2. Just above Earth’s atmosphere the intensity of sunlight is approximately 1.4

Question

2. Just above Earth’s atmosphere the intensity of sunlight is approximately 1.4 kW/m2.

(a) You want to light a room so that, standing 1.0 m away from the light, the light intensity is the same as sunlight. What does the power output of the lightbulb need to be? Can you just go to the store and buy a lightbulb that will light a room this brightly?

(b) Neptune is 30 times as far from the Sun as Earth is. What is the intensity of sunlight at Neptune?

(c) What power of lightbulb will produce light the same intensity as sunlight at Neptune when you are 1.0 m from the lightbulb? Based on this, do you think it would be comfortable to read by sunlight at Neptune?

Explanation / Answer

Given, Intensity I = 1.4kW/m2 ,

(a) Intensity at 1m from bulb = power of bulb / Area of sphere with radius 1.0m => 1400 W/m2 = P / (4*pi*r2)

=> P = (4*pi*(1m)2)* 1400 W/m2 = 17592 W= 17.6 KW

(b) Intensity is inversely proportional to square of distance

hence intensity of sunlight at neptune = 1.4 /302 KW/m2= 1.56*10-3 KW/m2

(c)Power = Intensity * area of sphere of sphere of radius 1 m = 1.56*10-3 KW/m2 * 4*pi*12=0.01956KW= 19.56 W

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