Snell's Law — Definition

Definition

Imagine you're running on a beach, and suddenly you decide to run into the water. As you hit the water, your speed changes, and if you enter at an angle, your direction of movement will also change. This change in direction is very similar to what happens when light travels from one transparent medium (like air) into another (like water or glass). This phenomenon is called refraction.

Snell's Law is a mathematical rule that helps us predict exactly how much the light will bend. It's named after Willebrord Snellius, a Dutch astronomer and mathematician. When light moves from one medium to another, say from air to water, it changes its speed. This change in speed causes it to bend or 'refract'. If the light enters the new medium perpendicularly (straight on), it slows down but doesn't change direction. However, if it enters at an angle, it bends.

The key idea behind Snell's Law is that the amount of bending depends on two main things: the angle at which the light hits the surface (called the angle of incidence, $\theta_1$) and the 'optical density' of the two materials. Optical density is quantified by a value called the refractive index ($n$). Each transparent material has its own refractive index. For example, air has a refractive index of approximately 1, water is about 1.33, and glass is around 1.5.

Snell's Law states that for a given pair of media, the ratio of the sine of the angle of incidence to the sine of the angle of refraction ($\theta_2$) is a constant, which is equal to the ratio of the refractive indices of the second medium to the first medium.

Mathematically, it's expressed as: $n_1 \sin \theta_1 = n_2 \sin \theta_2$. Here, $n_1$ is the refractive index of the first medium, $\theta_1$ is the angle of incidence, $n_2$ is the refractive index of the second medium, and $\theta_2$ is the angle of refraction.

Both angles are measured with respect to the normal, an imaginary line perpendicular to the surface at the point where the light ray hits. This law is fundamental to understanding how lenses work in our eyes, cameras, and microscopes, and how prisms split light into its constituent colors.