Refraction

This is the process whereby a wave changes direction as it moves from one medium to another. The incident ray bends as it crosses the boundary between the two media. Note again that the angles are measured relative to the normal line.

View

Credits: KeyStageWiki

Can we tell which direction the light will bend?

• The way in which light bends as it crosses between the two media depends on their optical densities
• When light passes from a less optically dense material to a more optically dense material (for example from air to glass), the ray bends towards the normal
• When light passes from a more optically dense material to a less optically dense material (for example from glass to air), the ray bends away from the normal

The laws of refraction

1. The incident ray, the refracted ray and the normal to the boundary between the two media all lie in the same plane
2. Snell’s Law The ratio of the sine of the angle of incidence to the sine of the angle of refraction is a constant (called the refractive index, $n$) for a given pair of media: $$ \begin{equation}\begin{aligned} _1n_2=\frac{\sin\theta_1}{\sin\theta_2}\\ \end{aligned}\end{equation} $$ The $1$ and $2$ represent the two media (the one from which the light is moving and the one into which the light is moving respectively). The angles $\theta_1$ and $\theta_2$ are thus the angles of incidence and of refraction respectively. Thus if we imagine a scenario where light travels from air to glass and the angle of incidence is $45\degree$ and angle of refraction is $28\degree$ then the equation for Snell’s law can be written: $$ \begin{equation}\begin{aligned} _an_g&=\frac{\sin\theta_a}{\sin\theta_g}\\ &=\frac{\sin45\degree}{\sin28\degree}\\ &\approx 1.5\ (1\ d.p.)\\ \end{aligned}\end{equation} $$ This ratio will evaluate to a constant which we can refer to as the refractive index of glass with respect to air, $_an_g$ (in the form: the refractive index of the second medium with respect to the first, $_1n_2$).

IMPORTANT: Most refractive indexes are given relative to/with respect to air since its absolute refractive index is $1$.