Photon Force Calculation in a Laser Beam

How to calculate the force exerted by photons on a black surface in a laser beam scenario?

Given a laser beam with a power of 0.5 J/s and a wavelength of 633 nm, what is the force F in units of nanoNewtons?

Photon Force Calculation

The force exerted by photons on a black surface when a laser beam of 0.5 J/s and 633 nm wavelength is totally absorbed is 1.67 nanoNewtons (nN).

Explanation:

The force F exerted by the photons on a black surface when a laser beam is completely absorbed can be determined by calculating the momentum change Δp over the time Δt during which the momentum changes. This force can be calculated using the power of the laser beam and the wavelength of light.

First, calculate the energy E of a single photon using the equation E = hc/λ, where h is Planck's constant and c is the speed of light. Then, determine the number of photons N emitted per second by the laser using the power and energy per photon. Next, use the momentum of a photon formula p = E/c, and calculate the total momentum change per second Δp/Δt as Np since the photons are entirely absorbed. The force exerted by the photons is the rate of change of momentum, given by F = Np.

To apply this formula to the given laser beam with power 0.5 J/s (or 500 mW) and λ = 633 nm:

• Energy per photon E = 3.14 x 10^-19 J
• Number of photons per second N = 1.59 x 10^18 photons/s
• Momentum per photon p = 1.05 x 10^-27 kg.m/s
• Total force F = 1.67 x 10^-9 N or 1.67 nN

Therefore, the force exerted by photons in this scenario is 1.67 nanoNewtons.