How does the particle theory of light describe the intensity of illumunation?  

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When you illuminate an object, you are shedding or directing light upon it.  Sir Isaac Newton's particle theory, or "corpuscular theory", as it was known then, would be a simple application of grouping together more of the "corpuscles" or particles, that made up light.  If one wants to increase the illumination, and the illumination is composed of particles traveling in a straight path at a defined velocity, all one has to do is increase  the number of particles that are being directed at the object.  Particle increase will equal increased illumination; particle decrease will decrease illumination.

It should be noted that Newton's particle theory was great at explaining light properties such as the photoelectric effect (photons), but fell short in explaining properties of interference and diffraction. 

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