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Intensity of a wave(carrier of energy) is defined as the energy crossing per unit area per second(Power/Area).
Intensity of a particle(Photon,quantum of energy) is defined the flux of no. of particles per second(means no. of photons passing per area per time). So in the photon picture of light if no. of photons increases then intensity of light increases.
Albert Einstein used this concept to describe photo-electric effect. He proposed that a photon collides with a single electron and transfers its all energy to the electron and electron leaves the metal surface. So if intensity of light is increased then more photon will incident on the surface and so more electrons will emerge.
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