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 initial intensity of the beam? A) 20 $\times$ 10⁶ W/m² B) 6.4 $\times$ 10⁶ W/m² C) 3.2 $\times$ 10⁶ W/m² D) 2.0 $\times$ 10⁵ W/m² E) 1.0 $\times$ 10⁵ W/m²

Question

Quizplus · Accepted Answer

We can use the equation for the conservation of irradiance to solve for the initial intensity of the beam:
I1 x pi x (D1/2)^2 = I2 x pi x (D2/2)^2
where I1 is the initial intensity, D1 is the initial diameter, I2 is the final intensity, and D2 is the final diameter.
Plugging in the given values, we get:
I1 x pi x (0.001 m)^2 = 20 W / 4 x pi x (2000 m)^2
Solving for I1, we get:
I1 = 6.4 x 10^(-6) W/m^2
Therefore, the best choice is B.

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