ScienceCBSE Class 10 · Light – Reflection and Refraction

Refraction of Light and Refractive Index

Q: What is refraction of light?

The change in direction of light when it passes obliquely from one transparent medium into another, because its speed is different in the two media.

Q: What are the laws of refraction?

The incident ray, refracted ray and normal lie in the same plane; and sin i/sin r is a constant (Snell's law) for a given colour and pair of media.

Q: What does refractive index tell us?

How much slower light travels in a medium than in vacuum or air: n = c/v. A larger value means more bending and an optically denser medium.

Q: Does refractive index have a unit?

No. It is a ratio of two speeds.

Q: Why does a pencil look bent in water?

Light from the dipped part bends away from the normal as it leaves water, so the part under water appears raised, making the pencil look bent at the surface.

Updated 14 October 2026 · Fact-checked

Refraction is the bending of light when it passes obliquely from one transparent medium to another, because light travels at different speeds in them. It obeys two laws, including Snell's law, sin i/sin r = constant. The refractive index n = c/v compares the speed of light in vacuum or air with its speed in the medium.

Understand Refraction of Light and Refractive Index

What refraction looks like. The bottom of a tank of water looks raised; a pencil dipped at an angle in water looks bent at the surface; a lemon in a glass of water looks bigger; letters seen through a thick glass slab look raised. All these happen because light changes direction when it crosses from one transparent medium into another at an angle.

Why it bends. Light travels fastest in vacuum, at $3 \times 1 0^{8}$ m/s. In air it is only marginally slower, but in glass or water it is considerably slower. When light enters a medium where it travels more slowly (optically denser), it bends towards the normal. When it enters a medium where it travels faster (optically rarer), it bends away from the normal. A ray that falls along the normal (perpendicular to the surface) passes straight through without bending.

Refraction through a rectangular glass slab. A ray entering the slab from air bends towards the normal; leaving the slab into air, it bends away. Because the two faces are parallel, the bending at the two faces is equal and opposite, so the emergent ray is parallel to the incident ray but shifted sideways (lateral displacement).

Laws of refraction.
1. The incident ray, the refracted ray and the normal to the interface at the point of incidence all lie in the same plane.
2. For light of a given colour and a given pair of media, the ratio of the sine of the angle of incidence to the sine of the angle of refraction is a constant: $\frac{s i n i}{s i n r} = constant$ . This is Snell's law; the constant is the refractive index of the second medium with respect to the first.

Refractive index. When light passes from medium 1 into medium 2, we write $n_{21}$ for the index of medium 2 relative to medium 1: $n_{21} = \frac{v _{1}}{v _{2}}$ (speed in medium 1 divided by speed in medium 2). If medium 1 is vacuum or air, we get the absolute refractive index: $n_{m} = \frac{c}{v}$ . NCERT's table gives values such as water 1.33, kerosene 1.44, crown glass 1.52 and diamond 2.42 (you need not memorise the table). Water's n = 1.33 means light is 1.33 times faster in air than in water. Useful results:

$n_{21} = \frac{n _{2}}{n _{1}}$ and $n_{12} = \frac{1}{n _{21}}$ .
Refractive index has no unit, since it is a ratio of speeds.

Optical density is not mass density. Of two media, the one with the larger refractive index is optically denser, and light is slower in it. Kerosene (n = 1.44) is optically denser than water (n = 1.33), even though its mass density is lower than that of water.

Refraction of Light and Refractive Index: formulas and key facts

Snell's law: $\frac{s i n i}{s i n r} = n_{21}$; For a given colour and pair of media.
Absolute refractive index: $n_{m} = \frac{c}{v}$; c = 3 × 10⁸ m/s; no unit.
Relative refractive index: $n_{21} = \frac{v _{1}}{v _{2}} = \frac{n _{2}}{n _{1}}$; Medium 2 with respect to medium 1.
Reverse direction: $n_{12} = \frac{1}{n _{21}}$; Swapping the media inverts the value.
Speed in a medium: $v = \frac{c}{n}$; Larger n means slower light and an optically denser medium.

How to solve Refraction of Light and Refractive Index questions

For refraction questions, decide whether you need direction (bending), speeds or angles.

1Identify the two media and which is optically denser (larger n).
2For direction: rarer → denser bends towards the normal; denser → rarer bends away; along the normal, no bending.
3For speed: use $v = \frac{c}{n}$ with c = $3 \times 1 0^{8}$ m/s.
4For relative index: $n_{21} = \frac{n _{2}}{n _{1}}$ (the medium light enters on top).
5For angles: use $sin r = \frac{s i n i}{n _{21}}$ with standard angles (30°, 45°, 60°).
6State the answer with the unit (m/s for speed; none for n) and a sense-check (light is slower in the denser medium).

Refraction of Light 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.

Speed of light and optical density

Suppose you are making a science-fair poster comparing how fast light travels in water (n = 1.33) and in a diamond (n = 2.42), and a visitor asks whether diamond is 'heavier for light'.

Find the speed of light in water and in diamond, the refractive index of diamond with respect to water, and explain what 'optically denser' means.

Try it first, then show the solutionSolution

Water: $v = \frac{c}{n} = \frac{3 \times 1 0 ^{8}}{1.33} \approx 2.26 \times 1 0^{8}$ m/s (check: $1.33 \times 2.26 \approx 3.0$ ).
Diamond: $v = \frac{3 \times 1 0 ^{8}}{2.42} \approx 1.24 \times 1 0^{8}$ m/s (check: $2.42 \times 1.24 \approx 3.0$ ).
Diamond with respect to water: $n = \frac{2.42}{1.33} \approx 1.82$ , equal to $\frac{2.26}{1.24} \approx 1.82$ .
Optically denser means light travels more slowly in it (larger refractive index); it has nothing to do with mass. Diamond is optically denser than water, and light from water into diamond bends towards the normal.

Answer: Water ≈ 2.26 × 10⁸ m/s; diamond ≈ 1.24 × 10⁸ m/s; n(diamond w.r.t. water) ≈ 1.82. Optically denser means slower light, not greater mass.

Memory hook: Bigger n, slower light, more bending.

Tricks to remember Refraction of Light and Refractive Index

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

FST: Fast to Slow, Towards
Going from a Fast medium to a Slow one, light bends Towards the normal (and away the other way).
Use it when: Predicting the direction of bending.
Top goes into
In $n_{21}$ , the medium light goes into (2) is on top: $n_{21} = \frac{n _{2}}{n _{1}}$ .
Use it when: Relative refractive index.
Slab = parallel shift
In a glass slab the ray comes out parallel, just shifted.
Use it when: Slab ray-diagram questions.

Refraction of Light and Refractive Index: solved examples

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

Example 1: Speed of light in glass · 2 marks · Very short answerBoard level

A glass block has refractive index 1.50. How fast does light travel inside it? (Take c = $3 \times 1 0^{8}$ m/s.)

Try it first, then show the solutionSolution

$n = \frac{c}{v}$ , so $v = \frac{c}{n}$ (1 mark).
$v = \frac{3 \times 1 0 ^{8}}{1.50} = 2 \times 1 0^{8}$ m/s. Check: $1.50 \times 2 \times 1 0^{8} = 3 \times 1 0^{8}$ (1 mark).

Answer: $2 \times 1 0^{8}$ m/s.

Example 2: Snell's law with standard angles · 3 marks · Short answerHarder board level

A ray of light passes from air into a medium of refractive index $2$ at an angle of incidence of 45°. (a) Find the angle of refraction. (b) Does it bend towards or away from the normal? (c) Find the speed of light in the medium.

Try it first, then show the solutionSolution

(a) $sin r = \frac{s i n i}{n} = \frac{s i n 45°}{2} = \frac{1/ 2}{2} = \frac{1}{2}$ , so $r = 30°$ (1½ marks).
(b) r < i: it bends towards the normal, entering a denser medium (½ mark).
(c) $v = \frac{3 \times 1 0 ^{8}}{2} = \frac{3 \times 1 0 ^{8}}{1.414} \approx 2.12 \times 1 0^{8}$ m/s (1 mark).

Answer: (a) 30°. (b) Towards the normal. (c) ≈ 2.12 × 10⁸ m/s.

Example 3: Relative refractive index · 3 marks · Short answerHarder board level

The refractive indices of water and crown glass are 1.33 and 1.52. Find (a) the refractive index of crown glass with respect to water, (b) the refractive index of water with respect to crown glass, (c) the ratio of the speed of light in water to that in crown glass.

Try it first, then show the solutionSolution

(a) $n_{g w} = \frac{n _{g}}{n _{w}} = \frac{1.52}{1.33} \approx 1.14$ (1 mark).
(b) $n_{w g} = \frac{1}{1.14} \approx 0.875$ (also $\frac{1.33}{1.52} = 0.875$ ) (1 mark).
(c) $\frac{v _{w}}{v _{g}} = \frac{n _{g}}{n _{w}} \approx 1.14$ : light is about 1.14 times faster in water (1 mark).

Answer: (a) ≈ 1.14 (b) ≈ 0.875 (c) ≈ 1.14.

Example 4: Glass slab · 3 marks · Short answerHarder board level

Draw a ray diagram for a ray of light passing obliquely through a rectangular glass slab. Mark the angles of incidence, refraction and emergence, and explain why the emergent ray is parallel to the incident ray but shifted.

Try it first, then show the solutionSolution

Diagram: incident ray, normal at the first face, refracted ray bending towards the normal inside the slab, normal at the second face, emergent ray bending away from the normal (1 mark).
Angles marked: i at entry, r inside, e at exit; e = i (1 mark).
The bending at the two parallel faces is equal and opposite (air to glass, then glass to air), so the emergent ray is parallel to the incident ray but laterally displaced (shifted sideways); the shift is larger for a thicker slab (1 mark).

Answer: Emergent ray parallel to incident ray (e = i), shifted sideways.

Example 5: Comparing media · 3 marks · Short answerHOTS / competency

Using NCERT's values (kerosene 1.44, turpentine oil 1.47, water 1.33): (a) In which of these does light travel fastest? (b) A ray travels from kerosene into water. Does it bend towards or away from the normal? (c) Kerosene floats on water. A student says kerosene must be optically rarer. Evaluate.

Try it first, then show the solutionSolution

(a) Water, which has the lowest refractive index of the three (1 mark).
(b) Kerosene (1.44) to water (1.33) is optically denser to rarer, so the ray speeds up and bends away from the normal (1 mark).
(c) Wrong. Floating depends on mass density; optical density depends on refractive index. Kerosene has a higher refractive index than water, so it is optically denser even though its mass density is lower (1 mark).

Answer: (a) Water. (b) Away from the normal. (c) Floating is about mass density; kerosene is optically denser.

Where students lose marks in Refraction of Light and Refractive Index

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

Mistake: Inverting the refractive index formula
Students write n = v/c.
Wrong working
n = v/c = (2 × 10⁸)/(3 × 10⁸) = 0.67.
Right working
n = c/v = (3 × 10⁸)/(2 × 10⁸) = 1.5 (always ≥ 1 for media).
Do this: Absolute refractive index is never less than 1.
Usually costs: The answer mark.
Mistake: Wrong direction of bending
Students memorise 'towards' without the condition.
Wrong working
Light going from glass to air bends towards the normal.
Right working
From glass (denser) to air (rarer), light bends away from the normal.
Do this: Check which medium is slower.
Usually costs: 1 mark in diagrams and MCQs.
Mistake: Confusing optical density with mass density
The word 'dense' suggests heaviness.
Wrong working
Water is optically denser than kerosene because it is heavier.
Right working
Kerosene (n = 1.44) is optically denser than water (n = 1.33).
Do this: Compare refractive indices, not mass.
Usually costs: 1 mark.
Mistake: Missing unit or adding one to n
Unit habits from other formulae.
Wrong working
n = 1.5 m/s.
Right working
n = 1.5 (no unit); speed in m/s.
Do this: A ratio of speeds has no unit.
Usually costs: ½ mark.

Exam tips

State both laws of refraction fully, including 'for a given colour and pair of media'.
Draw normals as dotted lines at the point of incidence and mark angles from the normal, not from the surface.
Write $v = \frac{c}{n}$ before substituting; examiners award the formula.
You need not memorise the refractive index table; values are given when needed.
Explain everyday effects (raised tank bottom, bent pencil) in terms of rays bending away from the normal as they leave water.

Practice questions on Refraction of Light 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
A ray of light enters water from air along the normal. Its angle of refraction is:
(a) 0° (b) 45° (c) 90° (d) depends on the refractive index
Hint
Light along the normal does not bend.
Answer
(a) 0°.
Q2 · 1 mark · Assertion-reasonBoard level
Assertion (A): A ray of light travelling from air into glass bends towards the normal.
Reason (R): The speed of light is greater in glass than in air.
(a) Both A and R are true and R is the correct explanation of A.
(b) Both A and R are true but R is not the correct explanation of A.
(c) A is true but R is false.
(d) A is false but R is true.
Hint
Is light faster or slower in glass?
Answer
(c). Light is slower in glass, so it bends towards the normal.
Q3 · 2 marks · Very short answerHarder board level
Diamond has a refractive index of 2.42. Explain in words what this number tells us, and calculate how fast light moves through diamond.
Hint
n = c/v.
Answer
It means the speed of light in air (vacuum) is 2.42 times its speed in diamond. v = (3 × 10⁸)/2.42 ≈ 1.24 × 10⁸ m/s.
Q4 · 4 marks · Case-basedHOTS / competency
Read the passage and answer.
Suppose a student shines a laser pointer from air into a block of a transparent material at an angle of incidence of 60° and finds the angle of refraction to be 30°.
(a) State Snell's law. (1 mark)
(b) Find the refractive index of the material. (1 mark)
(c) Find the speed of light in it and state, giving a reason, whether the beam would bend towards or away from the normal on leaving the block into air. (2 marks)
Hint
sin 60° = √3/2, sin 30° = 1/2.
Answer
(a) For a given colour and pair of media, sin i/sin r is constant. (b) n = sin 60°/sin 30° = (√3/2)/(1/2) = √3 ≈ 1.73. (c) v = (3 × 10⁸)/1.73 ≈ 1.73 × 10⁸ m/s. Leaving the block, light passes from denser to rarer, speeds up and bends away from the normal.
Q5 · 3 marks · Short answerHarder board level
The refractive index of medium A is 1.5 and of medium B is 1.2. (a) Find the refractive index of A with respect to B. (b) In which medium is light faster, and by what factor? (c) If light goes from A to B at an angle of incidence of 30°, will the angle of refraction be more or less than 30°? Explain without calculating.
Hint
Use n_AB = n_A/n_B.
Answer
(a) n_AB = 1.5/1.2 = 1.25. (b) In B; v_B/v_A = n_A/n_B = 1.25, so light is 1.25 times faster in B. (c) More than 30°: going from A (denser) to B (rarer), light bends away from the normal.
Q6 · 3 marks · Short answerHOTS / competency
A coin at the bottom of a bucket of water appears raised when seen from above. Explain using a ray diagram idea, and say whether the effect would be greater or smaller if the water were replaced by a liquid of higher refractive index.
Hint
Rays from the coin bend away from the normal as they leave the water.
Answer
Rays from the coin pass from water (denser) into air (rarer) and bend away from the normal. Our eyes trace the bent rays back in straight lines, which meet above the real coin, so it appears raised. With a liquid of higher refractive index, rays bend more on leaving, so the coin would appear raised even 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.Speed of light in vacuum?Show answer
$3 \times 1 0^{8}$ m/s.
2.State Snell's law.Show answer
sin i/sin r is constant for a given colour and pair of media.
3.Refractive index of water (NCERT)?Show answer
1.33.
4.Direction of bending from rarer to denser?Show answer
Towards the normal.
5.Emergent ray from a glass slab is...?Show answer
Parallel to the incident ray, laterally displaced.
6.Which is optically denser: kerosene or water?Show answer
Kerosene.

Refraction of Light and Refractive Index: frequently asked questions

What is refraction of light?

The change in direction of light when it passes obliquely from one transparent medium into another, because its speed is different in the two media.

What are the laws of refraction?

The incident ray, refracted ray and normal lie in the same plane; and sin i/sin r is a constant (Snell's law) for a given colour and pair of media.

What does refractive index tell us?

How much slower light travels in a medium than in vacuum or air: n = c/v. A larger value means more bending and an optically denser medium.

Does refractive index have a unit?

No. It is a ratio of two speeds.

Why does a pencil look bent in water?

Light from the dipped part bends away from the normal as it leaves water, so the part under water appears raised, making the pencil look bent at the surface.