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I had recently watched Prof. Walter Lewin's lecture on the Heisenberg Uncertainty principle, where he conducts an experiment where light enters a slit, and as the slit was made narrower the light spread out. The explanation given for this was that when the slit was made narrower the uncertainty in position decreased in the x direction, which would consequently increase the uncertainty of momentum in the x direction. Hence,the light was found to broaden.

Is this the similar reason why light spreads out when we narrow our eyes?

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No, we are not able to get our eyes "this closed". What you are describing "light spreading out when we narrow our eyes" is probably due to diffraction or closing narrowing our eyes deforms our lens'.

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