Radius of a concave mirror using the intensity of sunlight
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The intensity of sunlight is 1.00 kW/m^2. A highly reflective concave mirror is pointed at the sun to produce a power of at least 350 W at the image.
a) Find the radius r of the circular mirror.
b) Suppose the light intensity is to be at least 120 kW/m^2. Find the relationship between r (the radius) and R (the curvature) of the mirror. The disk of the Sun subtends an angle of 0.533 degrees at the Earth.
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Object size is (sun's diameter) angle = arc/radius
Arc(dia of the sun) = 0.533 x (pi/180) x 15 x 10^10 m = 14 x 10^8 m
where 15 x 10^10 is the distance of sun from the earth.
To find the image size:
1kW/m^2 is ...
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