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 35.0 cm and produces an image of the coils 3.40 m away from the mirror. Calculate the intensity of IR radiation in W/m2 projected by the concave mirror on a person 3.40 m away. Assume that the heating element radiates 1300 W and has an area of 80 cm2, and that half of the radiated power is reflected and focused by the mirror.

Explanation / Answer

Apply for the concave mirror, 1/f=1/v +1/u ; f=R/2 ; R-radius of curvature

1/(35/2)=1/340+1/u ;

distance between filament and mirror(u)=16.79 cm

magnification= v/u = 20.25

So, image area(A)= 80*20.25=1620 cm2

total reflected power(T)=1300/2= 650W. Since all the reflected energy is in the formed image, T is distributed over area 'A' and which is 3.4m away from the mirror.

Intensity= T/A = 4012.35 W/m2

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