Reflection and Refraction: How Light Changes Direction

The Law of Reflection

When a light ray strikes a surface, it bounces off in a predictable direction. The law of reflection states three things: the incident ray, the reflected ray, and the normal (perpendicular to the surface at the point of contact) all lie in the same plane; the angle of incidence equals the angle of reflection; and the incident and reflected rays are on opposite sides of the normal. Both angles are measured from the normal, not from the surface itself.

This law applies to every reflecting surface regardless of its shape. On a flat mirror, parallel incoming rays produce parallel reflected rays, forming a clear image. On a curved surface, each ray still obeys the reflection law locally, but the normals point in different directions at different points, causing rays to converge (concave mirrors) or diverge (convex mirrors). This is why concave mirrors can focus sunlight to a point and convex mirrors provide wide-angle views.

Specular reflection occurs on smooth surfaces where microscopic irregularities are smaller than the wavelength of light. The reflected rays maintain their parallel relationship, preserving image quality. Polished metals, still water, and glass all produce specular reflection. Diffuse reflection occurs on rough surfaces where irregularities are larger than the wavelength. Each tiny surface element still obeys the reflection law, but because the normals point in random directions, the overall reflected light scatters uniformly in all directions.

Most objects we see are visible through diffuse reflection. A white wall scatters ambient light in all directions, making it visible from any viewing angle. The wall itself emits no light, it merely redirects photons from light sources. The color of a diffusely reflecting surface depends on which wavelengths it absorbs versus reflects. A red surface absorbs blue and green while reflecting red wavelengths in all directions.

Understanding Refraction

Refraction occurs because light travels at different speeds in different materials. When a wavefront crosses a boundary at an angle, one side of the wavefront enters the new medium before the other. The side that enters first slows down (or speeds up), causing the wavefront to rotate, which bends the direction of travel. This is analogous to a car veering when one wheel hits a patch of sand before the other.

The degree of bending depends on the refractive indices of both materials and the angle of incidence. Snell law provides the exact relationship: n1 * sin(angle1) = n2 * sin(angle2), where n1 and n2 are the refractive indices and the angles are measured from the normal. When light enters a denser medium (higher n), it bends toward the normal. When it exits into a less dense medium, it bends away from the normal.

The refractive index of a material equals the ratio of light speed in vacuum to light speed in that material: n = c/v. Air has n approximately equal to 1.0003 (nearly vacuum speed). Water has n = 1.33. Crown glass has n = 1.52. Diamond has n = 2.42. The higher the refractive index, the more dramatically light bends when entering from air, and the slower light travels within the material.

Everyday examples of refraction are everywhere. A pencil appears broken at the water surface in a glass because light from the submerged portion refracts as it exits the water, reaching your eye from a different apparent direction. Swimming pools appear shallower than they are because refraction bends the light upward as it leaves the water. Mirages on hot roads occur because air near the pavement has a lower refractive index due to heating, bending light from the sky upward into your eyes so the road appears to reflect the sky like water.

Dispersion: Why Prisms Make Rainbows

The refractive index of most materials varies with wavelength, a property called dispersion. Typically, shorter wavelengths (blue, violet) have higher refractive indices than longer wavelengths (red, orange). This means blue light bends more than red light when entering or exiting glass. In a prism, white light enters at one face and refracts. The different wavelengths bend by different amounts, spatially separating the colors. Upon exiting the second face, further refraction increases the separation, producing a visible spectrum.

Rainbows are natural demonstrations of dispersion. Sunlight enters a raindrop, refracts at the entry surface with wavelength-dependent bending, reflects off the back interior surface, then refracts again upon exiting. The two refractions and one reflection produce a net deflection that varies by wavelength. Red light exits at about 42 degrees from the incoming sunlight direction, while violet exits at about 40 degrees. Each raindrop sends one color toward your eye depending on its position in the sky, and the collection of all raindrops at different angles creates the full arc of colors.

Chromatic aberration in lenses is an unwanted consequence of dispersion. A simple lens focuses blue light closer than red light because blue refracts more strongly. This means a simple lens cannot bring all colors to a single sharp focus simultaneously, producing color fringes around images. Achromatic doublets solve this by combining a convex lens of crown glass with a concave lens of flint glass. The two glass types have different dispersion characteristics that cancel each other while preserving the overall focusing power.

Total Internal Reflection

When light travels from a denser medium to a less dense one (like glass to air), it bends away from the normal. As the angle of incidence increases, the refracted ray bends further until it reaches 90 degrees, traveling along the surface. The angle of incidence that produces this 90-degree refraction is called the critical angle. Beyond the critical angle, no refraction occurs at all, and 100% of the light reflects back into the denser medium.

The critical angle depends on the ratio of refractive indices: sin(critical angle) = n2/n1, where n1 is the denser medium. For glass (n=1.5) to air (n=1.0), the critical angle is about 42 degrees. For water to air, it is about 49 degrees. For diamond to air, it is only 24.4 degrees, which means light is easily trapped inside diamond, bouncing around many times before finding an exit angle less than 24.4 degrees. This is why cut diamonds sparkle so intensely.

Optical fibers exploit total internal reflection to guide light over enormous distances. The core of a fiber has a slightly higher refractive index than the surrounding cladding. Light entering the fiber at a shallow angle hits the core-cladding boundary at angles exceeding the critical angle, reflecting perfectly with no energy loss at the reflection point. The light bounces thousands of times per meter, following the fiber around bends and curves. Signal loss in modern fibers comes primarily from absorption and scattering within the glass, not from the reflections themselves.

Prisms in binoculars and periscopes use total internal reflection instead of silvered mirrors. A 45-degree glass prism reflects light perfectly at its internal face because 45 degrees exceeds the critical angle for glass. Unlike metallic mirrors, which absorb a few percent of light at each reflection, total internal reflection wastes no light energy. This makes prism-based instruments slightly brighter than equivalent mirror-based designs.

Fresnel Equations and Partial Reflection

At every boundary between materials, some light reflects and some refracts. The Fresnel equations predict exactly how much light reflects and transmits based on the angle of incidence and the refractive indices of both materials. At normal incidence (perpendicular to the surface) on glass, about 4% of light reflects. This is why you see faint reflections in windows even though most light passes through.

The reflectance increases with angle, reaching 100% at grazing incidence for all materials. This is why a lake appears mirror-like when viewed at a shallow angle but transparent when viewed from directly above. At one particular angle (Brewster angle), the reflected light becomes completely polarized in one direction. For glass, Brewster angle is about 56 degrees. Photographers use polarizing filters to block these reflections selectively.

Anti-reflection coatings reduce unwanted reflections by adding thin transparent layers to surfaces. When the coating thickness equals one quarter of a wavelength, reflected waves from the top and bottom of the coating destructively interfere, canceling the reflection. Modern camera lenses have multiple anti-reflection coatings optimized for different wavelengths, reducing total reflection from 4% per surface to less than 0.2% per surface.