The refractive index of a material measures how much light slows when it enters that medium from air. It is calculated using Snell's law: n = sin i ÷ sin r, where i is the angle of incidence and r is the angle of refraction. Glass has a refractive index of about 1.5; air is 1.0.
What is the refractive index?
The refractive index (n) of a material is a number that describes how much slower light travels through that material compared with a vacuum. Air is so close to a vacuum that n = 1.0 is used for air in all GCSE calculations. A material with n = 1.5 means light travels at 1/1.5 (about two-thirds) of its speed in a vacuum through that medium.
The refractive index is always greater than 1 for real transparent materials, because light cannot travel faster through matter than it does through a vacuum. A higher refractive index means more bending (refraction) when light enters the medium at an angle, and a slower wave speed inside it.
How does light slow down in a denser optical medium?
When light passes from air into glass or water, it moves into a medium where its electromagnetic interaction with the material slows it down. Crucially, only the speed and wavelength change — the frequency stays constant. Because the wavelength shortens and the speed decreases by the same factor, the wave front pivots, and the ray changes direction at the boundary. This change of direction is refraction.
Predicting direction: when light enters a denser medium (higher n), it bends towards the normal. When it enters a less dense medium (lower n), it bends away from the normal. The normal is the construction line drawn at 90° to the surface at the point of entry.
What is Snell's law and how do you use it?
Snell's law relates the angle of incidence (i, measured from the normal in the first medium) to the angle of refraction (r, measured from the normal in the second medium):
$$n = \frac{\sin i}{\sin r}$$
This form assumes the first medium is air (n ≈ 1.0). The angles must always be measured from the normal, not from the surface itself — this is the most common source of error in exam answers.
Steps to apply Snell's law:
- Draw the normal at 90° to the surface at the point where the ray meets it.
- Measure the angle of incidence (i) between the incoming ray and the normal.
- Measure the angle of refraction (r) between the refracted ray and the normal.
- Substitute into n = sin i ÷ sin r.
How do you calculate the refractive index — worked example?
Worked example:
A ray of light enters a glass block. The angle of incidence is 40° and the angle of refraction inside the glass is 25°. Calculate the refractive index of the glass.
- Write the equation: n = sin i ÷ sin r
- Substitute the angles: n = sin 40° ÷ sin 25°
- Evaluate: sin 40° = 0.643; sin 25° = 0.423
- Divide: n = 0.643 ÷ 0.423 = 1.52
This confirms the material is glass (n ≈ 1.5 is the accepted value). The light bent towards the normal (from 40° to 25°), consistent with entering a denser medium.
How is refractive index related to wave speed?
The refractive index can also be calculated from wave speeds:
$$n = \frac{c}{v}$$
Where c is the speed of light in a vacuum (3.0 × 10⁸ m/s) and v is the speed of light in the medium.
| Material | Refractive index (n) | Speed of light (m/s) |
|---|---|---|
| Air | 1.00 | 3.0 × 10⁸ |
| Water | 1.33 | 2.26 × 10⁸ |
| Glass (typical) | 1.50 | 2.0 × 10⁸ |
| Diamond | 2.42 | 1.24 × 10⁸ |
Diamond's very high refractive index explains its exceptional brilliance: light bends dramatically at each surface, and a large proportion undergoes total internal reflection before finally exiting.
How does refractive index link to total internal reflection and the critical angle?
When light travels from a denser medium to a less dense medium (e.g. glass to air), above a certain angle it cannot exit — it reflects back inside. The critical angle (C) is the angle of incidence (inside the denser medium) at which the refracted ray just grazes along the surface (angle of refraction = 90°).
$$\sin C = \frac{1}{n}$$
For glass with n = 1.5: sin C = 1/1.5 = 0.667, so C = 41.8°. At any angle of incidence inside the glass greater than 41.8°, total internal reflection occurs. This is the principle behind optical fibres, which guide light signals around corners with negligible loss.
Frequently asked questions
What is the refractive index formula in GCSE physics?
The refractive index formula is n = sin i ÷ sin r, where i is the angle of incidence (from the normal in air) and r is the angle of refraction (from the normal in the denser medium). It can also be written as n = c ÷ v, where c is the speed of light in a vacuum (3.0 × 10⁸ m/s) and v is the speed in the material. Both forms appear in GCSE specifications and you should be comfortable with each.
Why must angles be measured from the normal, not the surface?
Snell's law is derived from the geometry of wavefronts arriving at a boundary, and this geometry naturally uses the angle between the wavefront and the surface, which equals the angle between the ray and the normal. Measuring from the surface instead of the normal gives the complement of the correct angle; substituting it into sin i ÷ sin r produces a completely wrong answer. Always draw the normal first, then measure angles to it.
What does a higher refractive index mean physically?
A higher refractive index means light travels more slowly through the material and bends more at the air–material boundary. It also means the critical angle for total internal reflection is smaller, so a wider range of internal angles will cause total reflection. Diamond's high refractive index (2.42) gives it a critical angle of only 24°, which is why facet-cut diamonds trap and return almost all the light that enters them.
How do you use n = c/v to find the speed of light in a material?
Rearrange to v = c ÷ n. For glass with n = 1.5: v = (3.0 × 10⁸) ÷ 1.5 = 2.0 × 10⁸ m/s. The equation shows directly that a higher refractive index corresponds to a lower wave speed. If a question gives two refractive indices and asks you to compare speeds, the material with the larger n has the slower speed — no calculator needed for that qualitative conclusion.
For Socratic GCSE physics with Professor Newton — predict which way the ray bends before writing n = sin i ÷ sin r, then test whether your particle-model picture of slowing down agrees — visit aitutors.me.