Refractive Index | CIE IGCSE Physics: Co-ordinated Sciences (Double Award) Revision Notes 2023

Refractive index as a ratio of speed

Extended tier only

The refractive index can be calculated in two different ways:

1. Using the ratio of speeds
2. Using the ratio of angles

The refractive index is a number that is always larger than 1 and is different for different materials
- Objects which are more optically dense have a higher refractive index, e.g. n is about 2.4 for diamond
- Objects which are less optically dense have a lower refractive index, e.g. n is about 1.5 for glass
Since the refractive index is a ratio, it has no units

The refractive index, n, for the ratio of speeds, is defined as:

The ratio of the speeds of a wave in two different regions

The refractive index, n, for the ratio of speeds, is given by the equation:

$n = \frac{speed of light in a vacuum}{speed of light in a material}$

Refractive index as a ratio of angles

Extended tier only

The refractive index, n, for the ratio of angles, is defined as:

The ratio of the sine of the angle of incidence and the sine of the angle of reflection of a wave in two different regions

The refractive index, n, for the ratio of angles, is given by the equation:

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

Where:
- n = the refractive index of the material
- i = angle of incidence of the light (°)
- r = angle of refraction of the light (°)

This equation can be rearranged with the help of the formula triangle:

A refractive index formula triangle

Formula triangle for the refractive index in terms of angles

See the example of Speed & velocity which explains how to use the formula triangle to rearrange equations

Worked example

A ray of light enters a glass block of refractive index 1.53 making an angle of 15° with the normal before entering the block.

Calculate the angle it makes with the normal after it enters the glass block.

Answer:

Step 1: List the known quantities

Refractive index of glass, n = 1.53
Angle of incidence, i = 15°

Step 2: Write the equation for refractive index in terms of the ratio of angles

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

Step 3: Rearrange the equation and calculate sin (r)

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

$\sin r = \frac{\sin 15}{1.53}$

$\sin r = 0.1692$

Step 4: Find the angle of refraction (r) by using the inverse sin function

$r = \sin^{- 1} (0.1692)$

$r = 9.7 = 10 °$

Examiner Tip

$n = \frac{\sin i}{\sin r}$ is also known as Snell's law but you do not need to know this for your exam.

Important: ( $\frac{\sin i}{\sin r}$ ) is not the same as ( $\frac{i}{r}$ ). Incorrectly cancelling the sin terms is a very common mistake!

When calculating the value of i or r start by calculating the value of sin i or sin r.

You can then use the inverse sin function (sin^–1 on most calculators by pressing 'shift' then 'sine') to find the angle.

One way to remember which way around i and r are in the fraction is remembering that 'i' comes before 'r' in the alphabet, and therefore is on the top of the fraction (whilst r is on the bottom).

Refractive Index (CIE IGCSE Physics: Co-ordinated Sciences (Double Award))

Revision Note

Refractive index as a ratio of speed

Refractive index as a ratio of angles

A refractive index formula triangle

Worked example

Examiner Tip

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Author: Ann H