Video: Calculating the Force Exerted by a Beam of Light on a Surface

Calculate the force exerted by a beam of light incident on a surface, if the beam has a power of 2.5 W. Assume that the beam of light is perfectly reflected from the surface. Take the speed of light to be 3 × 10⁸ m/s.

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Video Transcript

Calculate the force exerted by a beam of light incident on a surface if the beam has a power of 2.5 watts. Assume that the beam of light is perfectly reflected from the surface. Take the speed of light to be three times 10 to the eighth meters per second.

In this example, we have a beam of light which is incident on a surface. And then we’re told it’s perfectly reflected back from that surface. We want to calculate the force, 𝐹, exerted on the surface by the beam. We can understand this force in terms of the change of momentum of the photons in this beam of light. At first, they were moving with the speed of light to the right, and then they were moving with the speed of light to the left.

To calculate this force, we take the power of the beam, capital 𝑃, and we divide that by the speed of the beam. If this beam of light were perfectly absorbed by the surface, then this would be the force exerted on the surface by the beam. But since the light is reflected back, this quantity is doubled.

We know that, in this case, the speed of the beam is the speed of light. So this quantity, which is equal to the force that the beam exerts on the surface, is equal to two times 2.5 watts divided by three times 10 to the eighth meters per second. This is approximately equal to 1.67 times 10 to the negative eighth newtons. That’s the force exerted on the surface by the beam.

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