## 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}