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# Refractive Index

### Refractive Index

The ratio of the speed of light in a vacuum to its speed in a specified medium is the refractive index of that medium.

**Refraction** is defined by the **** change in speed that occurs when waves pass between two media of different density.

The also causes the waves to change **direction.**

We measure this change in direction by measuring the **angle of refraction** This is measured between the refracted ray and the...

Consider a light ray travelling from a denser medium into a less dense medium.

Does its speed 'increase' or 'decrease'?

Does the refracted ray move '**away**' or '**towards**' the normal? Hint: F.A.S.T.

Is the angle of refraction going to be '**smaller**' or '**larger**' than the angle of incidence?

Still considering a light ray, travelling from a more dense to a less dense medium...

What is the angle of incidence called when the angle of refraction is $90^o$?

What do we call the phenomenon of when the angle of incidence is larger than the critical angle, $\theta_c$?

If the critical angle of this light ray is $30^o$, and the angle of incidence is $45^o$, what will the angle of reflection be?

Certain media will refract light more than others. The way we measure this is with a **refractive index**.

The **refractive index, n,** of a material is the **ratio** of the speed of light in a vacuum (c) and the speed at which light travels at in the material (v).

```
$n=\frac{c}{v}$
```

The speed of light in air is approximately $3\times10^8m/_s$ , whereas in glass it is approximately $2\times10^8m/_s$ . Calculate the refractive index n for glass.

More generally, the refractive index is the ratio of the speed of a wave in the first medium, $v_1$ , and the speed of the wave in the second medium $v_2$ .

$n=\frac{v_1}{v_2}$

The speed of light in a vacuum is $3\times10^8m/_s$, and the speed of light in air is approximately $3\times10^8m/_s$ . What is the refractive index, n, for air?

What is the unit for the refractive index?

What would the equation for refractive index, $n=\frac{v_1}{v_2}$ , be in terms of wavelength? Use: $v=\lambda\times f$.

What is the relationship between the frequency of light and the refractive index of a medium?

You can find the relationship of refractive index and the angles of incidence and refraction using **Snell's Law**.

**Snell's Law** relates the ratio of the refractive indices of both media with the sin of the angles of incidence and refraction as follows:

$\frac{n_1}{n_2}=\frac{sin{\theta_i}}{sin{\theta_r}}$

We've seen that the refractive index for air is 1, so when the light is travelling from the medium into air, this equation is simplified to this:

$n=\frac{sin{\theta_i}}{sin{\theta_r}}$ where n is the refractive index of the medium at the boundary with air.

The **refractive index** of a medium is the ratio of the speed of light in a vacuum and the speed at which it travels in the medium.

$n=\frac{c}{v}$ or more generally, $n=\frac{v_1}{v_2}$.

**Snell's Law** relates the refractive index with the angles of incidence and refraction.
$\frac{n_1}{n_2}=\frac{sin{\theta_i}}{sin{\theta_r}}$
The refractive index of air is 1.