Refractive Index (Oxford AQA IGCSE Physics)

Revision Note

Author

Leander Oates

Expertise

Physics

Refractive Index

The refractive index is a number which is related to the speed of light in the material

$refractive index = \frac{speed of light in a vacuum}{speed of light in the medium}$

The refractive index is:
- always larger than 1
- always less than the speed of light in a vacuum
- different for different materials
- has no units because it is a ratio
Objects which are more optically dense have a higher refractive index
- For example, the refractive index is about 2.4 for diamond
Objects which are less optically dense have a lower refractive index,
- For example, the refractive index is about 1.5 for glass

Calculating Refractive Index

The refractive index can also be determined using the angle of incidence and the angle of refraction
- Also known as Snell's law

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

Where:
- n = the refractive index of the medium
- i = the angle of incidence measured in °
- r = the angle of refraction measured in °

Refraction ray diagram

Refraction of Light, for IGCSE & GCSE Physics revision notes — **The angle of incidence and angle of refraction at the air-to-glass boundary**

Worked Example

A ray of light approaches a glass block with a refractive index of 1.53. The ray meets the glass at an angle of 15° to the normal.

Calculate the angle between the ray and 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 out the appropriate equation

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

Step 3: Rearrange the equation to make sin r the subject

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

$\sin r = \frac{\sin (15 °)}{1.53}$

$\sin r = 0.1692$

Step 4: Find the angle of refraction by using the inverse sine function

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

$r = 9.739$

$r = 10 °$

Exam Tip

There are a lot of common errors that students make when performing these types of calculations. Here are some things to check if you got the wrong answer:

$\frac{\sin i}{\sin r}$ is not the same as $\frac{i}{r}$
- You cannot cancel the sine term
When multiplying or dividing with sine terms, make sure you close the bracket on your calculator to ensure you get the correct answer
Your calculator is in degrees and not radians mode
The inverse sine function, sin^-1, is usually found by pressing 'shift' then 'sin' on your calculator

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