how much further would it be to a point were the intensity is 40w/m^2?

Question

the intensity (I) of light from a light bulb varies inversely as the square of the distance (d) from the bulb. Suppose that I is 90w/m^2 (watts per square meter) when the distance is 5m.how much further would it be to a point were the intensity is 40w/m^2?

Answer 1

This is ratio reasoning - sometimes a hard thing for students to get the hang of.

Straight ratios are often okay, inverse ratios a bit harder, and inverse squares harder.

do yourself a favor and really try to understand this (not just be able to do it) because it will only get harder when you get to inverse cubes and more complicated.

 

Here is another answer that talks about ratio reasoning.

http://www.wyzant.com/resources/answers/34971/make_a_table_that_compares_the_surface_areas_and_the_volumes_of_the_seven_dolls

 

Now to your problem.

It almost always helps to draw a diagram of a problem to "see" what is going on.

 

Bulb -- 5 m -- (90 w/m²) ------- X meters ------- (40 w/m²)

 

If the distance had doubled (factor of 2)

    then the intensity would have changed by 2 squared (2²=4)

    and it would go down since it is an inverse relationship and the distance incerased

 

If the distance tripled the intensity would go down by 3² =  a factor of 9

 

Here the distance increased by 5 of X  and the intensity decreased by the ratio 40/90

therefor the SQRT of 90/40 must be the factor the distance changed by.

Since the intensity decreased the distance increased by √(90/40)

 

So    (5 m)  /  √(90/40))  = is amount distance increased by

 

or  5 m + ( 5 m / (√(90/40)) = new distance