Force exerted on mirror by laser beam

[cantdophysics]

How much force (in Newtons) is exerted on a mirror when a 12.0W laser beam of red light (675 nm) strikes the mirror normal to its surface? (Assume no light is absorbed)

How how how how?
kthx

 

[Doc Al]

Hint: how would you solve the problem of a rubber bullet bouncing off a wall? Think Impulse = Force x Time = change in Momentum.

Does light have momentum?

 

[M98Ranger]

bye

The force exerted on a mirror by a laser beam is determined by the momentum of the photons in the beam. This can be calculated using the formula F = (2P)/c, where F is the force, P is the power of the laser beam, and c is the speed of light. In this case, the power of the laser beam is given as 12.0W.

To calculate the force, we need to convert the wavelength of the red light from nanometers to meters, which gives us 675 x 10^-9 meters. Then, we can use the formula E = hc/λ, where E is the energy of a single photon, h is Planck's constant, c is the speed of light, and λ is the wavelength. This will give us the energy of a single photon as 2.94 x 10^-19 J.

Using the formula for momentum, we can calculate the momentum of a single photon as p = E/c, which gives us 4.36 x 10^-28 kg m/s.

Now, we can substitute the values into the formula for force, F = (2P)/c, which gives us F = (2 x 12.0)/(3 x 10^8) = 8.0 x 10^-8 N.

Therefore, the force exerted on the mirror by the laser beam is 8.0 x 10^-8 Newtons. It is important to note that this calculation assumes that no light is absorbed by the mirror, which may not be the case in reality. The force may be different if there is some absorption of the light by the mirror.