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Probably a stupid question, but I am wondering if there is an effect similar to Lenz's/Faraday's law of induction, but in optics. That is, rather than a changing magnetic field inducing a voltage in an inductor, is there some kind of semiconductor or other device that produces a voltage proportional to the rate of change of incident light?

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I haven't heard of a device that does what you describe, but it would be easy to make such a device: just amplify the current produced by a photovoltaic cell and feed it through an inductor. The voltage across the inductor would depend on the rate of change of current, which on turn would depend on the rate of change of light intensity illuminating the photovoltaic cell.

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