Take the 2-minute tour ×
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

I was working on some exercises when I came over a rather curious question.

Two lamps have intensities 40 and 5 candle-power and are 6 m apart. If the intensity of illumination I at any point is directly proportional to the power of the source, and inversely proportional to the square of the distance from the source, find the darkest point on the line joining the two lamps.

enter image description here

What puzzled me was how the intensity at any given point is both directly proportional to the power of the source, and inversely proportional to the square of the distance from the source.

Assuming only the latter statement I thought maybe I could figure it out by the equation $I=\frac{1}{x^2}+\frac{1}{(6-x)^2}$ and then finding when $\frac{dI}{dx}=0$. However that gave me 3, which is just the midpoint between the two points and does not rely at all on the brightness of each lamp. The book gives the answer 4m from the brightest lamp, but I am not certain on how to get there.

share|improve this question

1 Answer 1

up vote 5 down vote accepted

The equation you wrote doesn't factor in the strength of the light. Try the equation $$I = \frac{40}{x^2} + \frac{5}{(6-x)^2}$$

share|improve this answer

Your Answer

 
discard

By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.