# Refraction

Refraction is the "bending" of light (or any electromagnetic wave) when entering a different medium.
When electromagnetic waves enter a different medium the **speed changes**. The frequency stays the same, so the **wavelength must change**.

This causes the **waves to change direction** (except when they travel directly forward):

See how the distance between pulses (the wavelength) changes, but the frequency of pulses stays the same.

Note: the "directly forward" direction is called the **Normal**.

It is at right angles to the surface.

## Going to a Denser Medium

The angle goes **towards** the normal on entering a **denser** medium.

Imagine marching in formation:

And then going from **flat ground to a hill**

The pace slows down **on one side first**,

and to stay in ranks the **direction must change** a bit

But the direction stays the same when marching straight up the hill

## Going to a Less Dense Medium

The angle goes **away** from the normal on entering a **less dense** medium.

Here we see both entering and leaving a denser medium:

**Towards normal** on entering **denser** medium

**Away from normal** on going to **less dense** medium.

*And because it returns to the same medium it returns to the same angle!*

And here it is in real life, a ray of light being refracted in a plastic block.

* The plastic is denser, so the light changes
towards normal when entering
and changes away from normal on leaving.
Courtesy of wikipedia user ajizai*

And different shapes make for interesting effects:

The rays bunch up around the edge

Our eyes use refraction to focus incoming light onto the back of our eye:

Light refracts as it goes through our eyeballs,

That focuses the light beams at the back of our eye

where nerves detect the photons.

*Yes the image is upside down, but our eyes cope with that!*

## Refractive Index

The ratio of the **speed in a vacuum** to **speed in the medium** is called the Refractive Index (or Index of Refraction):

n = \frac{c}{v}

where

**n**is the Refractive Index**c**is the speed of light in vacuum and**v**is the speed of light in the medium

**A bigger refractive index means a lower speed!**

### Example: the Refractive Index of water is 1.333

So light travels 1.333 times **slower** in water than in a vacuum

- Speed in a vacuum: 300,000 km/s
- Speed in water: 300,000 km/s / 1.333 = 225,000 km/s

Some Refractive Index values:

Medium | Speedmillion m/s |
Refractive Indexn |
---|---|---|

Vacuum | 300 | 1 |

Ice | 228 | 1.31 |

Water | 225 | 1.333 |

Ethanol | 220 | 1.36 |

Glass | 205 | 1.46 |

Olive oil | 204 | 1.47 |

Diamond | 123 | 2.42 |

## Critical Angle

At a certain angle (the Critical Angle) the ray starts to point back inside!

The result is the light **reflects** back instead.

It is called **Total Internal
Reflection**:

Refraction |
Critical Angle |
Total Internal Reflection |

### Example: Water to Air

When looking from water to air we see the (usually 180° from horizon to horizon) world above the water
as a **cone of about 96°**.

Outside that 96° cone is a (much darker) reflection from the water below:

*Navy Diver 2nd Class Ryan Arnold viewed from below*

Note also that the water surface is not flat, so it cause a local ripple effect.

Have a play with it:

Try *Refraction Index 1 = 1*, *Refraction Index 2 = 1.33*, "*Down*" and "*Eye*" to create that effect of looking up from water.

## Snell's Law

How do we calculate the angles? We use **Snell's Law**:

n_{1} sin(θ_{1}) = n_{2} sin(θ_{2})

It works **up to the critical angle**, after that it is simple reflection:

n_{1}sin(θ_{1}) = n_{2}sin(θ_{2}) |
n_{1}sin(θ_{crit}) = n_{2} |
θ = _{1}θ_{1} |
||

because sin(90°)=1 | when θ_{1} > θ_{crit} |
|||

Refraction |
Critical Angle |
Total Internal Reflection |

### Example: What is the Critical Angle between air and water?

Index of Refraction of **air is 1.003**, and of **water is 1.333**

The Critical Angle is when **θ _{2}** is 90°

_{1}sin(θ

_{1}) = n

_{2}sin(θ

_{2})

_{1}sin(θ

_{1}) = n

_{2}

_{1}:sin(θ

_{1}) = \frac{n_{2}}{n_{1}}

_{1}= sin

^{-1}(\frac{n_{2}}{n_{1}})

_{1}= sin

^{-1}(\frac{1.003}{1.333})

_{1}= 48.8°

So θ_{crit} = 48.8°

You may prefer this form of Snell's Law, made by dividing both sides by sin(θ_{1}) and n_{2}:

\frac{n_{1}}{n_{2}} = \frac{sin(θ_{2})}{sin(θ_{1}) }

(Be careful though: **n** values go "1-over-2", but the **sin()** values go "2-over-1".)