Answer: b) 6
Step-by-step explanation:
Given : The illuminance of a surface varies inversely with the square of its distance from the light source.
i.e. for d distance and l luminance , we have
[tex]d^2\times l=k[/tex] , where k is constant. (1)
If the illuminance of a surface is 120 lumens per square meter when its distance from a certain light source is 6 meters.
From (1), we have
[tex]\Rightarrow (6)^2\times 120=k\\\\\Rightarrow\ k=4320[/tex] (2)
For the distance (d) corresponds to the illuminance to 30 lumens per square meter , we have
[tex]d^2\times 30=k[/tex]
Put value of k , we get
[tex]d^2\times 30=4320\\\\\Rightarrow\ d^2=\dfrac{4320}{30}=144\\\\\Rightarrow\ d^2=144\\\\\Rightarrow\ d= 12[/tex]
Then , the number of meters should the distance of the surface from the source be increased= 12 meters- 6 meters = 6 meters.
