Intensity of a laser through a converging lens

[k3N70n]

Homework Statement

A laser beam passes through a converging lens with a focal length of 19cm. At what distance past the lens has the laser beam's intensity increased by a factor of 6?

Homework Equations

$$I=\frac{c\epsilon_0 E_0^2}{2}$$??

The Attempt at a Solution

To be honest, I'm not even sure how to start on this question. I think I just need a hint to get started. Any help would be greatly appreciated.

 

[rl.bhat]

Intensity is inversely proportional to square of the distance. Assume that at focus the intensity is maximum, say Io.
What will be the intensity (I1) at the lens position?
What will be the intensity (I2) at a distance x from the focus?
What is the relation between I1 and I2?

 

[k3N70n]

Intensity is inversely proportional to square of the distance. Assume that at focus the intensity is maximum, say Io.
What will be the intensity (I1) at the lens position?
What will be the intensity (I2) at a distance x from the focus?
What is the relation between I1 and I2?

Thanks for the quick reply.

I'm now trying to understand the formula given in my text $I=\frac{P}{A}$

So I'm thinking that $$I_1=\frac{P}{\pi r^2}$$?


If so then $$I_2=\frac{P}{\pi r^2}=6I_1=\frac{6P}{\pi 0.17^2}$$.
so r=0.0694m. Thus the distance from from the lense is 10.1cm. I entered this into my assignment online and was informed I was incorrect. Any idea as to where I went wrong?

 

[rl.bhat]

Check your calculations. From where did get 0.17?
The equations should be I1 = P/pi*0.19^2
And I2 = P/pi(0.19- x )^2 where x is the distance from the lens. Put I2 = 6I1.Solve for x.

 

[k3N70n]

Thanks. Somehow .17 turned into .19. I've got it now. Really appreciate the help.