Final answer:
The intensity of IR radiation from the room heater focused by the concave mirror on a person 3.00 m away is 6.63 W/m².
Step-by-step explanation:
We can calculate the intensity of IR radiation in W/m² that is projected by the concave mirror on a person 3.00 m away. If the heating element radiates 1500 W and has an area of 100 cm², where half of this power is reflected and focused by the mirror, then the power reflected is 750 W.
The area over which this power is spread out at the distance of 3.00 m can be considered as a sphere segment with a surface area of 4πr², where r is the distance from the mirror to the person. Therefore, the area is 4π(3.00 m)² = 113.10 m².
The intensity of the IR radiation can then be calculated with the formula I = power/area, which in this case is I = 750 W / 113.10 m² = 6.63 W/m². This is the intensity of the IR radiation from the room heater at a distance of 3.00 m that would be felt by the person.