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So it goes like this; when you shoot a gun, there will be a “kick”, this is because of Newton’s third law. However, what’s the equal, and opposite reaction when a laser ram hits an object? I need an answer as simplified as possible so I can explain this to one of my students who asked about this. Is it heat? Is there a minuscule “kick”?

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Just treat the light as a buch of photons. Each one carries an energy depenent momentum $$ p = \frac{E}{c} = \frac{\hbar \omega}{c} = \hbar k$$ When a photon gets absorbed, it transfers its momentum to the target. If it gets reflected, twice its momentum is transferred.

So actually, as already pointed out in a comment, you can apply classical mechanics here.