengths, to the power four.
Answer
$\frac{I _{v}}{I _{b}} = (\frac{480}{400})^{4} = 1. 2^{4} \approx 2.07$ : violet is scattered about twice as much.
Q4 · 2 marks · Short answerBoard level
Why are red lights used as danger signals on tall buildings and railway lines?
Hint
Name the phenomenon and the property of red.
Answer
Red has the longest wavelength in the visible spectrum, so it is scattered least by air, dust and fog. It keeps its intensity over long distances and can be seen from far away.
Q5 · 2 marks · Short answerHarder board level
Light of a certain wavelength is scattered 16 times as strongly as red light of wavelength 720 nm. Find its wavelength.
Hint
Fourth root of 16 is 2.
Answer
$\frac{720}{λ} = 1 6^{1/4} = 2$ , so $λ = 360$ nm (ultraviolet).
Q6 · 3 marks · Short answerHarder board level
Two rays of different colours, A and B, fall at the same angle on a glass block; inside the glass, A bends more towards the normal than B. (a) Which ray travels more slowly in the glass? (b) Which has the shorter wavelength? (c) Which would be scattered more by air?
Hint
More bending, larger μ, shorter wavelength.
Answer
(a) A: more bending means a larger μ, so a smaller speed. (b) A: glass has a larger μ for shorter wavelengths. (c) A: shorter wavelengths are scattered more ( $I \propto \frac{1}{λ ^{4}}$ ).
Q7 · 2 marks · Short answerHarder board level
A beam of sunlight enters a dark, dusty room through a narrow gap. (a) Why is the path of the beam visible from the side? (b) Why does the beam look whitish rather than blue?
Hint
Compare the size of dust grains with the wavelength.
Answer
(a) Dust particles scatter some light sideways into the eye. (b) The dust grains are large compared with the wavelength of light, so they scatter all colours nearly equally.
Q8 · 2 marks · Short answerHarder board level
By what percentage is green light (540 nm) scattered more than orange light (600 nm)?
Hint
$(\frac{600}{540})^{4}$ .
Answer
$(\frac{600}{540})^{4} \approx 1.52$ , so green is scattered about 52% more.
Q9 · 3 marks · Short answerHOTS / competency
A planet has a thick atmosphere of very small molecules, like Earth's, but its star gives out mostly red and orange light with very little blue. A student predicts that its sky will be bright blue. (a) Is she right? (b) Which colour would its daytime sky most likely show? Explain.
Hint
Scattering can only redistribute colours that are present.
Answer
(a) No. Small molecules would scatter blue most strongly, but there is very little blue in the starlight to scatter. (b) Of the colours present, the shortest (orange, then red) would be scattered most, so the sky would look orange-ish, much dimmer than Earth's blue sky.

Test your recall

Answer in your head or on paper first, then open the card. Pulling an answer out of memory makes it stick far better than re-reading.

1.Relation between scattered intensity and wavelength?Show answer
$I \propto \frac{1}{λ ^{4}}$ .
2.Colour scattered least by air?Show answer
Red.
3.Why are clouds white?Show answer
Large droplets scatter all colours nearly equally.
4.Factor by which scattering rises when λ is halved?Show answer
16.
5.Colour of the sky seen from the Moon?Show answer
Black.

Scattering of Light: Blue Sky and Red Sunset: frequently asked questions

Why is the sky blue?

Air molecules are much smaller than the wavelength of light and scatter short wavelengths far more strongly. Blue light from the Sun is scattered in all directions, so it reaches our eyes from every part of the sky.

Why does the Sun look red at sunrise and sunset?

Near the horizon, sunlight travels through a much longer stretch of air. Most blue light is scattered out of the direct beam on the way, so the light reaching us is mainly red and orange.

Why are danger signals red?

Red has the longest wavelength of visible light, so it is scattered least by air, fog and dust. A red signal can therefore be seen clearly from the farthest distance.