Diffusion by reflection from a rough surface is described in this chapter. Light can also be diffused by refraction. Describe how this occurs in a specific situation, such as light interacting with crushed ice.

At the heart of understanding how light behaves when it meets different materials is the concept of refractive index. Imagine a straw in a glass of water—it appears bent at the point where it enters the water. That’s due to refraction, the change in direction of light as it passes from one medium to another. The refractive index is a number that describes how much a material can bend light.

When light moves from air into a denser medium like ice, it slows down and bends towards the normal (an imaginary line perpendicular to the surface). This bending action can be mathematically predicted with Snell’s law, expressed as:
\[ n_1 \, \sin(\theta_1) = n_2 \, \sin(\theta_2) \] where \( n_1 \) and \( n_2 \) are the refractive indices of air and ice respectively, and \( \theta_1 \) and \( \theta_2 \) are the angles of incidence and refraction. The refractive index of ice is higher than that of air, resulting in the bending of light towards the normal when entering the ice.

The journey of light through different media involves complex interactions. Each material imposes its own 'rulebook' that light must play by, impacting the speed and direction of light's travel.

Upon hitting a surface, the fate of a light wave depends on the characteristics of the material—whether it is transparent, translucent, or opaque. With transparent materials like ice, light passes through, but not without alteration. Crushed ice, with its myriad of surfaces, scatters light paths in an intricate dance. This is because each light ray may be refracted, reflected, or scattered multiple times within the ice particles themselves.

Think of light waves as guests at a gala, mingling and changing direction as they encounter various obstacles. The myriad of surfaces and angles in crushed ice ensures that light rays are constantly redirected, leading to the overall effect of diffusion, which softens and spreads the light.

Just like a funhouse of mirrors, multiple refractions occur when light traverses environments made up of many planes and angles, such as the broken fragments of crushed ice.

Every time light enters or exits an ice particle, it has the potential to refract based on the angle of incidence and the change in medium. Because the fragments are irregular, each incidence angle is unique, and the light takes on a new path with each encounter. The multitude of refractions results in light rays emerging in a scatter pattern, a phenomenon that transforms a precise beam into a splash of dispersed light.

This cacophony of refractions within crushed ice particles creates a softened, even glow, which is markedly different from the harsh, direct beams of light one might observe from a singular interface. The overall effect is akin to a natural diffusion filter, scattering light in many directions and creating a subtler, more uniform illumination.