If a 20 W laser beam, which has an initial diameter of 2.0 mm, spreads out to a diameter of 2.0 m after traveling 10,000 m, what is the final intensity of the beam?

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Quizplus · Accepted Answer

The intensity of a laser beam is given by the power per unit area. The initial area $A_i$ can be calculated using the formula for the area of a circle, $A = \pi r^2$, where $r$ is the radius of the circle. The initial radius $r_i$ is half of the initial diameter, so $r_i = 1.0 \times 10^{-3}$ m. The final radius $r_f$ is half of the final diameter, so $r_f = 1.0$ m. The initial area $A_i = \pi (1.0 \times 10^{-3})^2$ m$^2$ and the final area $A_f = \pi (1.0)^2$ m$^2$. The power of the laser beam remains constant at 20 W as it spreads out. The final intensity $I_f$ is the power divided by the final area, $I_f = \frac{P}{A_f} = \frac{20}{\pi (1.0)^2}$ W/m$^2$. This calculation results in a value that matches the option D, 6.4 W/m$^2$, indicating the intensity of the laser beam after it has spread out.

If a 20 W Laser Beam, Which Has an Initial