Illumination Problem... XD
Algebra
Level
2
The Illumination (I) from a source of light on a surface varies inversely as the square of the distance (d). A table is 25 cm. from a book. How far should the lamp be so that the book receives 5 times as much illumination?
10 cm.
5√5 cm.
5.5 cm.
25 cm.
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1 solution
By that problem, the equation of variation is I = k/(d^2)
By the problem, the distance stated is 25 cm.
So...
I = k/(d^2) -----> I = k/(25^2) -----> I = k/625
Since The problem says that the illumination should be 5 times as original,
Let i = new illumination:
Therefore,
5(I) = i = 5[(k/625)] = k/125
Comparing: I = k/(d^2) and i = k/125 ,
We can clearly see that :
d^2 = 125
therefore, d= 5√5 cm.
Final Answer: 5√5 cm.