Physics

13.4 - Refractive Index & Snell's Law

3 min

note 1 of 3

Refractive index

Light travels fastest in a vacuum. When it enters a transparent material such as glass or water, it slows down.
The refractive index of a material, $n$ , measures how much it slows light down.
It's the ratio of the speed of light in a vacuum, $c$ , to the speed of light in the material, $v$ .

Formula for refractive index

$n = \frac{c}{v}$

Where:

$n$ = Refractive index (no units)
$c$ = Speed of light in a vacuum, in metres per second (m/s)
$v$ = Speed of light in the material, in metres per second (m/s)

Because light travels fastest in a vacuum, $n$ is always 1 or greater. The more a material slows light down, the higher its refractive index.

Typical values

Glass - Around 1.5
Water - Around 1.33
Air - 1.00 (to 2 d.p.)

note 2 of 3

Snell's law

When a ray of light crosses the boundary into a material, the angle of incidence $i$ , the angle of refraction $r$ and the refractive index $n$ are linked by Snell's law.
Both angles are measured from the normal - the line drawn at right angles to the surface at the point where the ray hits it.

$An incident ray crosses a horizontal boundary from material 1 into material 2, bending towards the dashed normal and continuing as the refracted ray, with the angle of incidence and angle of refraction marked.$

Formula for Snell's law

$n = \frac{\sin i}{\sin r}$

Where:

$n$ = Refractive index (no units)
$i$ = Angle of incidence, in degrees
$r$ = Angle of refraction, in degrees

If a ray travels along the normal, it does not refract - it carries straight on without changing direction.

note 3 of 3

Worked example - Finding the angle of refraction

A ray of light passes from air into water. The angle of incidence is 35° and the refractive index of water is 1.33. Find the angle of refraction, to the nearest degree.

$An incident ray crosses the boundary from air into water, bending towards the dashed normal, with the angle of incidence labelled 35° and the angle of refraction below the boundary left unlabelled.$

Step 1 - Formula

$n = \frac{\sin i}{\sin r}$

Step 2 - Rearrange the formula

Make $\sin r$ the subject:

$\sin r = \frac{\sin i}{n}$

Step 3 - Substitution and calculation

$\sin r = \frac{\sin 35^{\circ}}{1.33} = 0.43 \dots$

Take the inverse sine to find $r$ :

$\begin{matrix} r & = \sin^{- 1} (0.43 \dots) \\ = 26^{\circ} (to the nearest degree) \end{matrix}$

key terms

TermDefinition

Refractive indexThe ratio of the speed of light in a vacuum to the speed of light in a material.

NormalA line drawn at right angles to a surface or boundary at the point where a ray or wave meets it. A force or pressure that acts at right angles to a surface is also said to act normal to it.

end of notes

Key points to remember

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13.5 - Total Internal ReflectionNext up

Refractive index

Light travels fastest in a vacuum. When it enters a transparent material such as glass or water, it slows down.

The refractive index of a material,

n

, measures how much it slows light down.

It's the ratio of the speed of light in a vacuum,

c

, to the speed of light in the material,

v

Formula for refractive index

$n = \frac{c}{v}$

Where:

n

= Refractive index (no units)

c

= Speed of light in a vacuum, in metres per second (m/s)

v

= Speed of light in the material, in metres per second (m/s)

Because light travels fastest in a vacuum,

n

is always 1 or greater. The more a material slows light down, the higher its refractive index.

Typical values

Glass - Around 1.5

Water - Around 1.33

Air - 1.00 (to 2 d.p.)