PhysicsICSE Class 10 · Refraction of Light

Refraction Through a Prism: Path of a Ray, Angle of Deviation and Minimum Deviation (ICSE Class 10)

Updated 15 October 2026 · Fact-checked

A ray passing through a glass prism is refracted at two inclined faces and bends towards the base at both, so it emerges deviated by an angle δ = i + e − A. Deviation depends on the angle of incidence, the angle of the prism, its refractive index and the colour of light. At minimum deviation, i = e.

Understand Refraction Through a Prism

A prism is a transparent solid bounded by refracting faces that are inclined to each other. For light, we use a triangular glass prism. The angle between the two refracting faces is the angle of the prism, $A$ ; the face opposite it is the base.

Path of a ray (how to draw it). Draw the triangle with its apex at the top. Let a ray PQ strike the left face obliquely at Q, and draw the normal there (dashed).
1. At Q the ray goes from air into glass (rarer to denser), so it bends towards the normal. Inside, it travels as QR towards the right face.
2. At R it goes from glass into air (denser to rarer), so it bends away from the normal (draw the normal at R too) and emerges as RS.
3. At both faces the bending is towards the base. Extend PQ forward and RS backward (dashed): the angle between them is the angle of deviation $δ$ .
Mark $i$ (at Q), $r_{1}$ , $r_{2}$ (inside) and $e$ (at R), with arrows on PQ, QR and RS.

Why a prism deviates but a glass block does not. In a rectangular block the two faces are parallel, so the bending at the second face exactly undoes the first: the emergent ray is parallel to the incident ray (only laterally displaced). In a prism the faces are inclined, so the two bendings add up, both towards the base.

Angle relations.

$r_{1} + r_{2} = A, δ = i + e - A .$

Factors affecting the angle of deviation.
1. The angle of incidence $i$ .
2. The angle of the prism $A$ : a larger $A$ gives a larger $δ$ .
3. The refractive index of the material: a larger μ gives a larger $δ$ .
4. The colour (wavelength) of light: violet is deviated most, red least, because μ is greatest for violet.
(The thickness or size of the prism does not matter.)

Minimum deviation. As $i$ is increased from a small value, $δ$ first decreases, reaches a minimum value $δ_{m}$ , then increases again (a U-shaped graph of $δ$ against $i$ ). At minimum deviation:

$i = e$ , and $r_{1} = r_{2} = \frac{A}{2}$ ;
the ray passes symmetrically through the prism; in an equilateral (or isosceles) prism the ray inside is parallel to the base;
$δ_{m} = 2 i - A$ .

For every other value of δ there are two angles of incidence that give it: by the principle of reversibility, if $i$ gives emergence at $e$ , then incidence at $e$ gives emergence at $i$ , with the same deviation.

Uses. The deviation of light by prisms is used to split white light into its colours (dispersion, studied in the chapter on the spectrum), and prisms are used in instruments to turn light through set angles.

Refraction Through a Prism: formulas and key facts

Angles inside the prism: $r_{1} + r_{2} = A$; A = angle of the prism.
Angle of deviation: $δ = i + e - A$; i = angle of incidence, e = angle of emergence.
Minimum deviation: $i = e, r_{1} = r_{2} = \frac{A}{2}, δ_{m} = 2 i - A$; Ray inside parallel to the base (equilateral or isosceles prism).
Snell's law at each face: $sin i = μ sin r_{1}, sin e = μ sin r_{2}$; μ = refractive index of the prism material.

How to solve Refraction Through a Prism questions

Almost every prism numerical uses only two lines: r₁ + r₂ = A and δ = i + e − A.

1List what is given: A, i, e, r₁, r₂, δ.
2Use $r_{1} + r_{2} = A$ for an unknown inside angle.
3Use $δ = i + e - A$ for the deviation, or rearrange it for i or e.
4At minimum deviation, put $i = e$ and $r_{1} = r_{2} = \frac{A}{2}$ , so $i = \frac{A + δ _{m}}{2}$ .
5If μ is given, apply Snell's law at the face where you know one angle.
6In a diagram, draw normals at both faces, show bending towards the base twice and put arrows on every ray.

Refraction Through 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.

Colours from a glass ornament

Suppose a triangular glass ornament hangs in a sunny window and throws a band of colours on the wall.

Why is the light bent, and why are the colours separated?

Try it first, then show the solutionSolution

Sunlight is refracted at two inclined faces and bent towards the base each time, so it is deviated.
Glass has a different μ for each colour, so each colour is deviated by a different amount: violet most, red least.

Answer: Deviation by refraction at two inclined faces, different for each colour.

Memory hook: Two inclined faces bend twice; different colours bend differently.

Deviation by a chandelier pendant

Imagine a light ray striking a 60° glass prism pendant on a chandelier at an angle of incidence of 50° and emerging at 47°.

Through what angle is the ray deviated?

Try it first, then show the solutionSolution

Write the deviation formula: $δ = i + e - A$ .
$δ = 50° + 47° - 60° = 37°$ ; the ray is turned towards the base of the pendant.

Answer: $37°$ .

Memory hook: In plus out minus A.

Tricks to remember Refraction Through a Prism

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

In plus out minus apex
δ = i + e − A: 'in plus out, minus the apex angle'.
Use it when: Deviation numericals.
Base-ward both times
A prism always bends light towards its base, at entry and at exit.
Use it when: Drawing the ray path.
Minimum means mirror-image
At minimum deviation the path is symmetric: i = e, r₁ = r₂ = A/2, ray inside parallel to the base.
Use it when: Minimum deviation diagrams.
Four factors: I AM Colour
Incidence angle, Angle of prism, Material (μ), Colour of light.
Use it when: 'State factors' questions; give only as many as asked.

Refraction Through a Prism: solved examples

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

Example 1: Direction of bending · 1 mark · MCQBoard level

When a ray of light passes through a glass prism, it bends:
(a) towards the apex at both faces
(b) towards the base at both faces
(c) towards the base at the first face and towards the apex at the second
(d) not at all if the faces are clean

Try it first, then show the solutionSolution

Entering, it bends towards the normal; leaving, away from the normal. With inclined faces, both bendings are towards the base.

Answer: (b) towards the base at both faces

Example 2: Using δ = i + e − A · 2 marks · Short answerHarder board level

A ray strikes one face of a prism of angle $60°$ at an angle of incidence of $40°$ and emerges at an angle of $61°$ . The angle of refraction at the first face is $25°$ . Find (a) the angle of deviation, (b) the angle of incidence $r_{2}$ inside the prism at the second face.

Try it first, then show the solutionSolution

(a) $δ = 40° + 61° - 60° = 41°$ . (1)
(b) $r_{2} = A - r_{1} = 60° - 25° = 35°$ . (1)

Answer: (a) $41°$ (b) $35°$

Example 3: Angles at minimum deviation · 3 marks · Short answerHarder board level

An equilateral glass prism gives a minimum deviation of $36°$ for a certain colour. Find (a) the angle of incidence, (b) the angle of emergence, (c) $r_{1}$ and $r_{2}$ . (d) How does the ray travel inside the prism?

Try it first, then show the solutionSolution

(a) $δ_{m} = 2 i - A$ , so $i = \frac{60° + 36°}{2} = 48°$ . (1)
(b) $e = i = 48°$ . (½)
(c) $r_{1} = r_{2} = \frac{60°}{2} = 30°$ . (1)
(d) Parallel to the base, since the path is symmetrical. (½)

Answer: (a) $48°$ (b) $48°$ (c) $30°$ each (d) Parallel to the base

Example 4: Changing the conditions · 3 marks · Short answerHarder board level

A ray of red light passes through a glass prism. State whether the angle of deviation increases, decreases or stays the same when (a) violet light is used instead of red, at an unchanged angle of incidence, (b) the prism is replaced by one of the same shape made of glass of higher refractive index, (c) a larger prism of the same glass and angles is used.

Try it first, then show the solutionSolution

(a) Increases: glass has a larger μ for violet. (1)
(b) Increases: larger μ gives more bending at both faces. (1)
(c) Stays the same: deviation does not depend on the size or thickness of the prism. (1)

Answer: (a) Increases (b) Increases (c) Same

Example 5: Minimum deviation from μ · 3 marks · Short answerHOTS / competency

An equilateral prism is made of glass of refractive index 1.5. A ray passes through it at minimum deviation. Find (a) the angle of refraction at the first face, (b) the angle of incidence, (c) the minimum deviation.

Try it first, then show the solutionSolution

(a) At minimum deviation $r_{1} = \frac{A}{2} = 30°$ . (1)
(b) $sin i = 1.5 \times sin 30° = 0.75$ , so $i \approx 48.6°$ . (1)
(c) $δ_{m} = 2 i - A \approx 2 \times 48.6° - 60° \approx 37.2°$ . (1)

Answer: (a) $30°$ (b) About $48.6°$ (c) About $37.2°$

Example 6: Case study: the deviation graph · 4 marks · Case-basedHOTS / competency

A student measures the deviation produced by a $60°$ glass prism for several angles of incidence:

$i$	$30°$	$40°$	$50°$	$60°$	$70°$
$δ$	$47.1°$	$38.5°$	$37.2°$	$38.9°$	$42.9°$

(a) Describe the shape of the graph of $δ$ against $i$ .
(b) Estimate the minimum deviation and the angle of incidence at which it occurs.
(c) At $i = 40°$ the ray emerged at $58.5°$ . Without measuring, predict the deviation for $i = 58.5°$ , and name the principle.
(d) How would the ray travel inside the prism at minimum deviation?

Try it first, then show the solutionSolution

(a) δ first falls, reaches a minimum and then rises: a U-shaped curve. (1)
(b) Minimum about $37°$ , near $i \approx 49°$ (between $40°$ and $60°$ , close to $50°$ ). (1)
(c) $38.5°$ again: by the principle of reversibility, incidence at $58.5°$ gives emergence at $40°$ , so $δ = 58.5° + 40° - 60° = 38.5°$ . (1)
(d) Symmetrically, parallel to the base, with $i = e$ . (1)

Answer: (a) U-shaped (b) About $37°$ at $i \approx 49°$ (c) $38.5°$ ; reversibility (d) Parallel to the base

Where students lose marks in Refraction Through a Prism

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

Mistake: Careless ray diagrams
Marks are given for arrows, normals, the ray inside parallel to the base at minimum deviation, and $e$ marked equal to $i$ .
Wrong working
Rays without arrows, dotted rays inside the prism, or the ray drawn reflecting off the second face.
Right working
Solid rays with arrows; inside ray parallel to the base; emergent ray bending away from the normal with $e = i$ marked.
Do this: Draw normals first, then the rays, then the arrows and angles.
Usually costs: Reported by CISCE examiners for 2024 Q5(iii).
Mistake: Giving extra or wrong factors for deviation
Deviation depends on i, A, μ and colour, not thickness; 'colour of prism' and 'refractive index of light' are wrong terms.
Wrong working
'Thickness of prism, colour of prism, refractive index of light.'
Right working
'Angle of the prism; refractive index of its material.' (Give only as many as asked.)
Do this: Learn the four factors in correct words; don't confuse deviation with lateral displacement.
Usually costs: Also reported for 2024 Q5(iii), where some gave more factors than asked.
Mistake: Using δ = i − e or forgetting A
The deviation formula needs all three angles.
Wrong working
$δ = 45° - 55°$ or $45° + 55°$ .
Right working
$δ = 45° + 55° - 60° = 40°$ .
Do this: Write the formula in words, 'in plus out minus A', before substituting.
Usually costs: The answer mark.
Mistake: Saying r₁ = r₂ = A at minimum deviation
The two inside angles share A between them.
Wrong working
Equilateral prism: $r_{1} = r_{2} = 60°$ .
Right working
$r_{1} = r_{2} = \frac{60°}{2} = 30°$ .
Do this: Remember $r_{1} + r_{2} = A$ always.
Usually costs: Method marks.

Exam tips

In 2024 Q5(iii) (equilateral prism, minimum deviation, $i = 45°$ ), the scheme wanted the ray inside parallel to the base and the emergent ray at $45°$ with arrows; the deviation would then be $2 \times 45° - 60° = 30°$ .
When asked for 'two factors', write exactly two, from: angle of incidence, angle of the prism, refractive index of the material, colour (wavelength) of light.
Label $i$ , $r_{1}$ , $r_{2}$ , $e$ and $δ$ on the diagram; unlabelled angles earn nothing.
Do not draw total internal reflection unless the question leads to it.

Practice questions on Refraction Through 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
In an equilateral prism at minimum deviation, the ray inside the prism is:
(a) perpendicular to the base
(b) parallel to the base
(c) along the first face
(d) totally reflected
Hint
The path is symmetric.
Answer
(b) parallel to the base
Q2 · 2 marks · Short answerBoard level
Define (a) the angle of the prism, (b) the angle of deviation.
Hint
One is a property of the prism, the other of the ray.
Answer
(a) The angle between the two refracting faces of the prism. (b) The angle between the direction of the incident ray and the direction of the emergent ray.
Q3 · 1 mark · Very short answerBoard level
A ray is incident at $45°$ on a prism of angle $60°$ and emerges at $55°$ . Find the angle of deviation.
Hint
$δ = i + e - A$ .
Answer
$δ = 45° + 55° - 60° = 40°$ .
Q4 · 2 marks · Short answerHarder board level
An equilateral prism produces a minimum deviation of $46°$ . Find the angle of incidence and the angle of refraction at the first face.
Hint
$i = \frac{A + δ _{m}}{2}$ ; $r = \frac{A}{2}$ .
Answer
$i = \frac{60° + 46°}{2} = 53°$ ; $r_{1} = 30°$ .
Q5 · 2 marks · Short answerHarder board level
In a $60°$ prism, a ray incident at $44°$ is refracted at $27.6°$ at the first face and emerges at $53.5°$ . Find $r_{2}$ and the deviation.
Hint
$r_{1} + r_{2} = A$ .
Answer
$r_{2} = 60° - 27.6° = 32.4°$ ; $δ = 44° + 53.5° - 60° = 37.5°$ .
Q6 · 2 marks · Short answerHarder board level
A ray passing through a rectangular glass block is not deviated, but a ray through a triangular prism is. Explain why.
Hint
Compare the two faces in each case.
Answer
The faces of the block are parallel, so the bending at the second face cancels that at the first and the ray emerges parallel to its original direction (only shifted). The faces of a prism are inclined, so both bendings are towards the base and add up to a net deviation.
Q7 · 3 marks · Short answerHOTS / competency
A glass prism (μ = 1.5) is placed in water (μ = $\frac{4}{3}$ ). (a) Find the refractive index of the glass relative to water. (b) Will a ray be deviated more or less than in air? Explain.
Hint
Deviation depends on how strongly the ray bends at each face.
Answer
(a) $_{w} μ_{g} = \frac{1.5}{4/3} = 1.125$ . (b) Less: the relative refractive index (1.125) is smaller than in air (1.5), so the ray bends less at each face.

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.Formula for the angle of deviation?Show answer
$δ = i + e - A$ .
2.Relation between $r_{1}$ , $r_{2}$ and $A$ ?Show answer
$r_{1} + r_{2} = A$ .
3.At minimum deviation, how are $i$ and $e$ related?Show answer
$i = e$ .
4.Which colour is deviated most by a glass prism?Show answer
Violet.
5.Does the size of a prism affect deviation?Show answer
No.

Refraction Through a Prism: frequently asked questions

Why does a prism bend light towards its base?

Entering the glass, the ray bends towards the normal; leaving, it bends away from the normal. Because the two faces are inclined, both bendings turn the ray towards the thicker part, the base.

What is meant by minimum deviation?

As the angle of incidence is increased, the deviation first decreases and then increases. Its least value is the minimum deviation, when the ray passes symmetrically through the prism with i = e.

On what factors does the angle of deviation depend?

The angle of incidence, the angle of the prism, the refractive index of the prism material and the colour (wavelength) of the light. It does not depend on the size of the prism.