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It's said that light is invisible because photons don't strike each other, then why we do see the reflected light from other objects?

Philip
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when photons strike material objects, they are not bouncing off other photons- they are bouncing off clouds of electrons. Depending on how those electrons are being shared by adjacent atoms, the incident photons can either be reflected off or absorbed.

niels nielsen
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Photons are not the only things in the universe. In fact, normal matter consisting of half-integer spin fermions do interact with light and can change their paths and reflect, absorb or emit them. Try reading Richard Feynman's quantum electrodynamics lectures. They are a good introduction to quantum electrodynamics and give you an accurate representation about our current best understanding of this light-matter interaction.