PhysicsICSE Class 10 · Spectrum and Scattering of Light

Dispersion of White Light by a Prism: Cause, Spectrum and Solved Problems (ICSE Class 10)

Updated 15 October 2026 · Fact-checked

Dispersion is the splitting of white light into its colours when it passes through a prism. It happens because the refractive index of glass is different for each wavelength: largest for violet, smallest for red. So violet travels slowest in glass and is deviated most, red least, giving the spectrum VIBGYOR.

Understand Dispersion of White Light by a Prism

What you see. Let a narrow beam of sunlight fall on one face of a glass prism and catch the emerging light on a white screen. Instead of a white patch you get a band of colours: violet, indigo, blue, green, yellow, orange, red (VIBGYOR). Red is nearest the apex side (least deviated) and violet nearest the base side (most deviated). This splitting of white light into its constituent colours is dispersion, and the coloured band is a spectrum.

White light is a mixture. Sunlight contains light of all wavelengths from about 400 nm (violet) to about 700 nm (red). A prism does not create the colours; it only separates colours that were already present.

Cause of dispersion.
1. In vacuum (and very nearly in air) all colours travel at the same speed, $c = 3 \times 1 0^{8}$ m/s, so they stay together.
2. In glass the speed depends on the wavelength: violet is slowed most, red least.
3. Since $μ = \frac{c}{V}$ , the refractive index of glass is greatest for violet and least for red.
4. A larger μ means more bending at each face, so violet is deviated most and red least. The colours leave the prism along different directions and spread out.

Colour	Wavelength	μ of glass	Speed in glass	Deviation
Red	longest	least	greatest	least
Violet	shortest	greatest	least	greatest

Deviation depends on colour. For the same prism and the same angle of incidence, $δ_{violet} > δ_{red}$ . Using $δ = i + e - A$ for each colour: violet emerges at a larger angle $e$ , so its deviation is larger. The difference $δ_{violet} - δ_{red}$ measures how much the prism spreads the colours.

What changes and what does not on entering glass.

Frequency does not change; it is fixed by the source. Colour is decided by frequency, so red light is still red inside glass.
Speed falls to $V = \frac{c}{μ}$ .
Wavelength falls to $λ_{glass} = \frac{λ _{air}}{μ}$ , because $V = f λ$ with $f$ unchanged.

Why a prism disperses but a glass slab does not show a spectrum. In a parallel-sided slab the colours do separate slightly at the first face, but the second face is parallel to the first and bends each colour back by the same amount. Every colour comes out parallel to the incident beam, the colours overlap and the light looks white. In a prism the faces are inclined, so the second face bends each colour further towards the base and the spread increases.

Monochromatic light is not dispersed. Light of a single colour (for example the yellow light of a sodium lamp) is deviated by a prism but not split, because it contains only one wavelength.

Recombination (Newton's experiment). Place a second, identical prism upside down against the first, so that the two together act like a parallel-sided slab. The second prism deviates each colour back by the same amount the first deviated it, the colours recombine and white light emerges, parallel to the original beam. This shows that the colours were present in the white light all along. A single colour taken from the spectrum and passed through another prism stays the same colour.

A natural spectrum: the rainbow. Raindrops act like tiny prisms: sunlight is refracted and dispersed on entering a drop, reflected inside it and refracted again on leaving. A rainbow is always seen with the Sun behind the observer.

Dispersion of White Light by a Prism: formulas and key facts

Refractive index for each colour: $μ_{colour} = \frac{c}{V _{colour}}, μ_{violet} > μ_{red}$; A slower colour in glass has a larger μ.
Deviation for each colour: $δ = i + e - A, δ_{violet} > δ_{red}$; Same i and A; violet emerges at a larger e.
Wavelength inside glass: $λ_{glass} = \frac{λ _{air}}{μ}$; Frequency is unchanged, so the colour is unchanged.
Order of the spectrum: Violet shortest wavelength, largest μ, slowest in glass, most deviated
Indigo, blue, green, yellow, orange in between, in this order
Red longest wavelength, smallest μ, fastest in glass, least deviated; VIBGYOR from most deviated to least deviated.

Violet	shortest wavelength, largest μ, slowest in glass, most deviated
Indigo, blue, green, yellow, orange	in between, in this order
Red	longest wavelength, smallest μ, fastest in glass, least deviated

How to solve Dispersion of White Light by a Prism questions

Dispersion questions ask you to explain the cause, compare colours, or calculate speed, wavelength or deviation for each colour.

1Write the chain: shorter wavelength → slower in glass → larger μ → more bending → more deviation.
2For speed in glass use $V = \frac{c}{μ}$ with the μ for that colour.
3For wavelength in glass use $λ_{glass} = \frac{λ _{air}}{μ}$ ; keep the frequency the same.
4For deviation of each colour use $δ = i + e - A$ with that colour's angle of emergence; subtract to find the spread.
5In a diagram, draw the colours separating from the first face, bending further towards the base at the second face, with red on top (least deviated) and violet at the bottom.

Dispersion of White Light by a Prism 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.

A rainbow in the garden

Suppose you water the garden with a fine spray on a sunny morning, and a small rainbow appears in the spray.

Where must the Sun be, and what do the water droplets do to the sunlight?

Try it first, then show the solutionSolution

The Sun must be behind you, shining into the spray.
Each droplet refracts and disperses sunlight as it enters, reflects it inside and refracts it again on leaving, so different colours reach your eye from different droplets.

Answer: Behind you; the droplets act like tiny prisms that disperse the light (with one internal reflection).

Memory hook: Back to the Sun, face the spray.

A chandelier's coloured flashes

Imagine a glass chandelier lit by a white bulb throws tiny patches of colour on the ceiling, red at one edge and violet at the other.

Why does each glass drop act like a prism, and which colour is bent more?

Try it first, then show the solutionSolution

Each cut drop has faces inclined to each other, like a prism, so white light entering it is deviated towards the thicker part.
Glass has a larger μ for violet, so violet is deviated more than red and the colours separate.

Answer: Inclined faces make each drop a small prism; violet is deviated most, red least.

Memory hook: Inclined faces split; parallel faces hide the split.

Tricks to remember Dispersion of White Light by a Prism

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

VIBGYOR from the base
Read the spectrum upwards from the base of the prism: Violet at the bottom, Red at the top. 'Violet Is Bent Greatly, You Observe Red least.'
Use it when: Labelling the spectrum on a diagram.
Slow violet
'Violet is a slow walker in glass': slowest speed, largest μ, largest bend.
Use it when: Explaining the cause of dispersion in one chain.
Frequency is the passport
Frequency (and so colour) is the passport that never changes at a border; speed and wavelength are the luggage that change.
Use it when: Questions on what changes when light enters glass.
Upside-down twin
A twin prism turned upside down undoes the split: together they make a slab, so white light comes out.
Use it when: Recombination questions.

Dispersion of White Light by a Prism: solved examples

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

Example 1: Violet compared with red · 1 mark · MCQHarder board level

Compared with red light, violet light inside a glass prism has:
(a) a larger refractive index and a larger speed
(b) a larger refractive index and a smaller speed
(c) a smaller refractive index and a larger deviation
(d) a smaller refractive index and a smaller speed

Try it first, then show the solutionSolution

Violet is slowed most by glass, so $μ = \frac{c}{V}$ is largest for violet; it is also deviated most. Only (b) fits.

Answer: (b) a larger refractive index and a smaller speed

Example 2: Defining and explaining dispersion · 3 marks · Short answerBoard level

(a) Define dispersion of light. (b) What property of glass is responsible for this splitting? (c) Which colour travels fastest inside the prism?

Try it first, then show the solutionSolution

(a) Dispersion is the splitting of white light into its constituent colours on passing through a medium such as a prism. (1)
(b) The refractive index of glass is different for different wavelengths (greatest for violet, least for red), so each colour is deviated through a different angle. (1)
(c) Red, because glass has its smallest refractive index for red and $V = \frac{c}{μ}$ . (1)

Answer: (a) Splitting of white light into its colours (b) μ of glass depends on wavelength (c) Red

Example 3: Speeds of red and violet in glass · 3 marks · Short answerHarder board level

For a crown-glass prism, μ = 1.50 for red light and μ = 1.53 for violet light. Calculate (a) the speed of red light, (b) the speed of violet light in the glass, (c) the ratio of their speeds. ( $c = 3 \times 1 0^{8}$ m/s)

Try it first, then show the solutionSolution

(a) $V_{r} = \frac{3 \times 1 0 ^{8}}{1.50} = 2.00 \times 1 0^{8}$ m/s. (1)
(b) $V_{v} = \frac{3 \times 1 0 ^{8}}{1.53} \approx 1.96 \times 1 0^{8}$ m/s. (1)
(c) $\frac{V _{r}}{V _{v}} = \frac{μ _{v}}{μ _{r}} = \frac{1.53}{1.50} = 1.02$ . (1)

Answer: (a) $2.00 \times 1 0^{8}$ m/s (b) About $1.96 \times 1 0^{8}$ m/s (c) $V_{r} : V_{v} = 1.02 : 1$

Example 4: Does red light change colour in glass? · 3 marks · Short answerHarder board level

Red light of wavelength 700 nm in air enters glass of refractive index 1.50 for red. (a) Find its wavelength in the glass. (b) Find its frequency in the glass. (c) A student says the light should look orange inside the glass because its wavelength is now shorter. Comment.

Try it first, then show the solutionSolution

(a) $λ_{g} = \frac{700}{1.50} \approx 467$ nm. (1)
(b) Frequency is unchanged: $f = \frac{3 \times 1 0 ^{8}}{700 \times 1 0 ^{- 9}} \approx 4.29 \times 1 0^{14}$ Hz. (1)
(c) Wrong: colour depends on frequency, which does not change on refraction, so the light is still red. (1)

Answer: (a) About 467 nm (b) About $4.29 \times 1 0^{14}$ Hz (c) It stays red; colour is set by frequency

Example 5: Deviation of red and violet compared · 3 marks · Short answerHarder board level

A narrow beam of white light falls at $50°$ on one face of a $60°$ glass prism. The red light emerges at $47.2°$ and the violet light at $49.8°$ . (a) Find the angle of deviation for each colour. (b) Find the angle between the emerging red and violet rays. (c) Which colour is refracted more at the first face?

Try it first, then show the solutionSolution

(a) $δ_{r} = 50° + 47.2° - 60° = 37.2°$ ; $δ_{v} = 50° + 49.8° - 60° = 39.8°$ . (1)
(b) Angle between them $= 39.8° - 37.2° = 2.6°$ . (1)
(c) Violet: it has the larger μ, so it bends more towards the normal at the first face (smaller angle of refraction). (1)

Answer: (a) Red $37.2°$ , violet $39.8°$ (b) $2.6°$ (c) Violet

Example 6: Race through a glass block · 4 marks · Short answerHOTS / competency

A short flash of white light passes straight (along the normal) through a glass block 5 cm thick. μ = 1.50 for red and 1.53 for violet. (a) Find the time each colour takes to cross the block. (b) By how much does red arrive earlier? (c) Why does the block not produce a spectrum, even though the two colours travel at different speeds?

Try it first, then show the solutionSolution

(a) $t = \frac{d}{V} = \frac{d μ}{c}$ . Red: $t_{r} = \frac{0.05 \times 1.50}{3 \times 1 0 ^{8}} = 2.5 \times 1 0^{- 10}$ s. (1)
Violet: $t_{v} = \frac{0.05 \times 1.53}{3 \times 1 0 ^{8}} = 2.55 \times 1 0^{- 10}$ s. (1)
(b) $t_{v} - t_{r} = 5 \times 1 0^{- 12}$ s. (1)
(c) At normal incidence no colour is bent, and in any case the parallel faces of a block undo at the second face whatever bending occurs at the first, so all colours leave parallel and overlap as white light. (1)

Answer: (a) Red $2.5 \times 1 0^{- 10}$ s, violet $2.55 \times 1 0^{- 10}$ s (b) $5 \times 1 0^{- 12}$ s (c) Parallel faces: colours emerge parallel and overlap

Example 7: Case study: Newton's two prisms · 4 marks · Case-basedHOTS / competency

A student repeats a famous experiment. Sunlight from a narrow slit falls on prism P, and a spectrum is formed. (a) A second prism Q, identical to P, is placed in the path of the spectrum, inverted with respect to P. What emerges from Q, and in which direction? (b) Q is removed and a slit in a card lets only the green part of the spectrum through to Q. What comes out of Q? (c) What do (a) and (b) together prove? (d) What would be seen if the sunlight were replaced by the yellow light of a sodium lamp?

Try it first, then show the solutionSolution

(a) White light, parallel to the original beam: Q deviates each colour back through the angle P deviated it, so the colours recombine. (1)
(b) Only green light, deviated by Q but not split further. (1)
(c) White light is a mixture of colours that the prism separates; the prism does not create colours, and a single colour cannot be split further. (1)
(d) A single yellow patch, deviated but not dispersed, because sodium light is (nearly) monochromatic. (1)

Answer: (a) White light parallel to the incident beam (b) Green only (c) White light is a mixture of colours (d) A yellow patch, no spectrum

Where students lose marks in Dispersion of White Light by a Prism

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

Mistake: Saying a prism 'adds' or 'produces' colours
The colours are already present in white light; the prism only separates them.
Wrong working
'The prism gives colour to the white light.'
Right working
'White light is made up of seven colours, which the prism separates because each is deviated by a different angle.'
Do this: Always mention that white light is a mixture.
Usually costs: The explanation mark.
Mistake: Reversing the speeds of colours in glass
Violet has the larger μ, so it is the slower colour in glass (V = c/μ).
Wrong working
'Violet travels fastest in glass, so it bends most.'
Right working
'Violet travels slowest in glass, has the largest μ and bends most.'
Do this: Write the chain short λ → slow → large μ → large deviation.
Usually costs: The reason mark in 'why is violet deviated most'.
Mistake: Drawing the colours separating only at the second face
Dispersion begins at the first face, where each colour is refracted through a different angle.
Wrong working
A single white ray inside the prism splitting only on leaving.
Right working
A fan of colours inside the prism from the first face, spreading further at the second face.
Do this: Start the fan at the point where white light enters.
Usually costs: The diagram mark.
Mistake: Thinking colour changes inside glass
Colour is fixed by frequency, which does not change on refraction; only speed and wavelength change.
Wrong working
'Red light becomes orange in glass because its wavelength decreases.'
Right working
'Its wavelength decreases to λ/μ, but its frequency, and so its colour, stay the same.'
Do this: Write 'f unchanged' as the first line of any such answer.
Usually costs: The mark for the comment or reason.

Exam tips

In a dispersion diagram, put red at the top and violet at the bottom of the screen when the base of the prism is at the bottom.
For 'why violet deviates most', write two linked facts: μ is greatest for violet, so it is deviated most.
For a deviation comparison, apply $δ = i + e - A$ separately to each colour; do not average.
When asked what the second inverted prism does, state both what emerges (white light) and its direction (parallel to the incident beam).

Practice questions on Dispersion of White Light by a Prism

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 · MCQBoard level
The splitting of white light into its constituent colours is called:
(a) deviation
(b) dispersion
(c) scattering
(d) total internal reflection
Hint
Think of the word for 'spreading apart'.
Answer
(b) dispersion
Q2 · 1 mark · Very short answerBoard level
Write the colours of the visible spectrum in order of increasing deviation by a glass prism.
Hint
Least deviated first.
Answer
Red, orange, yellow, green, blue, indigo, violet.
Q3 · 2 marks · Short answerBoard level
The refractive index of a glass for green light is 1.52. Find the speed of green light in this glass. ( $c = 3 \times 1 0^{8}$ m/s)
Hint
$V = \frac{c}{μ}$ .
Answer
$V = \frac{3 \times 1 0 ^{8}}{1.52} \approx 1.97 \times 1 0^{8}$ m/s.
Q4 · 3 marks · Short answerBoard level
Draw a labelled ray diagram to show the dispersion of white light by a glass prism. Mark the angle of deviation for red light and for violet light.
Hint
Separation begins at the first face.
Answer
Triangular prism with base at the bottom; a white ray strikes the left face and splits inside into a fan, violet bent most towards the base and red least; at the right face each colour bends further towards the base and reaches a screen with red at the top and violet at the bottom. Extend the incident ray forward (dashed): the angle between it and the emergent red ray is $δ_{r}$ , and with the emergent violet ray is $δ_{v}$ ( $δ_{v} > δ_{r}$ ). Arrows on all rays.
Q5 · 2 marks · Short answerHarder board level
Violet light of wavelength 400 nm in air enters glass of refractive index 1.53 for violet. Find its wavelength in the glass. Does its frequency change?
Hint
Divide the wavelength by μ.
Answer
$λ_{g} = \frac{400}{1.53} \approx 261$ nm. No, the frequency stays $7.5 \times 1 0^{14}$ Hz.
Q6 · 2 marks · Short answerHarder board level
Why does a parallel-sided glass slab not produce a visible spectrum, although white light is dispersed inside it?
Hint
Compare the two faces.
Answer
The second face is parallel to the first, so it bends each colour back through the same angle. All colours emerge parallel to the incident beam and to one another, overlap and appear white (only slightly displaced).
Q7 · 1 mark · Assertion-reasonHarder board level
Assertion (A): A beam of light from a sodium lamp is not split into colours by a prism.
Reason (R): Light from a sodium lamp contains (very nearly) a single wavelength.
(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
What does dispersion need?
Answer
(c) Both are true, and (R) explains (A): dispersion needs light of several wavelengths.
Q8 · 2 marks · Short answerHarder board level
Two prisms, one of crown glass and one of flint glass, have the same angle and receive white light at the same angle of incidence. The flint prism spreads the colours more. What does this tell you about how the refractive index of flint glass changes from red to violet, compared with crown glass?
Hint
Spread depends on the difference between μ for violet and μ for red.
Answer
In flint glass the refractive index increases more from red to violet (μ_violet − μ_red is larger), so the difference between the deviations of violet and red is larger.
Q9 · 3 marks · Short answerHOTS / competency
White light falls at $40°$ on a $60°$ prism. μ = 1.51 for red and 1.54 for violet; red emerges at $59.5°$ and violet at $62.9°$ . (a) Find the deviation of each colour. (b) Find the angular spread of the spectrum. (c) If the prism angle were reduced, would the spread increase or decrease? Give a reason.
Hint
$δ = i + e - A$ for each colour.
Answer
(a) $δ_{r} = 40° + 59.5° - 60° = 39.5°$ ; $δ_{v} = 40° + 62.9° - 60° = 42.9°$ . (b) $42.9° - 39.5° = 3.4°$ . (c) Decrease: a smaller prism angle deviates every colour less (the faces are closer to parallel), so the colours separate less.

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.Colour deviated most by a prism?Show answer
Violet.
2.Colour with the greatest speed in glass?Show answer
Red.
3.What stays unchanged when light enters glass?Show answer
Its frequency (and so its colour).
4.What emerges from two identical prisms placed one inverted against the other?Show answer
White light, parallel to the incident beam.
5.Is the light of a sodium lamp dispersed by a prism?Show answer
No, it is only deviated.

Dispersion of White Light by a Prism: frequently asked questions

What is dispersion of light?

Dispersion is the splitting of white light into its seven colours (VIBGYOR) when it passes through a prism, because each colour is deviated through a different angle.

Why is violet deviated most and red least by a prism?

Glass slows violet light the most, so its refractive index is greatest for violet and least for red. A larger refractive index means more bending, so violet is deviated most.

Why does a glass slab not show a spectrum?

Its two faces are parallel, so the second face undoes the bending at the first. All colours emerge parallel to one another, overlap and look white.