Refraction at Plane Surfaces

1. Refraction

Refraction is the bending of a ray of light as it passes from one transparent medium into another, caused by the change in the speed of light between the two media.

• Rarer medium: of a pair of media, the one in which light travels faster (for example, air compared with glass).
• Denser medium: the one in which light travels slower (for example, glass compared with air).

---

2. Laws of Refraction

1. The incident ray, the refracted ray and the normal at the point of incidence all lie in the same plane.
2. When light travels from a rarer to a denser medium it bends towards the normal; when it travels from a denser to a rarer medium it bends away from the normal.
3. For a given pair of media, 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. This is Snell's law:

$$ \begin{aligned} \frac{\sin i}{\sin r} &= {}_a\mu_b \ &= \text{constant} \end{aligned} $$

Here $_a\mu_b$ is the refractive index of medium $b$ with respect to medium $a$ (light passing from $a$ to $b$).

---

3. Refractive Index

In terms of speed, the (absolute) refractive index of a medium is the ratio of the speed of light in vacuum to the speed of light in that medium:

$$\mu = \frac{c}{v}$$

where $c = 3\times10^{8}\ \text{m s}^{-1}$ is the speed of light in vacuum and $v$ is its speed in the medium. Since $v < c$, the refractive index of any medium is greater than 1.

---