# Waves

## Refraction

Refraction is a process that happens when a wave changes medium It is the change in speed of a wave, not the change in direction

Partial reflection
Not all reflects

In refraction, as speed decreases, wavelength decreases also, but frequency remains constant \begin{align}c=f\lambda\end{align} When light is incident upon a boundary at a oblique angle, the wave changes direction.

### Snell’s law

When EM radiation transmits from one medium to another the sine of the angle of incidence is proportional to the sine of the angle of refraction \begin{align}sin(\theta_i)\propto sin(\theta_r)\end{align} \begin{align}sin(\theta_i)=nsin(\theta_r)\end{align} \begin{align}n=\frac{sin(\theta_i)}{sin(\theta_r)}\end{align}

Where $\theta_i$ is angle of incidence, & $\ \theta_r$ is the angle of refraction, & $n$ is the refractive index
Normal
right angle to the boundary
Towards the normal
slowing down
Away from the normal
speeding up

### Refractive index - $n$

Absolute refractive index
The ratio of speed of light in a vacuum to its speed in a given medium
How much light slows down by going from vacuum to medium
Always use the speed of light in air as speed of light in vacuum
Relative refractive index
The ratio of speed of light in one medium to its speed in another
How much light slows down by or accelerates by going from medium 1 to medium 2

Refractive indices are always $\geq1$ \begin{align}n=\frac{C_r}{C_i}.:C_1=\frac{C_v}{n_2}\end{align}

### Total internal reflection

Requires
$n_1 > n_2$
Critical angle (minimum angle required for TIR to occur)

The critical angle is a property of the boundary between two materials

\begin{align}\frac{sin(\theta)}{1}=\frac{n_2}{n_1} \end{align}