The Two Pinholes That Finally Proved Light Is a Wave

For nearly two hundred years, two completely different pictures of light competed for the same evidence. Descartes and, more famously, Newton championed a corpuscular model, treating light as a stream of tiny particles, which could explain reflection and refraction well enough, but made a very specific, testable prediction: since a particle bends toward the normal when it crosses into glass, the corpuscular model demanded that light must travel FASTER inside glass than in air. Christiaan Huygens, in 1678, proposed a rival wave theory instead, and it explained the very same bending, refraction toward the normal, but with the OPPOSITE prediction: a wave model demanded that light must travel SLOWER inside the denser medium. These two theories could not both be right, and deciding between them meant literally measuring the speed of light inside glass or water, a measurement far beyond the technology of Huygens' own time. Newton's towering authority, combined with the seemingly obvious objection that a wave ought to need some medium to wave IN, and light very obviously crosses empty vacuum to reach us from the Sun, kept the corpuscular model dominant for well over a century. Two results eventually broke that dominance. In 1801, Thomas Young demonstrated that light passing through two closely spaced slits produces a pattern of alternating bright and dark bands, a signature only a wave could produce, firmly establishing light's wave nature. And in 1850, Léon Foucault finally performed the decisive speed measurement directly, confirming that light genuinely does travel slower in water than in air, exactly as the wave theory had predicted and exactly opposite to the corpuscular model's own prediction. The vacuum objection itself was resolved only later still, when James Clerk Maxwell's equations of electricity and magnetism predicted self-sustaining electromagnetic waves needing no material medium at all, waves whose calculated speed matched light's own measured speed so closely that Maxwell concluded light itself must simply be an electromagnetic wave.

A wavefront is simply a surface of constant phase, every point on it oscillating perfectly in step: dropping a stone into a calm pool creates circular ripples, and every point on any one ripple ring, being the same distance from the point of impact, is oscillating in exactly the same phase, making that ring a wavefront. A point source radiating uniformly in all directions produces spherical wavefronts, expanding spheres of constant phase; far enough from the source, a small patch of any such sphere looks essentially flat, and is treated as a plane wave instead. Huygens' principle turns this simple idea into a genuine predictive tool: given a wavefront's shape at one instant, EVERY point on it can be treated as the source of its own tiny secondary wavelet, spreading outward at the wave's own speed, and the common tangent surface touching all of these secondary wavelets, their forward envelope, is the new position of the wavefront an instant later. One awkward loose end remained in Huygens' original construction: the same secondary-wavelet picture seems to predict a backward-travelling wave too, which is never actually observed; Huygens patched this with the ad-hoc assumption that secondary wavelets have maximum amplitude forward and zero amplitude backward, a fix that works but was only properly justified much later by a more rigorous, complete wave theory.

Rather than simply stating Snell's law, Huygens' construction can DERIVE it directly. Consider a plane wavefront AB striking the boundary between two media at angle i, with v1 and v2 the wave's speeds in the first and second medium. In the time t it takes point B to reach the boundary at C, the wavelet spreading from point A has travelled a distance v2t into the second medium; constructing the new wavefront as the tangent from C to this wavelet's sphere, and working through the resulting right-angled triangles, gives sin i = (v1t)/AC and sin r = (v2t)/AC -- and dividing one by the other, the travel time t and the shared hypotenuse AC both cancel out entirely, leaving sin i / sin r = v1/v2. Since refractive index is defined as n = c/v, this same relation converts directly into the familiar n1 sin i = n2 sin r, Snell's law, but now genuinely DERIVED rather than simply asserted -- and it carries a crucial, testable consequence: bending toward the normal (r less than i) requires v2 LESS than v1, confirming that light must slow down entering a denser medium, exactly the wave theory's prediction that Foucault's experiment later confirmed. A companion relationship follows from matching wavelengths at the boundary: if the crest at B reaches C in the same time that the crest at A reaches E in the second medium, then v1/λ1 = v2/λ2 -- so crossing into a denser medium, both speed AND wavelength decrease together, while the frequency stays completely unchanged. Running the identical construction for a wave entering a RARER medium instead defines the critical angle directly from the same relation, sin ic = n2/n1, the angle at which the refracted wavefront would need to bend to exactly 90°; beyond ic, no refracted wavefront can be constructed at all, and the wave undergoes total internal reflection. Reflection follows an even simpler version of the same construction: comparing the triangles formed by the incident and reflected wavefronts at a plane surface shows them to be exactly congruent, immediately proving that the angle of incidence equals the angle of reflection.

Every optical device already studied through rays can be reinterpreted, more deeply, through what it does to an entire wavefront rather than to individual rays. A plane wavefront crossing a thin prism gets delayed most where the glass is thickest; since the prism's base is thicker than its tip, the lower part of the wavefront lags behind the upper part, tilting the whole emerging wavefront exactly enough to reproduce ordinary ray-picture refraction. A plane wavefront crossing a thin convex lens suffers the SAME kind of delay, but now the centre, where the lens is thickest, lags most, while the edges, where the lens is thinnest, lag least; this reshapes a flat incoming wavefront into a converging spherical one, curving inward toward a single point, the focus, exactly the point where the ray picture also places it. A concave mirror does the analogous job by reflection rather than transmission, turning an incoming plane wavefront into a converging spherical wavefront that collapses to the same focal point the ray-tracing rules already predicted. A genuinely deep principle sits underneath all three pictures: the total TIME taken from any point on the object to the corresponding point on the image is exactly the same, measured along ANY ray whatsoever -- a ray straight through a lens's own centre travels a geometrically shorter path, but crosses more glass (where light moves more slowly), while a ray near the lens's edge travels a longer path through less glass; the two effects balance perfectly, so every possible route from object to image takes precisely the same time. Two further conceptual results round out this wave picture: the frequency of reflected and refracted light always exactly equals the incident frequency, because reflection and refraction both arise from atoms being forced to oscillate at the frequency of the light driving them, and simply re-radiating at that same driving frequency; and although light slows down entering a denser medium, this does NOT mean it loses energy, since a wave's energy depends on its amplitude, not its speed of propagation.

Whenever two or more waves overlap at the same point, the superposition principle applies: the resultant displacement is simply the sum of what each wave would have produced alone. Two needles dipped into a water tray, oscillating up and down in perfect step, produce exactly the pattern needed to explore this: since the phase difference between the two waves at any given point never changes with time, the two needles count as coherent sources. At any point P equidistant from both needles, waves from each source travel equal distances, arrive perfectly in phase, and their displacements simply double, quadrupling the intensity (since intensity scales with amplitude squared) compared to either source alone -- constructive interference. At a point where one source's path is exactly one full wavelength longer than the other's, the waves are STILL perfectly in phase (a whole extra cycle changes nothing), so this too gives constructive interference; more generally, whenever the path difference equals a whole number of wavelengths, nλ, the interference is constructive, with resultant intensity 4I0. But at a point where the path difference is exactly half a wavelength (or one-and-a-half, or any half-integer number), the two waves arrive perfectly out of step, one wave's crest meeting the other's trough, and they cancel completely -- destructive interference, giving zero intensity wherever the path difference equals (n+1/2)λ. For an arbitrary point with phase difference φ between the two arriving waves, the general resultant intensity works out to I = 4I0 cos²(φ/2), which correctly reduces to 4I0 at φ=0 and to zero at φ=π, matching both special cases already found. All of this depends entirely on the phase difference staying FIXED over time; if it instead drifts randomly and rapidly, as happens with two independent, ordinary light sources, no stable pattern of bright and dark regions can ever form, and the time-averaged result is simply the two intensities added plainly, I = 2I0, at every point -- this is what happens whenever two separate lamps illuminate the same wall.

Illuminating two pinholes with two completely separate sodium lamps produces no visible interference fringes at all, even though sodium light is nearly monochromatic -- the reason is that light from an ordinary source undergoes abrupt, random phase changes roughly every 10⁻¹⁰ seconds, so two independently-lit pinholes are simply incoherent sources, exactly like two randomly-moving needles would be. Thomas Young's decisive trick was to avoid using two separate sources entirely: a single bright source illuminates one narrow pinhole S, and the light spreading out from S then falls on two further, closely spaced pinholes, S1 and S2. Because S1 and S2 are both lit by the SAME original wavefront from S, any abrupt phase jump at the source affects both of them identically and simultaneously, so S1 and S2 remain perfectly locked in phase relative to each other, genuinely coherent, even though the original source S itself is just as erratic as any ordinary lamp. The resulting spherical waves from S1 and S2 overlap on a distant screen and produce exactly the bright-and-dark banding pattern already worked out for two coherent sources: bright fringes appear wherever the path difference from S1 and S2 equals a whole number of wavelengths, at screen positions x = nλD/d (D being the screen distance, d the separation between S1 and S2), and dark fringes appear at x = (n+1/2)λD/d -- both families of positions equally spaced, giving the alternating bright-dark banding actually observed. Subtracting the positions of consecutive bright fringes shows this equal spacing directly: successive bright fringes sit exactly λD/d apart, the fringe width, which grows wider for a longer wavelength, a larger screen distance, or a smaller slit separation.

Looking closely at the edge of a shadow cast by an opaque object reveals it is not perfectly sharp: alternating faint bright and dark bands appear right at the boundary, exactly the kind of pattern interference produces -- this is diffraction, light bending into the geometrical shadow region, a general behaviour shared by every kind of wave, sound, water, or light. A single narrow slit, rather than two, still produces a genuine pattern: replacing Young's double slit with one slit of width a, illuminated by monochromatic light, produces a broad central bright region flanked by progressively fainter alternating bright and dark bands. Treating every point across the open slit as its own secondary source (all in phase, since the incoming wavefront is parallel to the slit) and adding up their contributions at a screen point P, the analysis shows minima (complete darkness) at angles θ = nλ/a, and weaker secondary maxima roughly midway between them, near θ ≈ (n+1/2)λ/a, fading rapidly as n increases -- unlike Young's evenly-bright fringes, a single slit's pattern has one dominant central band and only much fainter satellites either side. As Richard Feynman himself observed, no one has ever pinned down a sharp, meaningful physical boundary between 'interference' and 'diffraction' -- as a rule of thumb, a handful of discrete sources tend to get called interference, while a continuous distribution (like every point across an open slit) tends to get called diffraction, but a real double-slit pattern is honestly a superposition of BOTH effects together: each slit's own single-slit diffraction envelope, multiplied by the two-slit interference fringes. This single-slit pattern is easy to see directly: holding two razor blades close together to form a narrow adjustable slit, and looking through it at a straight bulb filament, shows clear bright and dark diffraction bands immediately, with red and blue filters revealing that the pattern's spacing depends on wavelength, red fringes spacing out visibly wider than blue ones. Every diffraction and interference effect, however dramatic the pattern, redistributes existing light energy rather than creating or destroying any of it: energy lost from a dark band always reappears in a neighbouring bright one, fully consistent with conservation of energy.

A wave on a horizontal string, shaken up and down, displaces every point at right angles to the direction the wave itself travels along -- a transverse wave; since each point on the string moves along a single straight line (purely up-down), it is also a LINEARLY, or plane, polarised wave. If the shaking direction changes randomly and rapidly instead, the string carries an unpolarised wave, still transverse, but with no single, fixed direction of vibration. Light behaves exactly like the transverse string wave, not a longitudinal one: its electric field always oscillates at right angles to the direction light travels, and ordinary light, from the Sun or a lamp, is unpolarised, its electric field's direction changing rapidly and randomly. A polaroid sheet, built from long chain molecules all aligned in one direction, absorbs the component of a light wave's electric field running ALONG those aligned molecules, transmitting only the component running perpendicular to them, its pass-axis. Passing unpolarised light through a single polaroid always cuts its intensity exactly in half, however the polaroid is rotated, since on average, a random electric field's component along any fixed pass-axis carries exactly half the original intensity; this transmitted light is now genuinely, linearly polarised, oscillating only along that one pass-axis direction. Placing a SECOND identical polaroid in the beam reveals something a single polaroid never could: rotating this second polaroid dramatically changes the transmitted intensity, from nearly the full amount (when its pass-axis lines up with the first polaroid's) down to nearly zero (when the two pass-axes sit at 90° to each other, crossed polaroids) -- direct, visible proof that the light emerging from the first polaroid has a definite, single direction of vibration, something only a transverse wave could possibly have. Polaroids put this effect to genuinely practical use, controlling glare in sunglasses and windowpanes, and shaping the light captured by photographic and 3D-movie cameras.

Placing a second polaroid, P2, after the first, P1, with its pass-axis at some angle θ to P1's own pass-axis, only the component of the already-polarised electric field lying ALONG P2's pass-axis, E cos θ, actually gets through; since intensity scales with the square of the electric field's amplitude, the transmitted intensity works out to I = I0 cos²θ, where I0 is the intensity already leaving P1 -- this compact result is Malus' law. At θ=0° (pass-axes aligned), cos²θ=1 and the full I0 passes through; at θ=90° (crossed polaroids), cos²θ=0 and nothing passes through at all; in between, the intensity varies smoothly, tracing out the cos²θ curve as P2 is rotated through a full turn, passing through two complete maxima and two complete minima. A genuinely surprising twist appears when a THIRD polaroid, P3, is inserted between two initially crossed polaroids P1 and P3 (pass-axes 90° apart, transmitting nothing on their own): if the inserted middle polaroid P2 makes angle θ with P1, then Malus' law applies twice in succession, once from P1 to P2, and again from P2 to P3 -- where the angle between P2 and P3 works out to (90°-θ), since P1 and P3 are fixed 90° apart. Multiplying the two factors together, the final transmitted intensity is I = I0 cos²θ cos²(90°-θ) = I0 cos²θ sin²θ = (I0/4) sin²2θ, which is maximised exactly at θ=45°, giving a quarter of I0 through what would otherwise be two perfectly crossed, fully light-blocking polaroids -- simply inserting a third polaroid between two crossed ones can turn total darkness into a genuinely bright beam, a striking, hands-on demonstration that light truly has a direction of vibration that ordinary geometric ray optics never needed to mention at all.