What is the refractive index?

The refractive index (n) of a material is the ratio of the speed of light in a vacuum (c = 2.998 × 10⁸ m/s) to the speed of light in that material (v): n = c/v. A higher refractive index means light slows down more in that material. Glass has n ≈ 1.5, meaning light travels at about 2/3 its vacuum speed through glass.

Snell's law relates the angles of incidence and refraction when light crosses the boundary between two media: n₁ sin(θ₁) = n₂ sin(θ₂). When light enters a denser medium (higher n), it bends toward the normal. When it enters a less dense medium, it bends away from the normal.

What is total internal reflection?

When light travels from a denser medium to a less dense medium at an angle greater than the critical angle, it is completely reflected back rather than refracted. The critical angle θc = arcsin(n₂/n₁). This is the principle behind optical fibres.

What is the refractive index of water?

The refractive index of water at room temperature is approximately 1.333 for visible light. This means light travels at about 75% of its vacuum speed in water. The slight variation of refractive index with wavelength (dispersion) causes rainbows.

What is the refractive index of glass?

Common glass has a refractive index of about 1.5, though this varies by type: crown glass ≈ 1.52, flint glass ≈ 1.62, borosilicate glass ≈ 1.47. Diamond has n ≈ 2.42, which is why diamonds are so brilliant — they have a small critical angle and produce total internal reflection at many angles.

Science

Refractive Index Calculator

Calculate the refractive index from the speed of light in a medium, apply Snell's law to find angles of refraction, or calculate the critical angle for total internal reflection.

Speed of light in medium (m/s)

Refractive index

—

Speed in medium—

Formulan = c / v

Light slows to—

Refractive indices of common materials

Material	n	Speed in medium (m/s)
Vacuum	1.000	2.998 × 10⁸
Air (STP)	1.0003	2.997 × 10⁸
Water (20°C)	1.333	2.249 × 10⁸
Crown glass	1.52	1.973 × 10⁸
Flint glass	1.62	1.851 × 10⁸
Diamond	2.42	1.239 × 10⁸
Silicon	3.48	8.62 × 10⁷

Worked examples

Example 1 — Snell's law: light from air into glass at 30°:

n₁ = 1.0 (air), n₂ = 1.52 (crown glass), θ₁ = 30° sin θ₂ = (n₁/n₂) × sin θ₁ = (1.0/1.52) × sin 30° sin θ₂ = 0.658 × 0.5 = 0.329 θ₂ = arcsin(0.329) = 19.2° (bends toward normal entering denser medium)

Example 2 — Critical angle for glass-air interface:

n₁ = 1.52 (glass), n₂ = 1.0 (air) θc = arcsin(n₂/n₁) = arcsin(1.0/1.52) = arcsin(0.658) = 41.1° Above 41.1°: total internal reflection — the basis of optical fibres

Example 3 — Diamond brilliance:

n_diamond = 2.42 θc = arcsin(1.0/2.42) = arcsin(0.413) = 24.4° Diamond's very small critical angle means most internal reflections produce total internal reflection — giving diamonds their brilliance

Applications of refractive index

Optical fibres: Fibre optic cables use total internal reflection to guide light over thousands of kilometres. The fibre core (n ≈ 1.48) is surrounded by cladding (n ≈ 1.46), giving a critical angle of about 80°. Light entering within this acceptance cone is trapped and guided with minimal loss — enabling the internet.

Camera lenses and eyeglasses: High-refractive-index glass (n = 1.7–1.9) allows thinner lenses for the same optical power. This is why high-prescription eyeglasses use high-index materials — a lens that would be 12 mm thick in standard glass (n=1.5) is only 7 mm thick in high-index glass (n=1.74).

Rainbows and dispersion: The refractive index of water varies slightly with wavelength — red light (700 nm) has n ≈ 1.331 and violet light (400 nm) has n ≈ 1.344. This dispersion separates white sunlight into its component colours as it refracts through water droplets, creating a rainbow.

Gemology: The refractive index is a key identifier for gemstones. Diamonds (n=2.42), rubies (n=1.77), emeralds (n=1.58), and synthetic materials all have characteristic refractive indices measured with a refractometer — helping gemologists distinguish genuine stones from imitations.

Refractive indices of common materials

Material	n (at 589 nm)	Critical angle vs air
Vacuum / Air	1.000	N/A
Water (20°C)	1.333	48.6°
Fused silica	1.458	43.3°
Crown glass	1.52	41.1°
Borosilicate (Pyrex)	1.470	42.9°
Flint glass	1.62	38.1°
Sapphire	1.77	34.4°
Diamond	2.42	24.4°
Silicon (IR)	3.48	16.7°
Gallium arsenide	3.55	16.4°

Common questions

The refractive index (n) of a material is the ratio of the speed of light in a vacuum (c = 2.998 × 10⁸ m/s) to the speed of light in that material (v): n = c/v. A higher refractive index means light slows down more in that material. Glass has n ≈ 1.5, meaning light travels at about 2/3 its vacuum speed through glass.
Snell's law relates the angles of incidence and refraction when light crosses the boundary between two media: n₁ sin(θ₁) = n₂ sin(θ₂). When light enters a denser medium (higher n), it bends toward the normal. When it enters a less dense medium, it bends away from the normal.
When light travels from a denser medium to a less dense medium at an angle greater than the critical angle, it is completely reflected back rather than refracted. The critical angle θc = arcsin(n₂/n₁). This is the principle behind optical fibres.
The refractive index of water at room temperature is approximately 1.333 for visible light. This means light travels at about 75% of its vacuum speed in water. The slight variation of refractive index with wavelength (dispersion) causes rainbows.
Common glass has a refractive index of about 1.5, though this varies by type: crown glass ≈ 1.52, flint glass ≈ 1.62, borosilicate glass ≈ 1.47. Diamond has n ≈ 2.42, which is why diamonds are so brilliant — they have a small critical angle and produce total internal reflection at many angles.