25.1 The Ray Aspect of Light

Light as a Ray

Modes of Light Travel

Light interacts with matter in five key ways. Each mode describes something different about what happens when light encounters an object or medium.

• Emission generates light from a source (the sun, a light bulb, a laser).
• Absorption occurs when an object takes in light energy. That absorbed energy is typically converted to heat, though some materials re-emit light at a different wavelength (fluorescence is one example).
• Transmission allows light to pass through a medium without being absorbed. The speed of light may change depending on the medium's refractive index.
• Reflection causes light to bounce off a surface, changing its direction. The angle of incidence equals the angle of reflection.
• Refraction bends light as it passes between media with different refractive indices. The relationship is described by Snell's law: $n_1 \sin \theta_1 = n_2 \sin \theta_2$

Light Behavior as Rays

Geometric optics treats light as rays traveling in straight lines. This works well when light interacts with objects much larger than its wavelength (on the order of hundreds of nanometers). For everyday situations like light reflecting off mirrors or passing through lenses, the ray model is all you need.

Because rays travel in straight lines, an opaque object blocking light casts a shadow. The shadow's size and shape depend on the object's dimensions, the size of the light source, and the distance between the object and the surface where the shadow falls. A point-like light source produces a sharp shadow, while an extended source (like a fluorescent tube) creates a shadow with fuzzy edges.

A pinhole camera demonstrates the ray model nicely. A tiny aperture allows only a narrow set of rays from each point in a scene to pass through, forming an inverted image on the opposite wall. The smaller the pinhole, the sharper (but dimmer) the image.

Laws of Reflection and Refraction

These two laws form the foundation of geometric optics.

1. Law of Reflection: The angle of incidence equals the angle of reflection: $\theta_i = \theta_r$. The incident ray, reflected ray, and the normal to the surface all lie in the same plane.

2. Law of Refraction (Snell's Law): When light crosses a boundary between two media, the angles and refractive indices are related by: $n_1 \sin \theta_1 = n_2 \sin \theta_2$. Again, the incident ray, refracted ray, and normal all lie in the same plane. When light enters a medium with a higher refractive index, it bends toward the normal; when it enters a medium with a lower index, it bends away.

3. Total Internal Reflection: When light travels from a medium with a higher refractive index to one with a lower index (like from water into air), there's a critical angle beyond which all light reflects back into the first medium instead of refracting through. The critical angle is: $\theta_c = \arcsin\left(\frac{n_2}{n_1}\right)$ where $n_1 > n_2$. This is the principle behind fiber optics.

4. Dispersion: Different wavelengths of light have slightly different refractive indices in a given medium. This means white light separates into its component colors when it refracts. You see this in prisms and rainbows: violet light bends more than red because it has a higher refractive index in glass or water.

Wave-Particle Duality and Interference

Geometric optics is a simplification. Light also behaves as a wave (and as particles called photons), a concept known as wave-particle duality. When light waves overlap, they can interfere constructively (amplitudes add, producing brighter regions) or destructively (amplitudes cancel, producing darker regions). Observable interference requires coherent light sources, meaning the waves must maintain a consistent phase relationship.

For this unit on geometric optics, you'll mostly use the ray model. Wave behavior becomes central later when you study diffraction and interference in detail.