Can l apply force using light wave?

Question

Can I make light dig a hole by increasing it's frequency? Can I relate force with wave using the equation $c=$ wavelength$\times$frequency?

Answer 1

Yes! Sure enough you can apply force using light wave! Here's how:

For something to apply force, it must carry momentum. To calculate the momentum of photon we need it's mass while it's transversing which can be found out from the Einstein's mass energy relationship. $$E = mc^2$$ $$E = hf$$ where $f$ is the frequency of the light wave. Equating the two, $$m = \frac{hf}{c^2}$$ Hence the momentum of a photon will be: $$p = mc = \frac{hf}c$$ If the photon gets absorbed by the surface then, the change in momentum will be $p$. Now, $$F = \frac{\Delta p}{\Delta t} = \frac{hf}{c \Delta t}$$ By knowing the time, $\Delta t$ in which it gets absorbed or the power (or intensity) of the light, we can get the magnitude of the force.