13.2 Refraction

Snell's law

Now that we know that the degree of bending, or the angle of refraction, is dependent on the refractive index of a medium, how do we calculate the angle of refraction?

The angles of incidence and refraction when light travels from one medium to another can be calculated using Snell's Law.

Snell's Law

$$n_{1}sin{\theta }_1=n_{2}sin{\theta }_2$$

where

$n_1$ =	Refractive index of material 1
$n_2$ =	Refractive index of material 2
${\theta }_1$ =	Angle of incidence
${\theta }_2$ =	Angle of refraction

Remember that angles of incidence and refraction are measured from the normal, which is an imaginary line perpendicular to the surface.

Suppose we have two media with refractive indices $n_1$ and $n_2$ . A light ray is incident on the surface between these materials with an angle of incidence ${\theta }_1$ . The refracted ray that passes through the second medium will have an angle of refraction ${\theta }_2$ .

If

then from Snell's Law,

For angles smaller than ${90}^{\circ }$ , $sin\theta$ increases as $\theta$ increases. Therefore,

This means that the angle of incidence is greater than the angle of refraction and the light ray is bent toward the normal.

Similarly, if

then from Snell's Law,

For angles smaller than ${90}^{\circ }$ , $sin\theta$ increases as $\theta$ increases. Therefore,

This means that the angle of incidence is less than the angle of refraction and the light ray is away toward the normal.