Question

The heater is then placed in a parabolic mirror that puts all of the EM radiation in a perfectly collimated beam 70 cm in diameter. When the mirror is aimed at you, what intensity do you feel in W/m²?

Answer 1

When the mirror is aimed at you, you will feel an intensity of approximately 260 W/m².

The intensity of an electromagnetic wave is given by the power divided by the area over which the power is distributed³.

• Without the mirror: The heat source emits spherical waves, so the area over which the power is distributed is the surface area of a sphere with radius 3.4 m. The intensity I is then:

`$I = (P)/(A) = (P)/(4\pi r^2) = \frac{100 \, \text{W}}{4\pi (3.4 \, \text{m})^2} \approx 0.22 \, \text{W/m}^2$$`

• With the mirror: The mirror collimates the radiation into a beam with diameter 70 cm, so the area over which the power is distributed is the area of a circle with radius 35 cm. The intensity I' is then:

`$I' = (P)/(A') = (P)/(\pi r'^2) = \frac{100 \, \text{W}}{\pi (0.35 \, \text{m})^2} \approx 260 \, \text{W/m}^2$$`

So, when the mirror is aimed at you, you would feel an intensity of approximately 260 W/m².

The complete question: A heat source sits on the bench and can be treated as a 100 W spherical EM wave. You sit 3.4 m from the source. The heater is then placed in a parabolic mirror that puts all of the EM radiation in a perfectly collimated beam 70 cm in diameter. When the mirror is aimed at you, what intensity do you feel in W/m2?