Snell's law, explained with examples

By Ashraf Bhura, Co-Founder, STEM-Tutor · Updated October 2026

When light passes from one material into another, it changes speed and bends. Snell's law tells you exactly how much. It explains why a straw looks bent in water, how lenses focus, and how optical fibres carry the internet.

Why light bends

Light travels at 3.00 × 10⁸ m/s in a vacuum, and more slowly in materials such as water and glass. When a beam meets a boundary at an angle, one side of the wavefront slows down before the other, so the wavefront swings round and the beam changes direction. This is refraction. A useful picture is a car driving at an angle from a road onto sand: the wheel that reaches the sand first slows first, and the car turns.

All angles are measured from the normal, a line drawn perpendicular to the boundary at the point where the light hits it. Light entering a slower material bends towards the normal; light entering a faster material bends away from it. Light travelling along the normal does not bend at all, though it still changes speed.

Refractive index

The refractive index of a material is

n = c / v

where c is the speed of light in a vacuum and v is its speed in the material. n has no units and is always at least 1. Typical values: air 1.00, water 1.33, glass about 1.5, diamond 2.42. A higher refractive index means light travels more slowly and bends more.

Snell's law

n₁ sinθ₁ = n₂ sinθ₂

θ₁ is the angle of incidence in material 1 and θ₂ is the angle of refraction in material 2, both measured from the normal. The frequency of the light does not change at the boundary, so since v = fλ, the wavelength shrinks in the same ratio as the speed.

Worked examples

Example 1: air into glass

Light passes from air into glass (n = 1.50) at an angle of incidence of 40°. Find the angle of refraction.

• 1.00 × sin 40° = 1.50 × sinθ₂, so sinθ₂ = 0.643/1.50 = 0.429.
• θ₂ ≈ 25.4°, bent towards the normal.

Example 2: water into air

Light travels from water (n = 1.33) into air with an angle of incidence of 30°. Find the angle of refraction.

• 1.33 sin 30° = 1.00 sinθ₂, so sinθ₂ = 0.665.
• θ₂ ≈ 41.7°, bent away from the normal.

Example 3: speed in a material

Find the speed of light in diamond (n = 2.42).

• v = c/n = 3.00 × 10⁸/2.42.
• v ≈ 1.24 × 10⁸ m/s, less than half its speed in a vacuum.

Example 4: finding n

A ray enters a liquid from air at 50° and refracts at 35°. Find the refractive index of the liquid.

• n = sin 50°/sin 35° = 0.766/0.574.
• n ≈ 1.34, close to water.

The critical angle and total internal reflection

When light goes from a slower material into a faster one, such as glass into air, it bends away from the normal. As the angle of incidence increases, the angle of refraction reaches 90°, so the refracted ray runs along the boundary. The angle of incidence at which this happens is the critical angle C:

sin C = n₂ / n₁, which becomes sin C = 1/n for a material surrounded by air.

For angles of incidence greater than C, no light refracts out at all: it is all reflected back inside. This is total internal reflection. Two conditions are needed: the light must be travelling into a material with a lower refractive index, and the angle of incidence must be greater than the critical angle.

Example 5: critical angle of glass

Find the critical angle for glass (n = 1.50) in air.

• sin C = 1/1.50 = 0.667.
• C ≈ 41.8°. Light hitting the inside of the glass at more than 41.8° is totally internally reflected.

Example 6: glass in water

Find the critical angle for glass (n = 1.50) surrounded by water (n = 1.33).

• sin C = 1.33/1.50 = 0.887.
• C ≈ 62.5°. It is larger than in air, because the two refractive indices are closer together.

Optical fibres

An optical fibre is a thin strand of glass with a core of higher refractive index surrounded by cladding of lower refractive index. Light entering the core keeps hitting the core-cladding boundary at angles greater than the critical angle, so it is totally internally reflected again and again and travels along the fibre, even round gentle bends. Fibres carry internet and phone data as pulses of light, and endoscopes use bundles of fibres to let doctors see inside the body. The cladding protects the core and stops light leaking between neighbouring fibres.

Dispersion

The refractive index of glass is slightly different for different colours: violet light slows down more than red light. So when white light passes through a prism, each colour refracts by a slightly different angle and the light spreads into a spectrum. This is dispersion, and it is also how raindrops make rainbows.

Common mistakes

• Measuring angles from the surface instead of from the normal.
• Putting the refractive indices on the wrong sides of Snell's law.
• Expecting total internal reflection when light goes into a denser material; it only happens going into a less dense one.
• Thinking the frequency changes at a boundary; the speed and wavelength change, but the frequency stays the same.
• Having the calculator in radians instead of degrees.

Practice questions

Try each one before opening the answer.

Frequently asked questions

Is Snell's law on the AP Physics exams?

Yes. Geometric optics, including refraction and Snell's law, is part of AP Physics 2 in the current course framework.

Is Snell's law in GCSE or A level Physics?

GCSE covers refraction qualitatively, with separate Physics including more detail. A level Physics uses n₁sinθ₁ = n₂sinθ₂, critical angles and optical fibres.

Key takeaways

• Refraction happens because light changes speed between materials.
• n = c/v; a larger n means slower light and more bending.
• Snell's law: n₁sinθ₁ = n₂sinθ₂, angles from the normal.
• Critical angle: sin C = n₂/n₁; beyond it, total internal reflection.
• Optical fibres guide light by repeated total internal reflection.

Related guides

• A level Physics waves
• The electromagnetic spectrum
• The Doppler effect