Wave Optics
Ray optics breaks down when light encounters obstacles smaller than its wavelength.
Start with the simplest version: this lesson is about Wave Optics. If you can explain the core idea to a friend using everyday language, examples, and one clear reason why it matters, you have moved from memorising to understanding.
Ray optics breaks down when light encounters obstacles smaller than its wavelength. At the microscopic scale, light behaves not as rays but as waves, exhibiting interference, diffraction, and polarization. This chapter reveals phenomena that ray optics cannot explain: why the edges of shadows are blurry, why thin films shimmer with iridescent colors, why light bends around obstacles, and how two light sources can cancel each other. These effects arise because electromagnetic-waves spread like water waves, not rays.
Huygens-Fresnel Principle
Each point on a wavefront acts as a source of secondary wavelets that spread out spherically. The envelope of all these secondary wavelets forms the new wavefront. This principle explains reflection, refraction, and diffraction—all as consequences of wave spreading.
Interference of Light
When two light waves overlap, they interfere—they either reinforce (bright) or cancel (dark). This occurs because light is a wave and waves can superpose.
Constructive interference (bright fringe): Path difference = nλ (n = 0, 1, 2, ...)
Destructive interference (dark fringe): Path difference = (n + ½)λ
The key requirement: the two sources must be coherent—their phases must be related (constant). Ordinary light sources are incoherent, so interference is usually invisible unless carefully created (lasers, or two slits from the same source).
Young's Double Slit Experiment
Light from a single source is split by two slits. Each slit acts as a coherent source. On a screen beyond, an interference pattern emerges:
Bright fringes occur where path difference = nλ
Fringe spacing: Δy = λD/d
Where:
- λ is wavelength
- D is distance from slits to screen
- d is separation between slits
This experiment proved light is a wave—rays cannot explain bright and dark regions on the screen from two light sources.
Thin Film Interference
Light reflecting from the top and bottom surfaces of a thin film (soap bubble, oil slick) interferes. The path difference includes the extra distance traveled within the film plus a phase shift at reflection:
For constructive interference (bright color): 2nt cos(θ) = mλ (m = 0, 1, 2, ...)
Where n is the film's refractive index and θ is the angle of incidence.
This explains why an oil slick shows multiple colors—different wavelengths interfere constructively at different angles. As the film thickness varies, colors change position.
Diffraction
When light passes through a single slit, it spreads out (diffracts). The pattern shows a bright central maximum with alternating dark and bright fringes on either side.
Single slit diffraction minima (dark fringes): a sin(θ) = nλ (n = 1, 2, 3, ...)
Where a is the slit width.
Narrower slits → wider diffraction pattern. This illustrates the uncertainty principle preview: position and momentum cannot both be well-defined simultaneously. Confining light to a narrow slit (defined position) makes its direction (momentum) uncertain.
Diffraction Grating
A diffraction grating has thousands of parallel slits. Each slit diffracts light, and slits interfere. Bright fringes occur where diffraction maxima from all slits align:
d sin(θ) = mλ (m = 0, 1, 2, ...)
Where d is the slit spacing.
Different wavelengths diffract at different angles, separating white light into its spectrum. Gratings are used in spectrometers to analyze light composition.
Polarization of Light
From electromagnetic-waves, light is an EM wave with oscillating electric field. Unpolarized light has E vectors pointing randomly in all perpendicular directions. Polarized light has E vectors in one fixed direction.
When polarized light passes through a polarizer oriented at angle θ to its polarization direction:
Transmitted intensity: I = I₀ cos²(θ)
This is Malus's Law. At θ = 90° (crossed polarizers), no light transmits.
Polarization by reflection: Light reflecting from a surface becomes partially polarized. At Brewster's angle, reflected light is completely polarized perpendicular to the plane of incidence.
Related Topics
electromagnetic-waves | ray-optics-and-optical-instruments | dual-nature-of-radiation-and-matter
Socratic Questions
- Why do we see interference patterns only with coherent light sources, not with ordinary light from two separate bulbs? What does coherence really mean about the relationship between sources?
- The double-slit experiment shows that light interferes (wave behavior), yet photoelectric effect (dual-nature-of-radiation-and-matter) shows light delivers energy in packets (particle behavior). How can both be true?
- A thin film of water on a surface appears darker when very thin, then becomes bright at a slightly greater thickness. Why does the interference pattern flip?
- Why must light have a very small wavelength (visible light is hundreds of nanometers) for ray optics to be accurate? What happens if wavelength becomes comparable to object size?
- Polarized sunglasses eliminate glare from reflected light. Why is reflected light more polarized than incident light? What changes when light bounces off a surface?