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 65.0 cm and produces an image of the coils 2.70 m away from the mirror. Calculate the intensity of IR radiation in W/m2 projected by the concave mirror on a person 2.70 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

do = object distance = 2.70 m

di = image distance = ?

f = focal length = Radius of curvature /2 = R/2 = 65/2 = 0.325 m

Using mirror equation :

1/di + 1/do = 1/f

1/di + 1/2.70 = 1/0.325

di = 0.37 m

magnification is given as

m = - di/do = - 0.37/2.70 = -0.137

magnification of area of element = m (actual area) = 0.137 x 100 x 10-4 = 13.7 x 10-4 m2

actual Power reflected = P = 1200 /2 = 600 watt (since half of the power is reflected)

intensity is given as

I = P/magnified area = 600 / 13.7 x 10-4 = 438 x 103 watt/m2

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