Introduction

By the end of the nineteenth century, physics seemed, to many working physicists of the day, very nearly complete. Newtonian mechanics explained the motion of everything from falling apples to orbiting planets; Maxwell's electromagnetic theory, capped by the discovery of electromagnetic waves, had unified electricity, magnetism and optics into one coherent picture in which light itself was understood as a continuous, spread-out electromagnetic wave. The Optics unit taught earlier in this very semester built directly on that wave picture -- interference (Young's double slit), diffraction (bending around obstacles and single-slit spreading) and polarization all confirmed, again and again, that light genuinely behaves as a wave.

A different class of experiment. Yet a handful of experiments involving the interaction of light with matter -- most importantly, what happens when light shines on a clean metal surface -- stubbornly refused to fit the wave picture, however carefully it was applied. This chapter follows exactly how that mismatch was discovered, why it could not be patched up within the wave theory, and how its resolution (Einstein's photon, 1905) forced physics to accept that light possesses BOTH a wave character and a particle character -- neither on its own being the whole truth, each showing up depending on which experiment is performed.

How this unit is organised. Sections 11.2 and 11.3 trace the experimental discovery itself: Hertz's 1887 chance observation, followed by Hallwachs' and then Lenard's systematic investigation. Section 11.4 sets up the standard laboratory apparatus used to study the effect quantitatively and works through the two graphs (photocurrent versus applied voltage, and stopping potential versus frequency) that carry the crucial experimental facts. Section 11.5 collects these facts into formal laws and defines work function and threshold frequency precisely, with reference values for common metals. Section 11.6 shows, point by point, exactly why the classical wave theory of light cannot explain any of these laws. Section 11.7 gives Einstein's photoelectric equation, the single formula that resolves every one of the wave theory's failures. Section 11.8 draws out what this means for light itself -- introducing the photon as a genuine particle of radiation. Sections 11.9 and 11.10 then turn the argument around: de Broglie's 1924 hypothesis that matter, symmetrically, should show wave behaviour too, and the direct experimental confirmation (electron diffraction) that proved him right.