Snell's Law

The angles of incidence and refraction are related to the refractive index of a medium by an equation known as snell's Law:

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

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

'Sin' is the trigonometric function 'sine' which is on a scientific calculator
You can revise the concept of refraction using the revision notes Reflection & refraction

A formula triangle can help rearrange the snell's law equation

Snell triangle (2), IGCSE & GCSE Physics revision notes

Snell's law formula triangle

For more information on how to use a formula triangle refer to the revision note on Speed

Refractive index

The refractive index is a number which is related to the speed of light in the material (which is always less than the speed of light in a vacuum):

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

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, eg. n is about 2.4 for diamond
- Objects which are less optically dense have a lower refractive index, eg. n is about 1.5 for glass

Since the refractive index is a ratio, it has no units

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 snell's law

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

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

$r = \sin^{- 1} (0.1692) = 9.7 = 10 °$

Examiner Tip

Important: in snell's law $\frac{\sin i}{\sin r}$ is not the same as $\frac{i}{r}$ . Incorrectly cancelling the sin terms is a 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).

Snell's Law (Edexcel IGCSE Physics)

Revision Note

Snell's law

A formula triangle can help rearrange the snell's law equation

Refractive index

Worked example

Examiner Tip

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Author: Katie M