Final answer:
The intensity of a 3.0 mW laser that creates a 2.00 mm diameter spot on a screen is calculated by converting the given power to watts and the diameter to radius in meters, calculating the area of the spot, and then using the formula I = P/A to find the intensity, which is approximately 954.92 W/m².
Step-by-step explanation:
To calculate the intensity of the beam from a 3.0 mW laser pointer that creates a spot on a screen with a 2.00 mm diameter, we first need to convert the power into watts and the diameter into meters. A 3.0 mW laser is equivalent to 0.003 watts.
The diameter of the spot is 2.00 mm, which is 0.002 meters, but we need the radius for our calculation, which is half of that: 0.001 meters. The area of the spot can be found using the formula for the area of a circle, A = πr².
So, the area A = π * (0.001 m)² = 3.14159 * 10⁻¶ m². Now, intensity (I) is defined as power (P) divided by area (A), giving us I = P/A. Using the values we have, I = 0.003 W / (3.14159 * 10⁻¶ m²) which simplifies to I ≈ 954.92 W/m². Thus, the intensity of the laser beam is approximately 954.92 W/m².