- #1

Paul I.

- 8

- 3

## Homework Statement

Two light sources of identical strength are placed 8 m apart. An object is to be placed at a point

*P*on a line ℓ parallel to the line joining the light sources and at a distance

*d*meters from it (see the figure). We want to locate

*P*on ℓ so that the intensity of illumination is minimized. We need to use the fact that the intensity of illumination for a single source is directly proportional to the strength of the source and inversely proportional to the square of the distance from the source.

(a) Find an expression for the intensity

*I*(

*x*) at the point

*P*. (Assume the constant of proportionality is 1.)

(b) If

*d*= 4 m, use graphs of

*I*(

*x*) and

*I'*(

*x*) to find the value of

*x*that minimizes the intensity.

(c) If

*d*= 8 m, find a value of

*x*that minimizes the intensity.

(d) Somewhere between

*d*= 4 m and

*d*= 8 m there is a transitional value of

*d*at which the point of minimal illumination abruptly changes. Find this exact value of

*d*.

## Homework Equations

## The Attempt at a Solution

I'm not sure how to approach the problem at first glance. I started by writting dow this for (a):

[tex] I(x)= \frac{1}{d^2}[/tex]

I'm pretty sure I'm wrong with this. I just need enough to get me started.