Final answer:
The intensity of a helium-neon laser projected onto a circular spot can be calculated by dividing its power output by the area of the spot. Using the formula for the area of a circle, we can find the area of the circular spot and then find the intensity by dividing the power output by the area. In this case, the intensity is 31.83 W/m².
Step-by-step explanation:
The intensity of a laser beam can be calculated by dividing the power output of the laser by the area of the spot it is projected onto. In this case, the power output of the helium-neon laser is 0.250 mW and the diameter of the circular spot is 1.00 mm. To find the area, we use the formula for the area of a circle, which is πr². Since the diameter is given, we need to divide it by 2 to get the radius.
Radius = 1.00 mm / 2 = 0.50 mm = 0.50 × 10⁻³ m
Area = π(0.50 × 10⁻³)² = 3.14 × (0.50 × 10⁻³)² = 7.85 × 10⁻⁷ m²
Now, we can calculate the intensity using the formula:
Intensity = Power / Area
Intensity = 0.250 mW / 7.85 × 10⁻⁷ m² = 3.18 × 10² W/m²
So, the intensity of the helium-neon laser projected onto the circular spot is 3.18 × 10² W/m². Therefore, the correct answer is c) 31.83 W/m².