This letter proposes an explanation for the century-old puzzle of the wave-particle-duality of light, which thousands of physicists, including Einstein, Plank, Feynman …, have been trying to resolve. Since a ‘particle’ is localized in space, it is mathematically characterized here as an impulse-function in space. Then it is argued that if this ‘particle’ has anything to do with waves then we can know it by taking Fourier-transform of the impulse-function in space. When Fourier-transformed into wave-number-domain; we find that a ‘particle’ should contain a wide ‘set’ of waves, and not just a single frequency. Then we show that in the experiments performed so far [1] the red lasers had significantly wide line-width, means the sources have been producing a wide set of waves, and not just a pure single frequency. Similarly, in the single-particle interference-experiments incandescent filament-lamps were used with green filters inserted to isolate single photons; but it is obvious that at the frequencies of light very narrow-band-filters are not yet technically feasible, so the green filters used allowed significantly wide band of waves. So in the experiments performed so far we got ‘particles’ localized in space. And in the double-slit-interference-experiments this wide band of waves passed from both the slits, interfered like waves, and whenever and wherever they got coherently added, a ‘particle’ called ‘photon’ got detected. Atoms emit short-duration pulses of radiation, so their Fourier transform contains a wide band of frequencies. And at the time of detection, an atom needs only a small piece of continuous ‘wave’, of a suitable duration, amplitude and frequency, for ejection of an electron. So it is concluded here that: emission and detection of light is in the form of ‘photons’; whereas its propagation in space is in the form of a wide band of ‘waves’.