10.1.3 Dispersion Explained

Key Concepts

1. Definition of Dispersion

Dispersion is the phenomenon where light is separated into its constituent colors when it passes through a medium. This occurs because different colors of light travel at different speeds through the medium, causing them to refract (bend) by different amounts.

2. Refractive Index

The refractive index of a material is a measure of how much the speed of light is reduced inside the material. Different colors of light have slightly different refractive indices, leading to dispersion.

3. Prism and Dispersion

A prism is a common tool used to demonstrate dispersion. When white light enters a prism, it is refracted at the first surface, and then again at the second surface, causing the light to spread out into its constituent colors.

4. Rainbow Formation

Rainbows are a natural example of dispersion. When sunlight passes through water droplets in the atmosphere, it is refracted, dispersed, and reflected, creating the spectrum of colors we see in a rainbow.

Detailed Explanation

Definition of Dispersion

Dispersion occurs because the speed of light in a medium depends on its wavelength (color). Shorter wavelengths (blue and violet) travel slower than longer wavelengths (red and orange) in most materials. This difference in speed causes different colors to bend by different amounts when they pass through a medium, resulting in dispersion.

Refractive Index

The refractive index (n) of a material is given by the ratio of the speed of light in a vacuum (c) to the speed of light in the material (v): n = c/v. Since different colors of light have slightly different speeds in a material, they have slightly different refractive indices, leading to dispersion.

Prism and Dispersion

A prism is a transparent object with flat, polished surfaces that refract light. When white light enters a prism, it is refracted at the first surface. The different colors of light are refracted by different amounts because they have different refractive indices. At the second surface, the light is refracted again, spreading out into a spectrum of colors.

Rainbow Formation

Rainbows form when sunlight enters water droplets in the atmosphere. The light is refracted as it enters the droplet, dispersed into its constituent colors, reflected off the inside of the droplet, and refracted again as it exits the droplet. This process creates a spectrum of colors that appears as a circular arc in the sky.

Examples and Analogies

Example: Dispersion in a Prism

When you shine a beam of white light through a prism, you see a spectrum of colors ranging from red to violet. This is because the different colors of light are refracted by different amounts, spreading out into a rainbow.

Analogy: Dispersion as a Race

Think of dispersion as a race where different colored runners (light waves) start at the same time but run at different speeds. The faster runners (red and orange) finish first, while the slower runners (blue and violet) finish last. This creates a spread of runners (colors) across the finish line.

Example: Rainbow Formation

After a rain shower, you might see a rainbow in the sky. This occurs because sunlight is refracted and dispersed by water droplets in the atmosphere, creating a spectrum of colors that appears as a circular arc.

Analogy: Rainbow as a Water Slide

Consider a rainbow as a water slide where sunlight enters at the top (water droplet), slides down (refraction), takes a turn (reflection), and slides out (refraction) at different points depending on its color. This creates a spread of colors (rainbow) at the bottom of the slide.