Is Snell's law on the data sheet?

Yes. NESA's sample data sheet for the new (2025) syllabus includes nx = c ÷ vx, n1 sin θ1 = n2 sin θ2 and sin θc = n2 ÷ n1. The law of reflection is not an equation, so learn it in words. Check which sheet your school gives you for Year 11 exams.

What is the difference between reflection and refraction?

Reflection is light bouncing off a surface and staying in the same medium, with the angle of incidence equal to the angle of reflection. Refraction is light passing into a new medium and changing direction because its speed changes.

Why do you measure angles from the normal and not the surface?

Because the laws are written that way: Snell's law and the law of reflection only work with angles from the normal. The normal also works for curved surfaces, where 'the surface' has no single direction.

Does light bend towards or away from the normal?

Towards the normal when it goes into a higher refractive index and slows down (air into glass). Away from the normal when it goes into a lower refractive index and speeds up (water into air).

What are the two conditions for total internal reflection?

The light must be travelling towards a medium with a lower refractive index, and its angle of incidence must be greater than the critical angle.

Which situation can produce total internal reflection?

Light in glass meeting air at an angle of incidence bigger than the critical angle

Light in air meeting glass at an angle of incidence bigger than the critical angle

Light in glass meeting air at an angle of incidence smaller than the critical angle

Light in air meeting water along the normal

Diamond has a refractive index of 2.42. What is the critical angle for light inside diamond meeting air?

There is no critical angle for diamond.

Light passes from air into water. Which property of the light stays the same?

Its direction, at every angle of incidence

Year 11 Physics · Waves · Wave behaviours · 13 min read

Refraction and Snell's law

Light bends when it crosses from one material into another: a straw looks broken in a glass of water, and a pool looks shallower than it is. This is refraction, and it happens because light travels at different speeds in different materials.

This guide covers what Year 11 Physics asks you to do with light at a boundary: the law of reflection, the refractive index n = c/v, Snell's law, the critical angle and total internal reflection (the physics of optical fibres). Then come the common mistakes, a quick quiz and a full worked example. One rule runs through all of it: every angle is measured from the normal.

What you need to know

Describe the law of reflection and where you see it in real examples.
Analyse wave motion using ray diagrams and linear wavefront diagrams.
Show refraction between two media in a practical investigation.
Relate a medium's refractive index to the speed of light in it, and use n_x = c ÷ v_x to solve problems.
Solve problems with n₁ sin θ₁ = n₂ sin θ₂, the law of refraction (Snell's law).
Use sin θ_c = n₂ ÷ n₁ for critical angle and total internal reflection problems.
Relate light speeding up or slowing down at a boundary to the difference in refractive index across it.
Draw ray diagrams of refraction at a boundary and of reflection off plane mirrors.
Measure a material's refractive index in a lab experiment and assess how accurate the result is.

The equations you will use:

n_x = c ÷ v_xRefractive index of medium x. c = 3.00 × 10⁸ m s⁻¹. n has no unit and is never less than 1.

n₁ sin θ₁ = n₂ sin θ₂Snell's law. Medium 1 is where the light comes from. Both angles are measured from the normal.

sin θ_c = n₂ ÷ n₁Critical angle, for light going from the higher index n₁ to the lower index n₂.

angle of incidence = angle of reflection not on the data sheetThe law of reflection, both angles from the normal. It is a rule in words, not a data-sheet equation.

Dot points: PY11-WV-19, PY11-WV-20, PY11-WV-21, PY11-WV-22, PY11-WV-23, PY11-WV-24, PY11-WV-25, PY11-WV-26, PY11-WV-27, PY11-WV-28 (2025 Physics syllabus, Year 11), in our own words.

Mini lesson

Reflection: the normal comes first

The normal is a line drawn at 90° to a surface, at the point where the ray hits it. The law of reflection says the angle of incidence equals the angle of reflection, with both measured from the normal, and the incident ray, reflected ray and normal all lie in the same plane.

You see it in a bathroom mirror, in a still lake, in a periscope (two mirrors at 45°) and in a bike reflector. A smooth surface reflects a parallel beam as a parallel beam, so you see an image. A rough surface (paper, a wall) still obeys the law at every tiny patch, but the normals point every which way, so the light scatters and you see no image.

Law of reflection: i = r, both measured from the normal (the dashed line), never from the mirror.

Why light bends: it changes speed

Light travels at c = 3.00 × 10⁸ m s⁻¹ in a vacuum (air is so close that we use n = 1.00) and more slowly in water, glass and plastic. The refractive index says how much slower: n = c ÷ v. Glass with n = 1.50 slows light to 3.00 × 10⁸ ÷ 1.50 = 2.00 × 10⁸ m s⁻¹. A higher n means slower light.

A wavefront diagram shows why the change of speed bends the ray. One side of each wavefront reaches the boundary first and slows down while the rest is still moving fast, so the wavefront pivots. The frequency stays the same (it is set by the source), so the slower wave has a shorter wavelength (v = fλ), and the wavefronts bunch up.

Into a higher n (air into glass): light slows down and bends towards the normal.
Into a lower n (water into air): light speeds up and bends away from the normal.
Along the normal (angle of incidence 0°): the speed changes but the ray does not bend.

Wavefronts (grey) and a ray (orange). In the glass the wave is slower, so the wavelength is shorter and the ray turns towards the normal. The ray is always at 90° to the wavefronts.

Snell's law

Snell's law turns that bending into numbers: n₁ sin θ₁ = n₂ sin θ₂. Medium 1 is the one the light is leaving and θ₁ is the angle of incidence; θ₂ is the angle of refraction. Both are measured from the normal.

For example, light in air hits glass (n = 1.50) at 50° to the normal: sin θ₂ = 1.00 × sin 50° ÷ 1.50 = 0.511, so θ₂ = 30.7°. It went into a higher n, so it bent towards the normal: the angle got smaller, as it should.

θ₁ = 50° in air becomes θ₂ = 30.7° in glass. Both angles sit between the ray and the normal.

Critical angle and total internal reflection

When light goes from a higher n into a lower n (glass into air), it bends away from the normal. Make the angle of incidence bigger and the refracted ray swings out until it runs along the surface at 90°. That angle of incidence is the critical angle θ_c: put θ₂ = 90° into Snell's law and you get sin θ_c = n₂ ÷ n₁. For glass (1.50) into air, sin θ_c = 1.00 ÷ 1.50, so θ_c = 41.8°.

Above the critical angle no light gets out: all of it reflects back inside. This is total internal reflection (TIR), and it needs two conditions: the light must be going towards a lower n, and the angle of incidence must be greater than θ_c. An optical fibre uses it: a glass core with a lower-n cladding around it, so light meeting the wall above θ_c reflects again and again along the fibre with almost no loss. That is how internet signals and medical endoscopes carry light around bends.

Light inside glass hitting the surface at 30°, 41.8° (the critical angle) and 60°. Above θ_c nothing escapes: total internal reflection.

Measuring a refractive index

The standard experiment shines a ray box beam into a semicircular or rectangular glass (or perspex) block. Trace the block, mark the rays, draw the normal, and measure the angle in air (θ_air) and in the block (θ_block) for five or more angles of incidence.

Plot sin θ_air on the y-axis against sin θ_block on the x-axis. Snell's law with n_air = 1.00 says sin θ_air = n sin θ_block, so the points lie on a straight line through the origin and the gradient is n. A ruled line of best fit uses all the data, which beats working out n from one pair of angles.

To assess accuracy, compare your n with the accepted value (perspex is about 1.49) as a percentage difference. Thick pencil lines, a wide beam and a protractor read to ±1° are the usual sources of error, and they matter most at small angles.

Common mistakes

Using the angle between the ray and the surface (for example 'the ray hits the water at 60° to the surface') in Snell's law.Convert first: the angle from the normal is 90° − 60° = 30°. Every angle in reflection and refraction is measured from the normal.
Writing n = v ÷ c, and getting a refractive index less than 1.n = c ÷ v. Light is never faster than c, so n is 1 or more, and a bigger n means slower light.
Expecting total internal reflection when light goes from air into glass at a large angle.TIR only happens going towards a lower n (glass to air, water to air, core to cladding) and only when the angle of incidence is bigger than θ_c.
Flipping the critical angle ratio to sin θ_c = n₁ ÷ n₂ and getting a calculator error.sin θ_c = n₂ ÷ n₁ = lower n ÷ higher n. A sine can never be more than 1, so a 'math error' tells you the ratio is upside down.
Saying the frequency (or colour) of light changes when it enters glass.Frequency stays the same at a boundary. The speed and the wavelength change together (v = fλ).
Getting strange angles because the calculator is in radians.Check for DEG on the screen before any sin or sin⁻¹. A quick test: sin 30 should give 0.5.

Worked example

A diver underwater points a torch up at the flat surface of a swimming pool. The beam meets the surface at an angle of incidence of 28°. The refractive index of water is 1.33 and of air is 1.00.

(a) Calculate the angle the beam makes with the normal after it leaves the water. (3 marks)

(b) Calculate the largest angle of incidence at which the beam can still leave the water. (2 marks)

(5 marks)

I'll think out loud, the way you should in the exam, using KNOW-UD: Knowns, Not known, Organise, Work it out, Units, Direction.

Prediction first. The beam goes from water into air, a lower n, so it bends away from the normal: the angle in air will be bigger than 28°. sin 28° is about 0.47, and multiplying by 1.33 gives about 0.62, so I expect just under 40°. For (b), sin θ_c = 1.00 ÷ 1.33 is 0.75, so the critical angle should be between 45° and 50°.

K · Knowns

I draw the surface and the normal first, then put the angle on the water side, because that's where the beam starts. The water is medium 1 because the light is leaving it.

n₁ = 1.33 (water), n₂ = 1.00 (air)
θ₁ = 28° (from the normal)

Knowns on the sketch: water n₁ = 1.33, air n₂ = 1.00, angle of incidence 28° from the normal. Unknowns: θ₂ and the critical angle θ_c.

N · Not known

Part (a) wants an angle in the air, and part (b) wants the critical angle for water to air. Both answers are angles from the normal, in degrees.

(a) θ₂ = ?
(b) θ_c = ?

O · Organise

Snell's law links the two angles, so I rearrange it for sin θ₂ before I put any numbers in. For (b), the beam can still just leave when the refracted ray runs along the surface, which is the critical angle. Water to air is towards a lower n, so a critical angle exists.

(a) n₁ sin θ₁ = n₂ sin θ₂ → sin θ₂ = n₁ sin θ₁ ÷ n₂
(b) sin θ_c = n₂ ÷ n₁

W · Work it out

Calculator in degrees first. I keep the full sine values and only round the angles at the end.

(a) sin θ₂ = 1.33 × sin 28° ÷ 1.00 = 1.33 × 0.46947 = 0.62440
θ₂ = sin⁻¹(0.62440) = 38.64°
(b) sin θ_c = 1.00 ÷ 1.33 = 0.75188
θ_c = sin⁻¹(0.75188) = 48.75°

U · Units

Both are angles, so degrees. The data are to two or three significant figures, so I give the angles to the nearest tenth of a degree, which is the precision a protractor-based answer can carry.

(a) θ₂ ≈ 38.6°
(b) θ_c ≈ 48.8°

D · Direction

An angle needs its reference line, so I say 'from the normal'. As a sense check on (a): the light sped up going into air, so it should bend away from the normal, and 38.6° is bigger than 28°. Good. For (b), any angle of incidence bigger than 48.8° gives total internal reflection, so the diver would see the beam reflect back down.

(a) 38.6° from the normal, bent away from it
(b) 48.8° from the normal; above this the beam is totally internally reflected

(a) The beam leaves the water at 38.6° to the normal. (b) The largest angle of incidence that still lets the beam out is the critical angle, 48.8°.

Check against the prediction. I predicted just under 40° for (a) and between 45° and 50° for (b). 38.6° and 48.8° fit both, and the angle in air is bigger than the angle in water, as it must be for light speeding up.

Exam advice

What markers look for

Draw the normal on every ray diagram and mark each angle against it. A marker can only follow your method if they can see which line each angle was measured from. HSC feedback asks for clearly labelled diagrams and clear use of angles.General advice from NESA HSC marking feedback, 2021 to 2025, summarised
Write the formula, rearrange it, then substitute: sin θ₂ = n₁ sin θ₁ ÷ n₂. With clear working a marker can give method marks even if the final angle is wrong; a bare wrong number gives them nothing to mark.General advice from NESA HSC marking feedback, 2021 to 2025, summarised
Keep the full sine value in your calculator and round only the final angle. In 2025, better HSC responses substituted numbers only after the working was complete, to avoid rounding errors. sin⁻¹ is especially sensitive to rounding near 90°.NESA HSC marking feedback, 2025, summarised
For an 'explain' question about refraction or TIR, give the cause and the effect: light slows down in the higher-n medium, therefore it bends towards the normal. HSC feedback asks for clear cause-and-effect links in explanations.General advice from NESA HSC marking feedback, 2021 to 2025, summarised
In the practical, accuracy means how close your n is to the accepted value; reliability means whether repeat trials agree. Name a specific source of error (the width of the beam, reading the protractor) rather than 'human error'.CortexHSC teaching notes

Summaries in our own words. Read NESA's own feedback with the exam packs: 2025.

Where this leads in Year 12

Light comes back in Year 12 when you test models of light: double-slit interference, diffraction and polarisation support the wave model, you measure the speed of light, and photons link frequency to energy with E = hf. The idea from this topic that carries straight through is that light's speed in a medium sets how it behaves at a boundary, and that frequency is fixed by the source while wavelength changes.

FAQ

Is Snell's law on the data sheet?: Yes. NESA's sample data sheet for the new (2025) syllabus includes n_x = c ÷ v_x, n₁ sin θ₁ = n₂ sin θ₂ and sin θ_c = n₂ ÷ n₁. The law of reflection is not an equation, so learn it in words. Check which sheet your school gives you for Year 11 exams.
What is the difference between reflection and refraction?: Reflection is light bouncing off a surface and staying in the same medium, with the angle of incidence equal to the angle of reflection. Refraction is light passing into a new medium and changing direction because its speed changes.
Why do you measure angles from the normal and not the surface?: Because the laws are written that way: Snell's law and the law of reflection only work with angles from the normal. The normal also works for curved surfaces, where 'the surface' has no single direction.
Does light bend towards or away from the normal?: Towards the normal when it goes into a higher refractive index and slows down (air into glass). Away from the normal when it goes into a lower refractive index and speeds up (water into air).
What are the two conditions for total internal reflection?: The light must be travelling towards a medium with a lower refractive index, and its angle of incidence must be greater than the critical angle.

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