IGCSEPhysics: Co-ordinated Sciences (Double Award)CIERevision Notes3. WavesLightRefractive Index

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

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Ann H

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Refractive index as a ratio of speed

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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

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

$r = 9.7 = 10 °$

Exam 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).

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Author: Ann H

Ann obtained her Maths and Physics degree from the University of Bath before completing her PGCE in Science and Maths teaching. She spent ten years teaching Maths and Physics to wonderful students from all around the world whilst living in China, Ethiopia and Nepal. Now based in beautiful Devon she is thrilled to be creating awesome Physics resources to make Physics more accessible and understandable for all students no matter their schooling or background.