A 1700 W laser emits light with a wavelength of 700 nm into a 3.0 mm diameter beam. What force does the laser beam exert on a completely absorbing target?

Not knowing a formula outright, I decided to follow the units of some relationships I did know. Radiation pressure is defined as force per area and also intensity divided by velocity (the speed of light here of course). Breaking intensity down into power per area and isolating force gave me the relationship F=(Power/Velocity),where power is given and the velocity is a constant.

My work is in the attachment, where I double checked the units too, comment with any questions.

snehashish65 snehashish65 · Answer 2 · 2021-12-04T13:32:02+01:00

The force exerted by the beam on a completely absorbing target is of 0.0120 N.

Given data:

The power of laser beam is, P = 1700 W.

The wavelength of light emitted from the laser is, [tex]\lambda = 700 \;\rm nm[/tex].

The diameter of the beam is, [tex]d =3.00 \;\rm mm =3.00 \times 10^{-3} \;\rm m[/tex].

When the laser beam strikes the target, then the force exerted by the laser beam on the target is equal to the product of the laser power and the area of projection of beam.

Then the expression is,

[tex]P = \dfrac{F}{A}\\\\F = P \times \dfrac{\pi}{4} d^{2}[/tex]

Solving as,

[tex]F = 1700 \times \dfrac{\pi}{4} \times (3.00 \times 10^{-3})^{2}[/tex]

F = 0.0120 N

Thus, we can conclude that the force exerted by the beam on a completely absorbing target is of 0.0120 N.

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