Electric room heaters use a concave mirror to reflect infrared (IR) radiation fr

Question

Electric room heaters use a concave mirror to reflect infrared (IR) radiation from hot coils. Note that IR follows the same law of reflection as visible light. The mirror has a radius of curvature of 60.0 cm and produces an image of the coils 2.90 m away from the mirror. Calculate the intensity of IR radiation in W/m2 projected by the concave mirror on a person 2.90 m away. Assume that the heating element radiates 1200 W and has an area of 100 cm2, and that half of the radiated power is reflected and focused by the mirror.

Explanation / Answer

the formula for concave mirror equation is

1/f = 1/p + 1/q

1/p = 1/f - 1/q

    = 1/0.30 m - 1/ 2.90 m

p =0.33 m

area of mirror is

A = ( 1/4) 2 pi R (p)

    = pi/2 ( R) p

   = pi/2 ( 0.6 m) (0.33 m)

   =0.315 m^2

the intensity is

I = p/A

= 1200 W/ 0.315 m^2 = 3.8 kW/m^2

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