34.3 Refraction

Two things happen when a light ray is incident on a smooth boundary between two transparent materials, such as the boundary between air and glass:

Part of the light reflects from the boundary, obeying the law of reflection. This is how you see reflections from pools of water or storefront windows.
Part of the light continues into the second medium. It is transmitted rather than reflected, but the transmitted ray changes direction as it crosses the boundary. The transmission of light from one medium to another, but with a change in direction, is called refraction.

The photograph of FIGURE 34.13 shows the refraction of a light beam as it passes through a glass prism. Notice that the ray direction changes as the light enters and leaves the glass. Our goal in this section is to understand refraction, so we will usually ignore the weak reflection and focus on the transmitted light.

The photograph of a light beam refracting twice while passing through a glass prism.

FIGURE 34.13 Full Alternative Text

NOTE A transparent material through which light travels is called the medium. This term has to be used with caution. The material does affect the light speed, but a transparent material differs from the medium of a sound or water wave in that particles of the medium do not oscillate as a light wave passes through. For a light wave it is the electromagnetic field that oscillates.

FIGURE 34.14a shows the refraction of light rays in a parallel beam of light, such as a laser beam, and rays from a point source. Our analysis will be easier, however, if we focus on a single light ray. FIGURE 34.14b is a ray diagram showing the refraction of a single ray at a boundary between medium 1 and medium 2. Let the angle between the ray and the normal be $θ_{1}$ in medium 1 and $θ_{2}$ in medium 2. For the medium in which the ray is approaching the boundary, this is the angle of incidence as we’ve previously defined it. The angle on the transmitted side, measured from the normal, is called the angle of refraction. Notice that $θ_{1}$ is the angle of incidence in Figure 34.14b and the angle of refraction in FIGURE 34.14c, where the ray is traveling in the opposite direction.

The figure labeled ("a") consists of two parts that illustrate the refraction of parallel and point sources rays.

The figure labeled (b) illustrates a light ray refraction from a lower-index medium to a higher-index medium.

Full Alternative Text

Refraction was first studied experimentally by the Arab scientist Ibn al-Haitham, in about the year 1000, and later by the Dutch scientist Willebrord Snellius. Snell’s law says that when a ray refracts between medium 1 and medium 2, having indices of refraction $n_{1}$ and $n_{2}$ , the ray angles $θ_{1}$ and $θ_{2}$ in the two media are related by

\begin{matrix} n_{1} sin θ_{1} = n_{2} sin θ_{2} & (Snell ’ s law of refraction) \end{matrix}

(34.3)

Notice that Snell’s law does not mention which is the incident angle and which is the refracted angle.

34.3 Refraction

FIGURE 34.13 A light beam refracts twice in passing through a glass prism.

FIGURE 34.14 Refraction of light rays.