Reference Library

When the wavelength of light is much smaller than the objects and apertures it interacts with, light can be treated as travelling in straight-line rays — geometric optics. This approximation breaks down when apertures approach the scale of the wavelength itself, where diffraction effects become significant.

A ray reflecting off a smooth surface leaves at the same angle it arrived.

Light bends when it crosses into a medium where its speed differs.

Beyond a critical angle, light travelling into a less dense medium cannot refract out at all.

A curved mirror focuses parallel rays to a point (or appears to, for a diverging mirror) at a distance set by its curvature.

A single curved refracting surface bends light according to Snell's law applied point by point; combining two such surfaces — the front and back of a lens — gives the thin lens equation below.

A thin lens bends light at two refracting surfaces in quick succession, close enough together to treat as one.

The eye forms a real, inverted image on the retina using a variable-focal-length lens; a camera does the same on film or sensor with a fixed lens that moves to focus. A telescope combines two lenses (or a mirror and a lens) to magnify distant objects, trading field of view for angular magnification.

Two waves produce a stable interference pattern only if they are coherent — same frequency, and a constant phase relationship — with comparable amplitude. Independent sources are almost never coherent; a single source split into two paths (a pair of slits, a thin film) reliably is. The bright- and dark-fringe conditions follow the same path-difference rule developed generally for interference.

Light passing through two closely spaced slits produces a pattern of bright and dark fringes on a distant screen.

Light reflecting off both surfaces of a thin film interferes, producing the colours seen in soap bubbles and oil slicks.

An interferometer splits a beam into two paths and recombines them, converting a tiny path-length difference — even a fraction of a wavelength — into an observable shift in the interference pattern, among the most sensitive length-measuring techniques available, famously used to detect gravitational waves.

Light passing through a single slit spreads out and forms its own pattern of bright and dark fringes.

A diffraction grating is many parallel slits; its bright-fringe condition is identical to the double slit's, d sin θ = mλ, but with far more slits interfering, the bright fringes become much narrower and brighter — high resolution from many-beam interference.

Diffraction sets a fundamental limit on how finely any optical instrument can distinguish two close points.

Light's electric field oscillates in a particular direction (or randomly, for unpolarized light); a polarizer selects one component and blocks the rest.