PhysicsICSE Class 10 · Refraction of Light

Laws of Refraction and Refractive Index: Snell's Law, μ = c/V and Reversibility (ICSE Class 10)

Q: What are the two laws of refraction?

First, the incident ray, refracted ray and normal at the point of incidence lie in the same plane. Second, for a given pair of media and colour, sin i / sin r is a constant (Snell's law), the refractive index.

Q: Why does light bend when it enters glass?

Light travels more slowly in glass than in air. When a beam meets the surface at an angle, one side of it slows down first, so the beam swings round towards the normal.

Q: Does the refractive index depend on the angle of incidence?

No. It depends on the medium, the colour (wavelength) of light and the temperature. A different angle of incidence gives a different angle of refraction, but the ratio of their sines is the same.

Updated 15 October 2026 · Fact-checked

The laws of refraction: (1) the incident ray, refracted ray and normal lie in one plane; (2) for a given pair of media and colour, sin i / sin r is constant (Snell's law). This constant is the refractive index; the absolute refractive index is μ = c/V, the speed in vacuum ÷ the speed in the medium.

Going from rarer air into denser glass, light slows down and bends towards the normal, so r is less than i; sin i / sin r = μ.

Illustration drawn for QuestionBuddy.

Understand Laws of Refraction and Refractive Index

Refraction is the change in direction of light as it passes obliquely from one transparent medium into another. It happens because light travels at different speeds in different media. At the same boundary some light is also reflected: this is partial reflection, which is why a window shows a faint reflection.

Direction of bending.

Rarer to denser (e.g. air → glass, where light slows down): the ray bends towards the normal, $r < i$ .
Denser to rarer (e.g. water → air, where light speeds up): the ray bends away from the normal, $r > i$ .

A ray passes undeviated if (1) it falls normally on the boundary ( $i = 0°$ , so $r = 0°$ ), or (2) the two media have the same refractive index.

Laws of refraction.
1. The incident ray, the refracted ray and the normal at the point of incidence all lie in the same plane.
2. Snell's law: for a given pair of media and light of a given colour, the ratio of the sine of the angle of incidence to the sine of the angle of refraction is constant:

$\frac{s i n i}{s i n r} =_{1} μ_{2} .$

The constant $_{1} μ_{2}$ is the refractive index of medium 2 with respect to medium 1.

Absolute refractive index. For light going from vacuum (or, very nearly, air) into a medium:

$μ = \frac{c}{V} = \frac{speed of light in vacuum}{speed of light in the medium} .$

It has no unit and is always greater than 1.

Medium	Speed of light (m/s)	μ
Vacuum	$3 \times 1 0^{8}$	1
Air	about $3 \times 1 0^{8}$	about 1.0003
Water	about $2.25 \times 1 0^{8}$	1.33
Glass	about $2 \times 1 0^{8}$	1.5
Diamond	about $1.24 \times 1 0^{8}$	2.42

Relative refractive index. $_{a} μ_{b} = \frac{μ _{b}}{μ _{a}} = \frac{V _{a}}{V _{b}}$ .

Principle of reversibility. If the direction of a ray is reversed, it retraces its path. Hence

$_{a} μ_{b} \times_{b} μ_{a} = 1$ , so $_{b} μ_{a} = \frac{1}{_{a} μ _{b}}$ .

What μ depends on. (1) The nature of the medium; (2) the wavelength (colour) of light: μ is greater for violet than for red; (3) the temperature: μ falls slightly as the medium gets hotter and less dense. It does not depend on the angle of incidence: changing $i$ changes $r$ , but the ratio $\frac{s i n i}{s i n r}$ stays the same.

Speed, wavelength and frequency. On entering a new medium:

frequency stays the same (set by the source);
speed changes: $V = \frac{c}{μ}$ ;
wavelength changes in the same ratio, since $V = f λ$ : $λ_{medium} = \frac{λ _{vacuum}}{μ}$ .

The colour we see depends on the frequency, so light does not change colour inside glass.

Experimental verification of Snell's law. Fix a rectangular glass block on paper, trace its outline, and use pins to trace a ray through it for several angles of incidence. Measure $i$ and $r$ at the first face each time and calculate $\frac{s i n i}{s i n r}$ : it comes out the same (within error), which verifies the second law and gives μ of the glass.

Laws of Refraction and Refractive Index: formulas and key facts

Snell's law: $\frac{s i n i}{s i n r} =_{1} μ_{2}$; Given pair of media and colour.
Absolute refractive index: $μ = \frac{c}{V}$; c = 3 × 10⁸ m/s; μ has no unit.
Relative refractive index: $_{a} μ_{b} = \frac{μ _{b}}{μ _{a}} = \frac{V _{a}}{V _{b}}$; Ratio of speeds, first medium on top.
Principle of reversibility: $_{b} μ_{a} = \frac{1}{_{a} μ _{b}}$; Name it as 'principle of reversibility of light'.
Wave equation in a medium: $V = f λ, λ_{medium} = \frac{λ _{vacuum}}{μ}$; f is unchanged by refraction.

How to solve Laws of Refraction and Refractive Index questions

Decide which of the three tools fits: Snell's law for angles, μ = c/V for speeds, V = fλ for wavelengths.

1For angles: write $\frac{s i n i}{s i n r} = μ$ with $i$ in the first medium; rearrange for the unknown sine, then the angle.
2For speeds: $μ = \frac{c}{V}$ , or $_{a} μ_{b} = \frac{V _{a}}{V _{b}}$ for two media.
3For distances covered in equal times: speed is proportional to distance, so $μ = \frac{distance in vacuum}{distance in medium}$ .
4For a reversed path, use $_{b} μ_{a} = \frac{1}{_{a} μ _{b}}$ and name the principle of reversibility.
5For wavelength: keep $f$ fixed and divide $λ$ by μ.
6Check: μ > 1 for any medium relative to vacuum; going into a denser medium, $r < i$ .

Laws of Refraction and Refractive Index 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.

Light slows down in water

Suppose sunlight passes down through 3 m of water in a diving pool. (μ of water $= \frac{4}{3}$ , $c = 3 \times 1 0^{8}$ m/s)

How long does it take to cross the water, compared with 3 m of air?

Try it first, then show the solutionSolution

$V = \frac{3 \times 1 0 ^{8}}{4/3} = 2.25 \times 1 0^{8}$ m/s.
Water: $t = \frac{3}{2.25 \times 1 0 ^{8}} \approx 1.33 \times 1 0^{- 8}$ s.
Air: $t = \frac{3}{3 \times 1 0 ^{8}} = 1 \times 1 0^{- 8}$ s.

Answer: About $1.33 \times 1 0^{- 8}$ s, μ times as long as in air.

Memory hook: μ tells you how many times slower light is in the medium.

Partial reflection in a window

Imagine standing in a brightly lit room at night, looking out through a clear glass window.

Why do you see your own reflection, though you see none in the daytime?

Try it first, then show the solutionSolution

At the glass surface, most light is refracted through, but a small part is reflected (partial reflection).
At night, almost no light comes in from outside, so this faint reflected light is easy to see; by day, bright outside light swamps it.

Answer: Partial reflection at the glass, noticeable only when the other side is dark.

Memory hook: Every boundary reflects a little; darkness behind makes it show.

Tricks to remember Laws of Refraction and Refractive Index

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

FAST: Fast to slow bends Towards
Light going from a Fast medium to a Slow one bends Towards the normal; slow to fast bends away.
Use it when: Direction of bending.
Frequency is fixed
'The source sets the beat': frequency never changes at a boundary; speed and wavelength change together.
Use it when: MCQs on what changes in refraction.
μ = c over V, 'see over vee'
Speed in vacuum on top, so μ is always more than 1.
Use it when: Speed and refractive index numericals.
Reverse the path, flip the fraction
Going back the other way, the refractive index is the reciprocal: 9/8 becomes 8/9.
Use it when: Reversibility questions.

Laws of Refraction and Refractive Index: solved examples

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

Example 1: What μ depends on · 1 mark · MCQBoard level

The refractive index of a glass depends on:
(a) the angle of incidence
(b) the colour of the light
(c) the thickness of the glass
(d) the angle of refraction

Try it first, then show the solutionSolution

μ depends on the medium, the wavelength (colour) of light and temperature. Changing $i$ changes $r$ but not the ratio $\frac{s i n i}{s i n r}$ ; thickness affects only lateral displacement.

Answer: (b) the colour of the light

Example 2: Speed in a dense glass · 2 marks · Short answerBoard level

The refractive index of a dense flint glass is 1.6. Find the speed of light in it. ( $c = 3 \times 1 0^{8}$ m/s)

Try it first, then show the solutionSolution

$μ = \frac{c}{V}$ , so $V = \frac{c}{μ}$ . (1)
$V = \frac{3 \times 1 0 ^{8}}{1.6} = 1.875 \times 1 0^{8}$ m/s. (1)

Answer: $1.875 \times 1 0^{8}$ m/s

Example 3: Angle of refraction from Snell's law · 3 marks · Short answerHarder board level

A ray in air strikes the surface of a transparent liquid of refractive index $2$ at an angle of incidence of $45°$ . Find (a) the angle of refraction, (b) the angle through which the ray is deviated.

Try it first, then show the solutionSolution

(a) $sin r = \frac{s i n 45°}{2} = \frac{1/ 2}{2} = \frac{1}{2}$ . (1)
So $r = 30°$ . (1)
(b) Deviation $= i - r = 45° - 30° = 15°$ . (1)

Answer: (a) $30°$ (b) $15°$

Example 4: Relative index from speeds · 3 marks · Short answerHarder board level

Light travels at $2.4 \times 1 0^{8}$ m/s in medium A and at $1.8 \times 1 0^{8}$ m/s in medium B. ( $c = 3 \times 1 0^{8}$ m/s)
(a) Find the absolute refractive index of each.
(b) Find the refractive index of B with respect to A.
(c) Find the refractive index of A with respect to B, and name the principle you use.

Try it first, then show the solutionSolution

(a) $μ_{A} = \frac{3}{2.4} = 1.25$ ; $μ_{B} = \frac{3}{1.8} \approx 1.67$ . (1)
(b) $_{A} μ_{B} = \frac{V _{A}}{V _{B}} = \frac{2.4}{1.8} = \frac{4}{3} \approx 1.33$ . (1)
(c) $_{B} μ_{A} = \frac{1}{_{A} μ _{B}} = \frac{3}{4} = 0.75$ , by the principle of reversibility of light. (1)

Answer: (a) 1.25, about 1.67 (b) $\frac{4}{3}$ (c) 0.75; principle of reversibility

Example 5: Does light become invisible in glass? · 4 marks · Long answerHOTS / competency

Green light of wavelength 540 nm in air passes into glass of refractive index 1.5. ( $c = 3 \times 1 0^{8}$ m/s)
(a) Calculate its frequency.
(b) Calculate its speed and its wavelength inside the glass.
(c) Radiation of wavelength 360 nm in air is ultraviolet, which we cannot see. Does the green light become invisible inside the glass? Explain.

Try it first, then show the solutionSolution

(a) $f = \frac{c}{λ} = \frac{3 \times 1 0 ^{8}}{540 \times 1 0 ^{- 9}} \approx 5.56 \times 1 0^{14}$ Hz. (1)
(b) $V = \frac{3 \times 1 0 ^{8}}{1.5} = 2 \times 1 0^{8}$ m/s; $λ = \frac{540}{1.5} = 360$ nm. (2)
(c) No. What kind of radiation it is (and its colour) is fixed by its frequency, which refraction does not change; it is still green light, even though its wavelength in glass is 360 nm. (1)

Answer: (a) About $5.56 \times 1 0^{14}$ Hz (b) $2 \times 1 0^{8}$ m/s, 360 nm (c) No; the frequency, and so the colour, is unchanged.

Example 6: Case study: verifying Snell's law in the laboratory · 4 marks · Case-basedHOTS / competency

A student traces rays through a rectangular glass block and records:

$i$	$sin i$	$sin r$
$30°$	0.500	0.333
$45°$	0.707	0.471
$60°$	0.866	0.577

(a) Calculate $\frac{s i n i}{s i n r}$ for each, to two decimal places.
(b) What do the results show?
(c) Find the speed of light in this glass. ( $c = 3 \times 1 0^{8}$ m/s)
(d) Why does $r$ increase with $i$ even though μ does not change?

Try it first, then show the solutionSolution

(a) $\frac{0.500}{0.333} \approx 1.50$ ; $\frac{0.707}{0.471} \approx 1.50$ ; $\frac{0.866}{0.577} \approx 1.50$ . (1)
(b) The ratio is constant, verifying Snell's law; μ of the glass is 1.50. (1)
(c) $V = \frac{3 \times 1 0 ^{8}}{1.5} = 2 \times 1 0^{8}$ m/s. (1)
(d) μ fixes the ratio of the sines, so if $sin i$ increases, $sin r$ must increase in proportion. (1)

Answer: (a) 1.50 each (b) Snell's law holds; μ = 1.5 (c) $2 \times 1 0^{8}$ m/s (d) The ratio is fixed, so r rises with i.

Where students lose marks in Laws of Refraction and Refractive Index

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

Mistake: Naming the wrong principle
Finding $_{g} μ_{w}$ from $_{w} μ_{g}$ uses the principle of reversibility, not Snell's law.
Wrong working
'Principle used: Snell's law' or 'law of reflection'.
Right working
'Principle of reversibility of light.'
Do this: When a question says 'Name', give the name only; when it says 'State', give the statement.
Usually costs: Reported by CISCE examiners for 2024 Q5(i).
Mistake: Thinking μ depends on the angle of incidence
μ is a property of the media and the colour; changing $i$ just changes $r$ in step.
Wrong working
'Since μ = sin i / sin r, a larger i gives a larger μ.'
Right working
'μ is independent of i; it depends on the medium, wavelength and temperature.'
Do this: Learn the three factors and the one non-factor together.
Usually costs: Reported for 2025 Q2(i)(b).
Mistake: Forgetting that light is fastest in vacuum
In a given time light covers the greatest distance in vacuum; in any medium it covers less.
Wrong working
'In the time light travels 12 m in vacuum, it travels 15 m in glass: true.'
Right working
'False: light is slower in glass, so in that time it covers only $\frac{12}{1.5} = 8$ m.' In general, $μ = \frac{speed in vacuum}{speed in medium}$ , and for equal times $μ = \frac{distance in vacuum}{distance in medium}$ .
Do this: Write $V = \frac{distance}{time}$ for each medium first.
Usually costs: Reported for 2024 Q5(ii).
Mistake: Saying frequency changes on refraction
Only speed and wavelength change; frequency is set by the source.
Wrong working
'In glass the frequency decreases.'
Right working
'Frequency stays the same; speed and wavelength decrease.'
Do this: Memorise 'frequency fixed' before attempting such MCQs.
Usually costs: The MCQ mark; 2025 Q1(iv) saw guesswork here.

Exam tips

State both laws of refraction; the 'same plane' law is often forgotten.
For 'Yes or No' parts (such as 'does μ stay the same if the temperature changes?'), write a clear Yes or No first; the 2024 answer was No.
Show $μ = \frac{c}{V}$ before substituting, and give speeds in m/s with powers of ten.
In verification questions, tabulate $sin i$ , $sin r$ and their ratio.

Practice questions on Laws of Refraction and Refractive Index

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 speed of light in water is about:
(a) $3 \times 1 0^{8}$ m/s
(b) $2.25 \times 1 0^{8}$ m/s
(c) $2 \times 1 0^{8}$ m/s
(d) $1.24 \times 1 0^{8}$ m/s
Hint
μ of water is about 1.33.
Answer
(b) $2.25 \times 1 0^{8}$ m/s
Q2 · 2 marks · Short answerBoard level
State two conditions under which a ray of light passes from one medium into another without changing direction.
Hint
Think about the angle of incidence and the two media.
Answer
(1) The ray falls normally on the boundary ( $i = 0°$ ). (2) The two media have the same refractive index.
Q3 · 2 marks · Short answerHarder board level
Light travels at $2.04 \times 1 0^{8}$ m/s in a cooking oil. Find the refractive index of the oil. ( $c = 3 \times 1 0^{8}$ m/s)
Hint
$μ = \frac{c}{V}$ .
Answer
$μ = \frac{3 \times 1 0 ^{8}}{2.04 \times 1 0 ^{8}} \approx 1.47$ .
Q4 · 2 marks · Short answerHarder board level
In a certain time, light travels 24 cm in vacuum but only 15 cm in a transparent plastic. Find the refractive index of the plastic and the speed of light in it.
Hint
In equal times, speed is proportional to distance.
Answer
$μ = \frac{24}{15} = 1.6$ ; $V = \frac{3 \times 1 0 ^{8}}{1.6} = 1.875 \times 1 0^{8}$ m/s.
Q5 · 3 marks · Short answerHarder board level
For light passing from water into a certain glass, the relative refractive index is 1.2. (a) What is the refractive index for light going from this glass into water? Name the principle used. (b) If the absolute refractive index of the glass is 1.56, find that of water.
Hint
$_{w} μ_{g} = \frac{μ _{g}}{μ _{w}}$ .
Answer
(a) $_{g} μ_{w} = \frac{1}{1.2} \approx 0.83$ ; principle of reversibility of light. (b) $μ_{w} = \frac{1.56}{1.2} = 1.3$ .
Q6 · 3 marks · Short answerHarder board level
A ray travelling in glass (μ = 1.5) meets the glass–air surface at an angle of incidence of $30°$ . Find the angle of refraction in air. Does the ray bend towards or away from the normal?
Hint
Going from glass to air, $\frac{s i n i}{s i n r} = \frac{1}{1.5}$ .
Answer
$sin r = 1.5 \times sin 30° = 0.75$ , so $r \approx 48.6°$ . It bends away from the normal.
Q7 · 4 marks · Long answerHOTS / competency
A red ray and a violet ray strike the same face of a glass block at the same angle of incidence. Which ray (a) bends more on entering, (b) travels more slowly in the glass, (c) has the shorter wavelength in the glass, (d) suffers the greater lateral displacement? Give one reason that links all four.
Hint
Glass has a larger μ for violet.
Answer
Violet in every case. The glass has a higher refractive index for violet, so violet slows down more ( $V = \frac{c}{μ}$ ), its wavelength shrinks more ( $λ = \frac{λ _{0}}{μ}$ ), it bends more, and so it is displaced more.

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 absolute refractive index?Show answer
$μ = \frac{c}{V}$ .
2.Which quantity does not change when light is refracted?Show answer
Frequency.
3.Refractive index of a medium in which light travels at $2.25 \times 1 0^{8}$ m/s?Show answer
$\frac{4}{3} \approx 1.33$ .
4.If $_{a} μ_{b} = 1.25$ , what is $_{b} μ_{a}$ ?Show answer
0.8.
5.Air to glass: towards or away from the normal?Show answer
Towards.

Laws of Refraction and Refractive Index: frequently asked questions

What are the two laws of refraction?

First, the incident ray, refracted ray and normal at the point of incidence lie in the same plane. Second, for a given pair of media and colour, sin i / sin r is a constant (Snell's law), the refractive index.

Why does light bend when it enters glass?

Light travels more slowly in glass than in air. When a beam meets the surface at an angle, one side of it slows down first, so the beam swings round towards the normal.

Does the refractive index depend on the angle of incidence?

No. It depends on the medium, the colour (wavelength) of light and the temperature. A different angle of incidence gives a different angle of refraction, but the ratio of their sines is the same.